WO2002033941A1

WO2002033941A1 - Method and apparatus for testing voice and data lines in a telecommunication system

Info

Publication number: WO2002033941A1
Application number: PCT/US2001/029138
Authority: WO
Inventors: John Kelvin Fidler; Jiliang Yu
Original assignee: Porta Systems Corp
Current assignee: North Hills Signal Processing Corp
Priority date: 2000-10-16
Filing date: 2001-09-19
Publication date: 2002-04-25
Anticipated expiration: 2003-04-16
Also published as: AU2001294583A1; GB2367971A; GB0025316D0

Abstract

The method for accurately determining the location of a fault on a telephone line. The method includes the steps of obtaining a transfer function of the telephone line and performing a Fourier transform on the transfer function. Fourier transform includes a spike having a time component that is representative of a discontinuity, which is located a known discontinuity and the time component associated with the fault are then used to calculate the distance from the end of the telephone line to the fault. The time component and distance associated with the known discontinuity can also be used to calculate a propagation speed of the telephone line. The method may be implemented, in either a single-ended or double-ended manner, between various elements of a telecommunication network, such as a customer's modem (50), a public switch (52), a remote test unit (54), a digital subscriber line access module(56), and a remote access server (58).

Description

METHOD AND APPARATUS FOR TESTING VOICE AND DATA LINES

IN A TELECOMMUNICATION SYSTEM

BACKGROUND OF THE INVENTION

Field of the Invention

This invention relates generally to telecommunication networks, and more particularly to the accurate testing and determination of the location of faults on and the propagation speed of telephone lines commonly used in such networks.

Description of the Prior Art

Telecommunication systems are generally complex electrical systems that are subject to failure from a variety of fault modes. The rapid and accurate classification and isolation of a fault within a telecommunication system is highly desirable to minimize dispatch and repair costs associated with such faults. Therefore, it is a long-standing objective within the telecommunication industry to provide a system that can use measured data to automatically diagnose one of several failure modes.

The accurate diagnosis of faults within a telecommunications system is hampered by the limited accessibility of test points within the system as well as the complex relationships between faults and measurable system parameters. An automated line testing system (LTS), which is currently used to perform this function, is illustrated in Figure 1. In the LTS of Figure 1 , a remote test unit (RTU) 10 is employed at each local exchange (EX) 12 within the telecommunication system. The RTU 10 is a hardware device, which generates test signals. These test signals are introduced into the system through the EX 12. The test signals propagate through a main distribution frame (MDF) 14 and into telephone lines 16. The signals typically pass through a cross-connect switch 18, to one or more distributing points (DP) 20. Ultimately, the signals reach various customer apparatus (CA) 22 such as a modem, facsimile machine, telephone handset, and the like,

The telecommunication system, when operating normally, exhibits characteristic parameters in response to the RTU 10 test signal. These parameters include voltage, current, resistance, capacitance, and the like. The RTU 10 samples and evaluates these parameters tlirough the use of software. During a fault condition, these parameters change in response to a given fault. Diagnostic software 24 implements a simple heuristic algorithm. The algorithm includes decision rules, which compare one or more measurements with threshold values to determine whether a fault exists. As an example, the algorithm may compare measured resistance values between a pair of lines against a set of expected threshold values, which are stored in the program to decide whether a fault exists in either the exchange 12 or customer apparatus 22. The algorithm uses linear decision rules to perform these functions.

The LTS is also capable of recording the measured parameters in a database 26 for future reference. Additionally, the LTS has the capability of accepting manually entered data 28 regarding each fault from an operator via a keyboard. This information may include customer fault reports and service personnel codes, which indicate the actual location of a fault. In this way, a large amount of data is assembled regarding fault history and parameter values associated with various fault locations. However, the LTS is unable to use this data to improve its own operation. If desired, the data stored in the database 26 may be evaluated periodically, and the decision thresholds employed by the algorithm may be manually updated. This is an extremely labor intensive, and therefore expensive, operation. Therefore, it is a long-standing objective in the field of telecommunication diagnostics to develop a system that can overcome this limitation.

Local networks play an important role in telecommunication networks since they directly connect customers to exchanges and failures in the local network will directly affect services provided to the customer. Unlike other parts of the telecommunication network, twisted-pair copper wires have dominated local networks since the birth of telephony and promise to do so for the foreseeable future. While the rest of the telecommunication network has undergone substantial improvements and modernization, the local network is rapidly becoming the weak link in terms of reliability and transmission performance. For example, the local network accounts for about 90% of all faults in the telecommunication network.

Although automatic LTS have widely been used in the maintenance of local networks, LTS techniques can typically only locate a fault to the exchange, local network, cable, or customer's premises. This technique is not accurate enough to enable an engineer repairing the fault to proceed directly to the fault without further testing. In practice, portable equipment must be connected at various points along the cable to accurately locate the fault. The use of such portable equipment is time-consuming and often creates additional faults since it involves significant mechanical interference with the network, such as splicing the telephone line. Thus, equipment that can accurately and non-invasively determine the location of faults from the exchange would be invaluable in maintaining the local network.

The time domain reflectrometry (TDR) technique, although widely used with conventional portable equipment, is also not ideal for an exchange-based test system. The TDR technique essentially involves applying an impulse or spike to a telephone line and recording the delay until the reflection of the impulse is received. However, the relatively high attenuation and limited frequency band of local network cable seriously attenuates and distorts the narrow impulse typically used in the TDR technique. If a spike of greater amplitude is used, the function and reliability of components, such as switches, in the telecommunication network are likely to be compromised. In addition, the TDR technique inherently requires a wide assortment of pulse widths to accurately characterize the line. This significantly increases the length of time required to locate the fault.

Further details regarding methods for determining the location of faults in communication lines can be found in the following references, the relevant portions of which are incorporated herein by reference:

1. B. Clegg, "Underground Cable Fault Location", McGraw-Hill Book Company, London, (1993);

2. T. Hanrahan, et al., "Subscriber Line Testing for Digital Switching Offices", IEEE Transactions on Communications, COM-29, volume 10, pp. 1434-1441, (1981);

3. L. Biesen. et al., "High Accuracy Location of Faults on Electrical Lines Using Digital Signal Processing", IEEE Transactions on Instrumentation and Measurement, volume 1 , pp. 175- 179, (1990); and

4. C. W. Davidson, "Transmission Lines for Communications with CAD Programs", Macmillan Publishing Company, 2nd Edition (1989).

OBJECTS AND SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method and apparatus, which locates faults in a telephone line more quickly and accurately than conventional techniques, such as time domain reflectrometry (TDR), and currently available portable equipment, such as automatic line testing systems (LTS).

It is a further object of the present invention to provide a method and apparatus, which locates faults in a telephone line by their application to any end, such as an exchange end, of a telephone line.

It is still a further object of the present invention to provide a method and apparatus, which can locate faults in a telephone line while the telephone line is in use.

It is yet a further object of the present invention to provide a method and apparatus, which locates faults in a telecommunication network in an ongoing manner by using continuous excitation of telephone lines.

It is another object of the present invention to provide a method and apparatus, which locates faults in a telephone line and that can readily be integrated as an enhancement to conventional line testing systems (LTS).

It is yet another object of the present invention to provide a method and apparatus, which locates faults in a telephone line without physical interference with the telephone line.

It is an object of the present invention to provide a method and apparatus, which determines a propagation speed of a telephone line more quickly and accurately than conventional techniques.

It is a further object of the present invention to provide a method and apparatus, which determines a propagation speed of a telephone line by their application at any end, such as an exchange end, of a telephone line.

It is still a further object of the present invention to provide a method and apparatus, which can determine a propagation speed of a telephone line while the telephone line is in use.

It is another object of the present invention to provide a method and apparatus, which determines a propagation speed of a telephone line without physical interference with the telephone line.

In accordance with the present invention, a method of determining the location of a fault on a telephone line is provided, which includes the steps of calculating a first transfer function of the telephone line without the fault, and calculating a first inverse Fourier transform of the first transfer function. The telephone line includes at least one discontinuity and an end. The discontinuity is a distance M from the end, and is associated with a first time component T in the first inverse Fourier transform. A second echo transfer function of the telephone line with the fault is calculated, from which a second inverse Fourier transform is calculated. A second time component x, which is associated with the fault, is determined from the second inverse Fourier transform, and a distance m to the fault is then calculated using the following equation:

m = M — . T

The method may also be performed from a second end of the telephone line. A mean, median, or average may then be calculated from the distance to the fault from the first end and the distance to the fault from the second end to further enhance accuracy. The method may be utilized between various components of a telecommunication network, even while it is in use, and may be integrated with conventional line testing systems.

In further accordance with the present invention, a method of determining the location of a fault on a telephone line is provided, in which the first and second time components are calculated from the same echo transfer function and inverse Fourier transform.

In still further accordance with the present invention, a method of determining a propagation velocity of a telephone line is provided, which includes the steps of calculating a first transfer function of the telephone line, calculating a first inverse Fourier transform of the transfer function, and calculating the propagation velocity υ of the telephone line using the following equation:

^~ r ^'

The telephone line includes an end and at least one discontinuity, which is a distance M from the end. The discontinuity is associated with a first time component T in the first inverse Fourier transform.

The method may also be performed from a second end of the telephone line. A mean, median, or average may then be calculated from the propagation velocity υ calculated from the first end and the propagation velocity υ calculated from the second end to further enhance accuracy. The method may be utilized between various components of a telecommunication network, even while it is in use, and may be integrated with conventional line testing systems.

These and other objects, features, and advantages of the present invention will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a block diagram of a conventional line testing system (LTS).

Figure 2 is a model of a conventional telephone line.

Figure 3 is a Dirac distribution of the inverse Fourier transform of a normalized echo transfer function of the telephone line shown in Figure 1.

Figure 4 is a Dirac distribution of the inverse Fourier transform of a normalized transfer function of a telephone line having multiple discontinuities.

Figure 5 is a Dirac distribution of the inverse Fourier transform of a normalized transfer function obtained over a narrower frequency range than that shown in Figure 5.

Figure 6 is a block diagram showing preferred testing schemes using the methods in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The subject invention enables faults, which occur in the so-called "final mile", to be accurately located. The final mile describes the twisted-pair copper wires in a telecommunication network that run from a public switch to a customer^'s premises. As more and more homes become data dependent there is a concomitant need to more accurately identify the electrical characteristics of this link to the customer. Such information is extremely useful in determining the precise location of a failure or fault in the telecommunication network.

The present invention essentially uses the time component of signals associated with discontinuities in a telephone line, which are located at a known distance from the source of an excitation signal applied to the line, to determine the distance from the source to unknown faults on the same telephone line. The time components are obtained from an inverse Fourier transform of a transfer function of the telephone line stimulated by the excitation signal. The excitation signal preferably includes a wide variety of frequency components to ensure that the transfer function accurately represents the telephone line.

The transfer function is preferably calculated from measurements obtained at the exchange end of the telephone line. The frequency range of the signals used to calculate the transfer function should typically be from about 100 Hz to about 500kHz for a telephone line having a length of about 3000m. The frequency range may be smaller for shorter lines, but the number of signal frequencies is preferably greater than 100 within the frequency range to ensure the accuracy of the echo transfer function and the resulting Fourier analysis.

The measurements required to obtain the transfer function may be done in many different ways depending upon the system being used. For instance, a signal generator may be used to sweep the frequency range or generate a complex signal containing a wide variety of frequency components. The echo response of the telephone line is then processed using digital signal processing techniques or time domain analysis to obtain the transfer function.

Alternatively, an adaptive filter may be used on the telephone line to measure the transfer function over a broad frequency range. Such a technique may even be used while the line is in use, and is similar to a method used by echo cancellation circuits in devices, such as modems and speaker phones, to measure the transfer function.

The following is provided as a brief summary of the mathematical principles upon which the method of the present invention is based. Figure 2 shows a model of a telephone line having a finite length L, terminated in a load impedance ZL 30, and stimulated by an alternating current (ac) source 30. The ac source 32 includes an internal impedance Z₍ 34. The value of a reflected voltage VA at point A is provided by the following equation:

l _A = - l ,pt: . ⁽ 1 )

where Vi is the voltage of the ac source 32, 1 is the distance from the ac source 32 to a discontinuity, ω is the frequency in radians per second, and p is a reflection coefficient of the load Z_L 30. The reflection coefficient p of the load ZL 30 may be written using the following equation: P = W (2)

where θ is a phase angle of the reflected waveform, p may be obtained from the equation:

p = ⁷^A . (3) z_L + z₀

The term Z₀ is the characteristic impedance of the telephone line, γ is the propagation factor of the telephone line given by the following equation:

γ(ω) = a(ω) + jβ(ω) , (4)

where α(ω) is an attenuation factor and β(ω) is a phase factor of the telephone line. Thus, the transfer function of the reflection path of the telephone line (known as the echo transfer function) can be found using the following equation:

or

When considering relatively high frequencies, the phase shift of the reflection coefficient p is substantially independent of frequency for a resistive load. It is then possible to write

where L and C are inductance and capacitance per unit length of the telephone line, respectively, and υ is a propagation velocity of the telephone line. The echo transfer function Η(ω) may then be normalized to yield the following equation:

and the inverse Fourier transform of equation (8) yields the following equation:

E-' (H„ (ω)) = Λ (τ - 2-) , (9) υ

where δ represents the delta function, which is used to generate a Dirac distribution, and τ is the time component of elements in the Dirac distribution.

Figure 3 shows a Dirac distribution of the inverse Fourier transform of the normalized echo transfer function represented by equation (8). As is clearly shown in Figure 3, the Dirac distribution in this example includes a spike 36 having a time component of about 50μs, which is associated with the discontinuity in the telephone line. In general, the time component will be directly proportional to the distance 1 from an end of the telephone line to the fault for a given propagation velocity.

In practice, there is typically more than one discontinuity in the local network due to joints, faults, and mismatched loads. If there are n discontinuities, the echo transfer function of the telephone line is as follows:

H(ω = ^ = £-^l k_lPle-^^> (10)

V, (ω) ι=l

H(ω) = ∑-|/ ₁ -²''^{α(ω >} _e-^{2Λ/i tω}^^,Θ'^{(ω ,+}'"⁾ ₃ (1 1) ι=ι 2

where k; is the transmission coefficient given by

and

is a reflection factor of the z^'th discontinuity. The inverse Fourier transform of the echo transfer function is then given by the following equation:

r' ( /(ffl)) = f e^J,βl^^]/ι, (τ - 2^ , (14) where

is the inverse Fourier transform of an amplitude portion of the th component of the echo transfer function. At relatively high frequencies, the attenuation factor α(ω) is roughly proportional to -Jω .

Figure 4 is a Dirac distribution of the inverse Fourier transform of the echo transfer function of the telephone line with multiple discontinuities. From equation (14), it becomes apparent that for a line with n discontinuities, the inverse Fourier transform of the reflection transfer function includes n components shifted in time corresponding to the distances of the discontinuities from the source of the excitation signal. This is shown in Figure 4 by a spike 40 at 53.030μs. a spike 42 at 79.545μs, and a spike 44 at 92.803μs. Therefore, by analyzing the distribution shown in Figure 4, it becomes readily feasible to accurately locate any discontinuity along the telephone line.

Equation (14) also provides a method for calculating the propagation velocity of the telephone line within the measurement frequency range. The propagation speed is conventionally approximated by the following equation:

assuming that the line capacitance C and inductance L are independent of the measurement frequency. However, this may introduce unacceptable errors at relatively low frequencies.

By using equation (14) and the actual discontinuities along the telephone line, the propagation velocity can be calculated more accurately. For instance, suppose there is a known discontinuity at a distance M from the source of the excitation signal, and that the time corresponding to this discontinuity is T. From equation (14), it follows that the propagation speed of the telephone line is given by the following equation:

fvl υ = 2~ . (17)

T If the inverse Fourier transform time component corresponding to a fault is τ , and the distance to the fault is m_h then:

m, v = 2^- (18)

and the distance to the fault m, is provided by the following equation:

m_t = →τ_t = M ^τ . (19)

The following is provided as an example of the application of the method of locating faults in accordance with the present invention. Figure 4 shows the Dirac distribution of the Fourier transform of the normalized transfer function of a 3.5km screened telephone cable. The telephone cable has a discontinuity at 2 km, which corresponds to the spike 40 at 53.030μs; a fault, which corresponds to the spike 42 at 79.545μs; and a mismatched load at the end of the cable, which corresponds to the spike 44 at 92.803μs. The measurements were simulated using PSpice™ on a personal computer. The calculation of the normalized transfer function and the Fourier transform was performed by Probe™, a graphical tool, which is included with the PSpice™ software package.

Since it is known beforehand that the component of the distribution at T=53.03μs is caused by the discontinuity at M = 2000m, the distance m, corresponding to the unknown fault at τ,-=79.545μs may be calculated using equation ( 19) as follows:

τ 79 545 _m = Λ ~ⁱ- = 2000—^-^ = 3000m . (20)

T 53.03

Thus, the distance to the unknown fault is 3000m.

The distance to the fault may also be calculated by using the parameters of the line L and C in accordance with equations (7) and (19), which results in the following equation:

m. 2999.5/77 , (21)

where L=3.725μH and C=47.2pF. This method yields an error of 0.5m or about 0.017%. However, when the frequency response is calculated over a narrower frequency range from about 100Hz to about 500kHz, the conventional assessment of the propagation velocity yields a larger error. The Dirac distribution for this narrower frequency range is shown in Figure 5. A spike 46 at 52.010μs, a spike 48 at 78.016μs, and a spike 49 at 90.018μs correspond, respectively, to the spikes 40, 42, and 44 in Figure 4. The distance to the fault m. using the preferred method of the present invention is as follows:

₌ ⁷⁸-⁰¹⁶ _x 2000 = 3000.038 , (22)

' 52.010

which yields an error of about .038m or about .001%. However, the distance to the fault using the parameters of the telephone line is given by the following equation:

,„, -. l-^ ' 78.016 ₌ ,₉

2 ΪC 2 ^3.725 x 47.2

which yields a larger error of about 58.2m or about 2%.

It is anticipated that the method of the present invention may be used with existing line testing systems (LTS). Such systems generally have digital signal processing capabilities, which may be used to calculate the Fourier transform used in the method of the present invention. For instance, the LTS system may be used to quickly test and locate the fault to the exchange, cable, or customer's premises. If the LTS system determines the fault to be in the cable, then the method of the present invention may be utilized to further pinpoint the location of the fault.

It is also anticipated that the method of the present invention may be used in conjunction with or to augment a telecommunication database containing Fourier distributions of telephone lines with only the normally occurring discontinuities. When a fault is reported along a particular line, the echo transfer function of the line is measured and processed to obtain the corresponding Fourier distribution. The Fourier distribution of the line with only the expected discontinuities is then retrieved from the database and compared to the Fourier distribution with the fault to accurately locate the fault.

A simulation of the method in accordance with the present invention using PSpice yields only a 30cm error in the location of a fault on a 3000m line. Thus, conventional portable equipment, which relies on audio signals, tones, or heat to detect faults, may essentially be eliminated.

The time required to complete the method in accordance with the present invention may significantly be decreased by using adaptive filtering techniques to obtain the transfer function. The time to perform the method may be further reduced by taking measurements while the line is in use. In either case, the method of the present invention is significantly faster than the conventional application of portable equipment to the line at various locations, which may take several hours.

The following is a description of several different implementations of the method in accordance with the present invention. By utilizing modems located throughout the telecommunication network, the line may be stimulated, the Fourier transform of the transfer function may be calculated, and the resulting information may be analyzed independently or applied to the LTS. Once in the LTS, this information is preferably used with other records concerning the telecommunication network to more accurately locate and identify faults.

Figure 6 is a block diagram showing four preferred implementations (A) - (D) of the method of the present invention to a telecommunication network. The implementations outline various schemes in which single and dual-end testing is preferably used or combined to enhance line-testing capabilities. The path for each of the implementations is indicated between circled reference designations corresponding to the specific implementation. For instance, implementation A is shown between a modem 50 and a public switch 52. implementation B is shown between the modem 50 and a remote test unit (RTU) 54, implementation C is shown between the modem 50 and a digital service line access module (DSLA^*M) 56, and implementation D is shown between the modem 50 and a remote access server (RAS) 58. The term "communication module" is used to refer to at least one of the customer's modem, the public switch, the remote test unit, the digital subscriber line access module (DSLAM). and the remote access server (RAS).

The bold lines between elements of the telecommunication network in Figure 6, such as the customer's modem 50 and the public switch 52, represent the twisted-pair copper wires of an analog portion of the network. The remaining lines between elements of the telecommunication network in Figure 6, such as the public switch 52 and the RTU 54, represent a digital portion of the network. Implementation A enables the telephone line from the customer's modem 50 to the public switch or exchange 52 to be tested. This implementation is preferably initiated by the user's modem 50 using specialized hardware and/or software designed to apply the method of the present invention to the telephone line and determine the condition of the line and its ability to carry voice and data.

Implementation B enables the telephone line from the customer's modem 50 to the RTU 54 to be tested. This implementation may be initiated by the user's modem 50, which provides single-ended information concerning the telephone line. However, if the RTU 54 includes an intelligent modem, either the user's modem 50 or the RTU 54 may initiate the test, either sequentially or concurrently, which provides double-ended information regarding the telephone line. Double-ended information significantly increases the accuracy in determining the location of the fault by, for instance, calculating a mean or average of the distance to the fault calculated from the ends of the line. The resulting test information is preferably collated at the RTU 54 and made available to a line test system (LTS) 60.

Implementation C enables a high frequency path from the customer's modem 50 to the DSLAM 56 to be tested. The increased bandwidth of the high frequency path significantly increases the accuracy of fault location while enabling the test to be automated from a remote location. This implementation may be initiated by the user's modem 50, which provides single- ended information concerning the telephone line. However, since the DSLAM 56 commonly incorporates an intelligent modem, either the user's modem 50 or the DSLAM 56 may sequentially or concurrently initiate the test, which would provide double-ended information regarding the telephone line.

Implementation D enables the telephone line from the customer's modem 50 to the RAS 58 to be tested. This implementation may be initiated by the user's modem 50. which provides single-ended information concerning the telephone line, or the RAS 58, either sequentially or concurrently, which would provide double-ended information. Since the RAS 58 is preferably coupled to the public switch 52 by a digital path, the RAS 58 can act as a virtual modem on the telephone line to initiate and monitor testing of the line. The RAS 58 may alternatively be controlled by a digital line test system 62, which is preferably accessible to the customer via the Internet 64. The digital line test system 62 preferably provides information concerning the results of the test to the line test system to further enhance the accuracy of fault location. From the foregoing description, it will be appreciated that the method and apparatus in accordance with the present invention locates faults in a telephone line more quickly and accurately at any end of the line, even while the line is being used, than conventional techniques, such as time domain reflectrometry (TDR), and currently available portable equipment, such as automatic line testing systems (LTS). Further, it will be appreciated that the method and apparatus in accordance with the present invention can readily be integrated as an enhancement to conventional line testing systems (LTS), or can be used as a standalone system without physical interference with the telephone line.

From the foregoing description, it will also be appreciated that the method and apparatus in accordance with the present invention determines the propagation speed of a telephone line more quickly and accurately at any end of the line than conventional techniques, even while the line is in use. Further, it will be appreciated that the method and apparatus in accordance with the present invention does not require physical interference with the telephone line.

Although illustrative embodiments of the present invention have been described herein with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention.

Claims

WHAT IS CLAIMED IS:

1. A method of determining the location of a fault on a telephone line, the method comprising the steps of:

(a) calculating a first echo transfer function of the telephone line without the fault, the telephone line including at least one discontinuity, the telephone line including a first end, the at least one discontinuity being a first distance M from the first end;

(b) calculating a first inverse Fourier transform of the first echo transfer function, the at least one discontinuity being associated with a first time component T from the first inverse Fourier transform;

(c) calculating a second echo transfer function of the telephone line with the fault;

(d) calculating a second inverse Fourier transform of the second echo transfer function;

(e) determining a second time component τ,. from the second inverse Fourier transform, the second time component τ being representative of the fault; and

(f) calculating a second distance m, from the first end to the fault using the following equation:

m. - M — .

T

2. The method of locating a fault on a telephone line as defined by Claim 1 , further including the step of normalizing the first echo transfer function

3. The method of locating a fault on a telephone line as defined by Claim 1. wherein at least one of the steps of calculating the first echo transfer function and calculating the second echo transfer function includes the steps of:

generating an excitation signal;

applying the excitation signal to the first end of the telephone line; and measuring a response of the telephone line to the excitation signal.

4. The method of locating a fault on a telephone line as defined by Claim 3, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a plurality of frequencies within a range from about 100Hz to about 500kHz.

5. The method of locating a fault on a telephone line as defined by Claim 3, wherein the step of generating the excitation signal includes the step of sweeping a range of frequencies.

6. The method of locating a fault on a telephone line as defined by Claim 3, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a complex signal, the complex signal including a plurality of frequency components.

7. The method of locating a fault on a telephone line as defined by Claim 3, further including the step of processing the response using at least one of a digital signal processing technique, a time domain technique, and an adaptive filtering technique.

8. The method of locating a fault on a telephone line as defined by Claim 1, wherein at least one of the steps of calculating the first echo transfer function and calculating the second echo transfer function includes the step of calculating at least one of the first echo transfer function and the second echo transfer function using the following equation:

H ω) = _j^\k_lP - ^alω)e-² '^{PM jtd}'^{ω)^' ι=l -

where Hfω) is a transfer function. /' is an indexing variable, m is a quantity of discontinuities, k, is a factor related to reflections of the discontinuities before the th discontinuity, p, is a reflection coefficient of the /th discontinuity, /, is a distance to the /th discontinuity, ω is a frequency, α(ω) is an attenuation factor of the telephone line. β(ω) is a phase factor of the telephone line, θ,(ω)is a phase angle of a reflected waveform from the /th discontinuity, and φ, is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection.

9. The method of locating a fault on a telephone line as defined by Claim 1, wherein at least one of the steps of calculating the first inverse Fourier transform and calculating the second inverse Fourier transform includes the step of calculating at least one of the first inverse Fourier transform and the second inverse Fourier transform by using the following equation:

where F(H(ω)) is a Fourier transform of a transfer function, / is an indexing variable, m is a quantity of discontinuities, /,-is a distance to the /th discontinuity, ω is a frequency, θ, is a phase angle of a reflected waveform from the /th discontinuity, φ,- is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection, H, is a transfer function at the /th discontinuity, τ is a time component of the Fourier transform, and υ is a propagation speed of the telephone line.

10. The method of locating a fault on a telephone line as defined by Claim 1 , wherein the telephone line includes a second end, the method further including the steps of:

performing steps (a) through (f) from the second end to calculate the second distance m, to the fault from the second end; and

calculating at least one of a mean, an average, and a median of the second distance m,- to the fault calculated from the first end and the second distance m, to the fault calculated from the second end.

1 1. The method of locating a fault on a telephone line as defined by Claim 1 , further including the step of performing steps (a) through (f) between at least two of a customer^'s modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM), and a remote access server (RAS).

12. The method of locating a fault on a telephone line as defined by Claim 1 , further including the step of outputting the second distance m, to a line testing system (LTS).

13. The method of locating a fault on a telephone line as defined by Claim 1 , further including the step of performing steps (a) through (f) while the telephone line is in use.

14. A method of determining a propagation velocity of a telephone line, the method comprising the steps of:

(a) calculating an echo transfer function of the telephone line, the telephone line including at least one discontinuity, the telephone line including a first end, the at least one discontinuity being a first distance M from the first end; (b) calculating an inverse Fourier transform of the echo transfer function, the at least one discontinuity being associated with a first time component T from the Fourier transform; and

(c) calculating the propagation velocity speed υ of the telephone line using the following equation:

υ = 2 — . T

15. The method of determining a propagation velocity of a telephone line as defined by Claim 14, further including the step of normalizing the echo transfer function.

16. The method of determining a propagation velocity of a telephone line as defined by Claim 14, wherein the step of calculating an echo transfer function includes the steps of:

generating an excitation signal;

applying the excitation signal to the first end of the telephone line; and

measuring a response of the telephone line to the excitation signal.

17. The method of determining a propagation velocity of a telephone line as defined by Claim 16, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a plurality of frequencies within a range from about 100Hz to about 500kHz.

18. The method of determining a propagation velocity of a telephone line as defined by Claim 16, wherein the step of generating the excitation signal includes the step of sweeping a range of frequencies.

19. The method of determining a propagation velocity of a telephone line as defined by Claim 16, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a complex signal, the complex signal including a plurality of frequency components.

20. The method of determining a propagation velocity of a telephone line as defined by Claim 16, further including the step of processing the response using at least one of a digital signal processing technique, a time domain technique, and an adaptive filtering technique.

21. The method of determining a propagation velocity of a telephone line as defined by Claim 14, wherein the step of calculating the transfer function includes the step of calculating the transfer function using the following equation:

where H(ω ) is a transfer function, / is an indexing variable, m is a quantity of discontinuities, k_t is a factor related to reflections of the discontinuities before the /th discontinuity, p,- is a reflection coefficient of the /th discontinuity, /, is a distance to the /th discontinuity, ω is a frequency, α(ω) is an attenuation factor of the telephone line, β(ω) is a phase factor of the telephone line, θ,(ω)is a phase angle of a reflected waveform from the /th discontinuity, and φ, is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection.

22. The method of determining a propagation velocity of a telephone line as defined by Claim 14. wherein the step of calculating the inverse Fourier transform includes the step of calculating the inverse Fourier transform by using the following equation:

-' (H(ω)) = V^{,Bl +<p}' '/ τ - 2^)

-=1

where FfHfω )) is a Fourier transform of a transfer function. / is an indexing variable, m is a quantity of discontinuities, /, is a distance to the /th discontinuity, ω is a frequency, θ, is a phase angle of a reflected waveform from the /th discontinui . φ_? is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection. H, is a transfer function at the /th discontinuity, τ is a time component of the Fourier transform, and υ is a propagation speed of the telephone line.

23. The method of determining a propagation velocity of a telephone line as defined by Claim 14. wherein the telephone line includes a second end, the method further including the steps of: performing steps (a) through (c) from the second end to calculate the propagation speed υ of the telephone line; and

calculating at least one of a mean, an average, and a median of the propagation velocity υ calculated from the first end and the propagation speed υ calculated from the second end.

24. The method of determining a propagation velocity of a telephone line as defined by Claim 14, further including the step of performing steps (a) through (c) between at least two of a customer^'s modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM), and a remote access server (RAS).

25. The method of determining a propagation velocity of a telephone line as defined by Claim 14, further including the step of performing steps (a) through (c) while the telephone line is in use.

26. A method of determining the location of a fault on a telephone line, the method comprising the steps of:

(a) calculating an echo transfer function of the telephone line, the telephone line including at least one discontinuity, a fault, and a first end, the at least one discontinuity being a first distance M from the first end;

(b) calculating an inverse Fourier transform of the echo transfer function, the at least one discontinuity being associated with a first time component T in the inverse Fourier transform;

(c) determining a second time component τ, from the inverse Fourier transform, the second time component τ,₍ being representative of the fault; and

(d) calculating a second distance m, from the first end to the fault using the following equation:

m. = M^- .

T

27. The method of locating a fault on a telephone line as defined by Claim 26, further including the step of normalizing the echo transfer function.

28. The method of locating a fault on a telephone line as defined by Claim 26, wherein the step of calculating the echo transfer function includes the steps of:

generating an excitation signal;

applying the excitation signal to the first end of the telephone line; and

measuring a response of the telephone line to the excitation signal.

29. The method of locating a fault on a telephone line as defined by Claim 28, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a plurality of frequencies within a range from at least about 100Hz to about 500kHz.

30. The method of locating a fault on a telephone line as defined by Claim 28, wherein the step of generating the excitation signal includes the step of sweeping a range of frequencies.

31. The method of locating a fault on a telephone line as defined by Claim 28, wherein the step of generating the excitation signal includes the step of generating the excitation signal including a complex signal, the complex signal including a plurality of frequency components.

32. The method of locating a fault on a telephone line as defined by Claim 28, further including the step of processing the response using at least one of a digital signal processing technique, a time domain technique, and an adaptive filtering technique_^.

33. The method of locating a fault on a telephone line as defined by Claim 26. wherein the step of calculating the echo transfer function includes the step of calculating the echo transfer function using the following equation:

where H(ω) is a transfer function, / is an indexing variable, m is a quantity of discontinuities, k, is a factor related to reflections of the discontinuities before the /th discontinuity, p. is a reflection coefficient of the /th discontinuity, /, is a distance to the /th discontinuity, ω is a

99 frequency, α(ω) is an attenuation factor of the telephone line, β(ω) is a phase factor of the telephone line, θ,(ω)is a phase angle of a reflected waveform from the /th discontinuity, and φ, is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection.

34. The method of locating a fault on a telephone line as defined by Claim 26, wherein the step of calculating the inverse Fourier transform includes the step of calculating the inverse Fourier transform by using the following equation:

where F(H(ω)) is a Fourier transform of a transfer function, / is an indexing variable, m is a quantity of discontinuities, /, is a distance to the /th discontinuity, ω is a frequency, θ, is a phase angle of a reflected waveform from the /th discontinuity, φ, is a phase angle of a waveform reflected by the /th discontinuity at a point of reflection, H, is a transfer function at the /th discontinuity, τ is a time component of the Fourier transform, and υ is a propagation speed of the telephone line.

35. The method of locating a fault on a telephone line as defined by Claim 26, wherein the telephone line includes a second end. the method further including the steps of:

performing steps (a) through (d) from the second end to calculate the second distance m, to the fault from the second end; and

calculating at least one of a mean, an average, and a median of the second distance m, to the fault calculated from the first end and the second distance m, to the fault calculated from the second end.

36. The method of locating a fault on a telephone line as defined by Claim 26, further including the step of performing steps (a) through (d) between at least two of a customer's modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM), and a remote access server (RAS).

37. The method of locating a fault on a telephone line as defined by Claim 26 further including the step of outputting the second distance m, to a line testing system (LTS).

38. The method of locating a fault on a telephone line as defined by Claim 26 further including the step of performing steps (a) through (d) while the telephone line is in use.

39. An apparatus for determining the location of a fault on a telephone line, the apparatus comprising:

a telephone line; and

a communication module, the communication module including at least one of a customer^'s modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM). and a remote access server (RAS). the communication module calculating a first transfer function of the telephone line without the fault, the telephone line including at least one discontinuity, the telephone line including a first end, the at least one discontinuity being a first distance M from the first end, the communication module calculating a first Fourier transform of the first transfer function, the at least one discontinuity being associated with a first time component T from the first Fourier transform, the communication module calculating a second transfer function of the telephone line with the fault, the communication module calculating a second Fourier transform of the second transfer function, the communication module determining a second time component τ,, from the second Fourier transform, the second time component τ, being representative of the fault, the communication module calculating a second distance m. from the first end to the fault using the following equation:

40. An apparatus for determining the location of a fault on a telephone line as defined by Claim 39, further including a line testing system (LTS). the second distance m_t being outputted to the LTS.

41. An apparatus for determining the location of a fault on a telephone line, the apparatus comprising:

a telephone line: and

a communication module, the communication module including at least one of a customer's modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM), and a remote access server (RAS). the communication module calculating a transfer

74 function of the telephone line, the telephone line including at least one discontinuity, the telephone line including a first end, the at least one discontinuity being a first distance M from the first end, the communication module calculating a Fourier transform of the transfer function, the at least one discontinuity being associated with a first time component T from the Fourier transform, the communication module calculating the propagation speed υ of the telephone line using the following equation:

υ = 2— . T

42. An apparatus for determining the location of a fault on a telephone line, the apparatus comprising:

a telephone line; and

a communication module, the communication module including at least one of a customer's modem, a public switch, a remote test unit, a digital subscriber line access module (DSLAM), and a remote access server (RAS), the communication module calculating a transfer function of the telephone line, the telephone line including at least one discontinuity, a fault, and a first end, the at least one discontinuity being a first distance M from the first end, the communication module calculating a Fourier transform of the transfer function, the at least one discontinuity being associated with a first time component T in the Fourier transform, the communication module determining a second time component τ,_v from the Fourier transform, the second time component τ,. being representative of the fault, the communication module calculating a second distance m, from the first end to the fault using the following equation:

43. An apparatus for determining the location of a fault on a telephone line as defined by Claim 42, further including a line testing system (LTS), the second distance m, being outputted to the LTS.