DE102009005203A1 - Digitized signals smoothing method, involves generating smoothed signal value during scanning by sum of all individual regression coefficients of samples that are multiplied with time interval - Google Patents

Abstract

The method involves producing regression lines by linear regression such that last signal values are provided for linear regression at a time point of a scanning in a time interval. A distance of the actual signal value for the regression lines of the preceding signal is reduced by a divisor that contains a number of the signal values. A smoothed signal value is generated during scanning by a sum of all individual regression coefficients of samples that are multiplied with the time interval.

Description

The The invention relates to a smoothing method for digitized Signals by means of linear regression with reduced number of measuring points.

Usually will for smoothing of digitized signals Filters of all kinds used for disturbing signal noise and signal peaks largely suppress. When the components and Storage costs to be kept low, worthwhile, no consuming Digital filter. In such cases averaging such as moving average or that offer themselves arithmetic mean. The moving averaging is needed though fewer variables, but the signal delay is significantly larger than when using the arithmetic mean.

The signal smoothing Both methods have a major shortcoming: the connections of the sample points remain with corresponding signal noise jagged with acceptable signal delay. The invention now allows over the linear regression contained in the payload and by the Scanning changed Signal interference, compared to averaging at approximately the same signal delay, stronger with little effort to belittle. Different sampling times have, as usual, effects on the frequency response the useful signal.

und (1) umgestellt ergibt den Altwert m[i] plus Zuwachs, als Bruchteil des Abstands vom Signalwert z[i] zum Altwert m[i]

The moving average m results from the equal part retroactive calculation of the current mean value m [i] in the step index i, the proportional current signal value z [i] and the number n of the assumed elements. For all representations a constant measuring distance Δt (sampling) is assumed. The moving average m is

and (1) converted gives the old value m [i] plus gain, as a fraction of the distance from the signal value z [i] to the old value m [i]

In contrast, it is known that the arithmetic mean ma over n values z

The Sum of the difference z [i] - m [i - 1] of the moving average in (2) corresponds to the original value at n = 1 z [i] and the smoothing effect increases with n. With n also the signal delay increases. The signal tracking happens continuously with the current mean value m [i]. Also the arithmetic Means left to track by taking the last n values of the measured value sequence in (3) and cached.

For example, let the arithmetic mean with n = 2 tracked averaged values and the moving average, also given n = 2. The following values are equal to z [i] = z [i - 1]. Each moving average m [i] of the following values is divided by each arithmetic mean ma [i]. This yields with n = 2 for each successor i and i ≥ n

The approximation the quotient against 1 occurs gradually at constant z. There where the arithmetic mean is constant as z, the moving one rushes Mean according to the arithmetic mean. That is also generalizing in case of signal delay the case, because the moving average more cycles necessary, to bridge the difference up to a defined actual value.

aus der Steigung substituieren.After (2) the increase increases with larger n and the level of the mean value follows the original signal more strongly, the signal delay increases. The increase in (2) can also be obtained from a sequence of points with the constant distance Δt

substitute from the slope.

If one puts the n as nt on the other side in (4), the slope base is extended to nt points. Then it is possible to reduce fluctuations in the dot values, based on the extended slope basis nt · Δt. For this, the linear regression is used at each point over the last nt points (regression window width). The regression coefficient now corresponds to tan, and for the signal smoothing results from this the smoothed signal value mr from the sum of the distances tanψ [i] .Δt of the underlying regression coefficient mr [i] = mr [i-1] + tanψ [i] · Δt. (5)

However, it is disadvantageous that historical values (eg nt = 32) must be maintained. If, on the other hand, you accept a slightly higher signal delay (which is often possible), nt can be greatly reduced. For this purpose, the respective current signal value z [i] for the regression to the calculated value z_neu [i] is adapted by reducing its distance to the previous value zh [i-1] of the regression line from the previous signal values, with the divisor (nt + nx) With

Of the Fixed value nx serves to increase the effect and it is z. B. nx = 8. The number of regression points nt is z. B. nt = 8 or can be changed to change the regression window width. The fixed value nx remains unaffected. zh [i - 1] is an external value on the regression line, which recalculates for each sample becomes. The divisor (nt + nx)> 1 determines the degree of smoothing.

to Realization uses only the signal values themselves, the time level is generated. In each case the last nt signal values of the Signal data stream in the data field elements y [0] to y [nt - 1] held, where y [0] is the element side with the current calculated value z_neu [i]. For the Timeline are integer auxiliary parameters used for simplicity, all of which represent products of constant sampling time Δt with equal factors. As mathematically assigned x-sizes for linear regression, they correspond to the index values 0 to nt - 1.

at The linear regression is known to apply to the regression line yr with the regression coefficient b and the coefficient a over nt points

The position of zh [i - 1] on the regression line yr can be varied for the application. The value zh [i-1] is assigned to the current signal value z [i] and has already been calculated during the preceding sampling, when in the current sampling the data element y [0] was overwritten with z_neu [i]. At the time of computation of z_new [i], zh [i-1] and the regression coefficient b of the previous sampling continue with Δt zh [i-1] = a [i-1] + b [i-1] nt. (7)

The anticipatory value is zh [i] for the subsequent sample and it applies to the current regression window width zh [i] = a [i] + b [i] · (nt - 1). (8th)

Suitable for the application is the current scan zh [i] = a [i] + b [i] · (nt - k), where k ≥ 0. (9)

at k> 1 makes it Signal distortion already stronger noticeable, so that in (7) and (8), applied in (9) with 0 ≤ k ≤ i, smoothing and Set signal delay well.

at every sample Δt Now, in the first calculation step, the calculated values of the regression points become known the downhill current data elements y [nt - 1] until y [0] is shifted by 1 position (shift register) and finally becomes the current calculated value z_new [i] from the signal value z [i] according to (6) calculated and kept in the released data element y [0]. To is the from the previous passage of the second calculation step noted external value zh [i - 1] on the regression line yr.

Of the second calculation step first determines the coefficient a and the Regression coefficients b of the down-swept time interval Δt · (nt-1) to Δt · 0 to the Signal values y [nt - 1] to y [0]. Subsequently, will according to (9) with the help of the coefficients a and b, the external value zh [i] of the current regression line yr for subsequent sampling calculated. For the time values x [i] of the signal values z [i] are, as already mentioned, linear Regression uses the integer index of the data elements y [].

In the third calculation step, the smoothed signal value mr [i] is determined according to (5). For the regression coefficient b applies tanψ [i] = b [i] and since the computational time interval Δt = 1 exists in the time interval for each signal point with x [i], the distance is given in (5) as the regression coefficient multiplied by the time interval Δt tanψ [i] · Δt = tan ψ [i].

Becomes instead of (5) the arithmetic mean is used as mr → Σy [i] / nt the signal smoothing less well in detail.

The Indexing 0 starting from the current signal value until nt - 1 happens declining, which is why the regression coefficient b receives a negative sign.

besonders grafisch vorteilhaft zu vermitteln. Dagegen vergrößert sich der Korrelationskoeffizient in Richtung Nulllinie stark und ist daher als Veranschaulichung der Glättung weniger geeignet. Das Frequenzspektrum gibt zwar die Größenrelationen der Signalveränderungen wieder, der Darstellungsaufwand hierfür ist allerdings größer.Smoothing is indicated by the change of the level differences per sample Δt

particularly graphically advantageous to convey. In contrast, the correlation coefficient towards the zero line increases greatly and is therefore less suitable as an illustration of the smoothing. Although the frequency spectrum is the size relations of the signal changes again, but the presentation effort for this is greater.

2. Muster:

This is followed by two executable small sample programs. In the first pattern, a regression window width of nt = 8 digits is fixed and there are no loops for faster processing. In the second pattern 4 digits are processed simultaneously. The free choice of nt is possible, as far as nt divisible by 4. 1st pattern:

2nd pattern:

Claims (1)

Smoothing method for digitized signals, characterized in that a) that a regression line is generated by means of the linear regression in such a way that always the last nt signal values at the time of sampling in the time interval .DELTA.t, are used for linear regression and b) that the distance of each current Signal value to the regression line of the previous signal values, is reduced by a divisor which contains the number of nt signal values and c) that in the case of a sampling, the sum of all the individual regression coefficients of the samples, which are multiplied by the time interval Δt, yields the smoothed signal value.