DE102024201676A1 - Method and device for data processing - Google Patents

Abstract

The invention relates to a method and a device for data processing, as well as to a use thereof. In a data processing method, an analog electrical input signal (4) is multiplied continuously by a matrix (A, B). This enables a continuous-time projection of the input signal into a function space.

Description

The invention relates to a method and a device for data processing and a use.

By projecting continuous analog input signals into a typically high-dimensional function space, the input signals can be approximated and/or mapped. This has a wide range of applications, for example, in data compression, data transmission, pattern recognition, and filtering. The signals can be transformed into the frequency domain, as in Fourier analysis. It is then possible to reconstruct the input signals.

Digital circuits are the standard for such data processing. The first step is typically the analog-to-digital conversion of the input signals using suitable converters (ADCs or DA converters). The precision (resolution) and sampling rate depend on the expected signals, the algorithm requirements, and the specific application. The ADC must be designed for the "worst case," i.e., for the case of maximum requirements, and therefore typically consumes a large portion of the power and chip area required for the entire data processing.

The respective algorithm is then executed. This occurs either in a circuit specifically designed for the respective algorithm (application-specific integrated circuit, ASIC) or in a conventional computer system (general-purpose processor, GPP). In the former case, the algorithm can be executed efficiently and with minimal resource consumption, but in return, flexibility is limited; other algorithms cannot be executed or can only be executed to a very limited extent. Conventional computer systems, on the other hand, can execute various algorithms, which in return generally require significantly more resources, such as energy and chip area.

Depending on the application, digital data processing can involve many steps and the buffering of signal components. This can result in significant delays and high space and energy consumption, especially in the case of general-purpose processors. ASICs, on the other hand, are not very flexible, as described above.

An example of an algorithm for projecting continuous analog input signals into a high-dimensional function space is the "high-order polynomial projection" (HiPPO). Here, the analog input signal is projected into a higher-dimensional space of polynomial functions using matrix multiplication. Coefficients are calculated from which the input signal can be reconstructed. The algorithm corresponds to a first-order differential equation. Since the computational complexity of matrix multiplications increases quadratically with the dimension of the matrices and thus the projection dimension of the HiPPO algorithm, such an algorithm is associated with a high time and energy expenditure.

The object of the invention is to improve data processing. In particular, the aforementioned disadvantages are to be at least partially remedied.

This object is achieved by the data processing method according to claim 1, as well as by the device and the use according to the independent claims. Advantageous embodiments are specified in the subclaims.

A data processing method is used to solve this problem. An analog electrical input signal is multiplied continuously by a matrix.

This enables the projection of the electrical input signal into a high-dimensional function space in a continuous-time manner, i.e., in real time. Furthermore, the projection is possible with continuous values, meaning that non-discrete, analog signals can be used as input signals. This significantly increases the speed compared to digital data processing. In digital space, a very inefficient, repetitive matrix multiplication would have to occur. The computational complexity of continuous or analog data processing depends on the dimension of the matrix. Therefore, even very high-dimensional matrices can be multiplied in real time.

In particular, the input signal is projected into a higher-dimensional function space. Typically, several polynomials are superimposed, which are particularly orthogonal to each other or non-replicating. These can be, for example, Fourier polynomials and/or polynomial functions.

A matrix contains elements, such as values or terms, arranged rectangularly or in rows and columns. The elements of the matrix are also called coefficients. The matrix can be understood as several vectors. arranged in rows or columns one after the other.

If the input signal is multiplied by the matrix, it is multiplied by at least some of the values and/or terms of the matrix, for example, by a vector. It is not necessary for the input signal to be multiplied by all elements of the matrix. During multiplication, the input signal is multiplied by values or coefficients of the matrix. The matrix can be technically implemented as a resistive matrix. The matrix serves as a projection into a function space and can therefore be referred to as a projection matrix.

The multiplication occurs continuously over time. A subdivision into discrete time steps is neither intended nor necessary. In particular, the multiplication occurs analogically, for example, in an analog data processing device. A continuous-time input signal can be processed continuously and/or in real time.

The result of the multiplication typically results in a continuous-time vector. This vector can serve as an input for another part of the matrix.

The input signal is, in particular, a voltage signal. In particular, the input signal is fed directly into the matrix, i.e., without any intermediate steps. Preferably, no sampling or digitization of the input signal takes place. The input signal is fed into the matrix. The input signal is typically a voltage signal. Another data signal can be used, for example, a current signal. This can then be converted into a voltage signal.

In particular, the matrix is chosen to execute a high-order polynomial projection (HiPPO) algorithm. In one embodiment, a HiPPO algorithm is used to project the input signal into a Fourier basis space. Here, the signal is represented with sine and cosine functions at different frequencies. Thus, a transformation similar to a Fourier transform can be achieved in a continuous manner. The matrix, in particular, comprises real values. The real-valued matrix can be implemented in a resistive matrix, e.g., by linear mapping.

In one embodiment, the matrix comprises a vector and a square matrix. The matrix can be understood as a vector and a directly adjacent square matrix. The square matrix has m rows and m columns and thus the dimension m. The matrix has m rows and n columns and thus the dimension m × n. In particular, n = m + 1. In particular, the number of elements of the vector corresponds to the number of rows m of the matrix.

The vector and the square matrix can fulfill different functions, for example, different signals can be introduced into the vector and the square matrix.

In one embodiment, the input signal is multiplied by the vector. The input signal is multiplied by the vector as part of the matrix. The input signal is thus fed into the vector. The result is again a vector. If the input signal is a voltage signal, the result of the multiplication by the vector is a vector of current signals. This vector obtained as a result of the multiplication can be added to the result of the product of the square matrix and a vector of signals.

In one embodiment, a signal vector is introduced into the square matrix. The vector of signals is then input into the matrix. Specifically, the signals are voltages. Typically, the vector has m elements. The number of elements in the vector thus corresponds to the dimension of the square matrix.

Typically, the vector is multiplied by the matrix. This typically results in currents. In particular, the currents are added according to Kirchhoff's law. The output signal from the square matrix and/or the sum of the addition can be a current vector. The output signal from the square matrix typically corresponds to the output signal of the matrix.

In one embodiment, an output signal of the matrix is integrated over time. This means that the output signal of the matrix is integrated over time. This is done in particular in an integrator. The output signal of the matrix can, as described, be a vector of currents (current vector) and/or an output signal of the square matrix. The output signal is typically the sum of the products of the input signal and the vector on the one hand, and the product or products of the vector with signals and the square matrix on the other. The result of the integration can then be a voltage vector. The values of this voltage vector are also referred to as coefficients. The output signal of the matrix can be an output signal of the square matrix.

In one embodiment, the integrated output signal from the matrix is fed into the square matrix as a signal vector. This creates a feedback loop. The integrated output signal of the matrix is fed back into the matrix or into a part of the matrix, namely the square matrix. The integrated output signal can be fed into the matrix directly or indirectly. With indirect feeding, one or more processing steps of the output signal can occur between integration and feeding; for example, an output signal can be inverted.

The output signal of the matrix typically corresponds to a time derivative of the signal vector.

• - Komprimieren eines Ausgangssignals der Matrix,
• - Abtasten und/oder Digitalisieren eines Ausgangssignals der Matrix,
• - Rekonstruieren des Eingangssignals aus einem Ausgangssignal der Matrix.

In one embodiment, the method comprises at least one of the following steps:

• - Compressing an output signal of the matrix,
• - Sampling and/or digitizing an output signal of the matrix,
• - Reconstructing the input signal from an output signal of the matrix.

Several of the above steps can be performed in any combination. The output signal of the matrix is, in particular, a voltage vector comprising coefficients as described.

Compression can be performed, for example, to transmit the input signal over one or more limited and/or noisy channels. The method can include this transmission. By transmitting the result of the compression or the coefficients instead of the input signal, a bandwidth reduction can be achieved. The coefficients can be sampled and, if necessary, digitized for this purpose or for any other purpose. The resulting digital signal can be transmitted at a lower frequency and/or on the same or a reduced number of channels.

A transformation into a frequency domain can be performed, similar to a Fourier analysis. For example, "Mel Frequency Cepstrum Coefficients" (MFCC) can be determined. This can be used, for example, for automatic speech processing. Instead of Fourier domain, projection can be performed into another domain.

The output signal can be used for the aforementioned purposes directly or indirectly. In the case of indirect use, one or more processing steps can be performed in between. The compression, digitization, and/or reconstruction of the input signal is performed primarily based on the coefficients.

In one embodiment, the vector B, the square matrix A, and/or the matrix A, B are learned using a neural network training method. In other words, the vector, the square matrix, and/or the matrix itself are learned. In this way, a learning process can be enabled to enable desired projections.

The method can be used to recognize patterns. For example, certain events can be detected that exhibit certain patterns. This allows the need for maintenance of a technical system, for example, to be identified in advance. Such an approach can be implemented, for example, as part of predictive maintenance.

For reconstruction, the determined coefficients can be multiplied by a suitable time-constant vector. This vector can be determined from the square matrix A and the vector B.

The input signal is, in particular, a one-dimensional input signal, for example, an audio signal. However, with a suitable choice of matrix, a multidimensional input signal, for example, a two- or three-dimensional one, can also be processed.

In one embodiment, a multidimensional input signal is used and multiplied continuously with a multidimensional matrix.

If the input signal is two-dimensional, such as a video signal (without sound), a two-dimensional matrix is also used. Instead of a vector and a square matrix, a matrix and a cubic or three-dimensional matrix are used. Input signals with more dimensions can also be processed if appropriate matrices are used. Processing is generally continuous-time.

When editing a video, each pixel can first be processed continuously in time according to the invention. In particular, coefficients can then be generated to represent the spatial variation. This can be done, for example, using convolution, which allows the differences between neighboring pixels to be considered.

In one embodiment, the input signal is a static or moving image signal. These can be represented in higher-dimensional function spaces in the style of a variational problem. This allows for significant savings in data rate, since the frequency dynamics of realistic images, in particular, are often lower than those of audio signals. In one configuration, the input signal is a video signal. Compression of a video signal can be performed. For this purpose, a three-dimensional memristive matrix, for example, can be used.

A further, independent aspect of the invention is a data processing method in which an analog electrical input signal is multiplied by a matrix in discrete-time space and/or in a discrete-time manner, wherein the matrix comprises, in particular, resistive, preferably memristive elements. All features, advantages, and embodiments of the method described above can apply analogously to this aspect.

A further aspect of the invention is a data processing device. This device comprises an input for inputting an analog electrical input signal, a matrix for continuously processing the input signal by multiplying it by the matrix, and an output for outputting an output signal. All features, advantages, and configurations of the method described above can apply analogously to the device, and vice versa. In particular, the device is an analog device or a device for analog data processing.

The device can be designed as a power-off-grid device, e.g., for an IoT (Internet of Things) application. A device designed in this way can include a rechargeable battery for powering the device and/or an interface for communication with a network such as a Wi-Fi or mobile internet. The device enables energy-efficient operation and is cost-effective to manufacture. These advantages make it particularly suitable as a power-off-grid device.

The device is suitable for multiplying the input signal by the matrix continuously over time. The device can also be suitable for multiplying the input signal by the matrix in a discrete-time space and/or in a discrete-time manner. In this case, the calculation would also be performed using analog signals. The advantage of fast calculation would be retained.

In one embodiment, the matrix comprises resistive elements. The matrix is therefore a resistive matrix and can also be referred to as a resistive array. In particular, the matrix is constructed from or represented by resistive elements. This means that resistive elements arranged in columns and rows form the matrix or represent a technical implementation of the matrix. In the simplest case, a resistive element is a resistor. It has been shown that resistive elements are particularly well suited for performing matrix multiplication in a continuous-time manner. This is therefore possible in real time. This embodiment also enables particularly low space requirements.

In one embodiment, the matrix comprises memristive elements. In particular, the elements of the matrix are memristive elements. Memristive elements, also referred to as memristive switching elements, are elements or circuits that emulate an ideal memristor. A memristor is a hypothetical passive electrical component that has an electrical resistance between its two terminals that depends on the history of the applied voltages. The resistance is thus variable or adjustable. This enables rapid programming, even runtime programming. Various designs of memristive elements are known that are sufficiently close to an ideal memristor.

Memristive elements are capable of storing data in the form of resistors. The values of the matrix can be implemented in this way. In particular, connections can be provided to program the memristive elements, for example, a column of memristive elements, i.e., to write the values of the matrix. These connections can be implemented as access transistors, for example. This makes it possible to implement different matrices in one device to project the input signal into different function spaces.

In addition to its low space requirement, this design also allows for adaptation of the matrix, so that the device can be used to execute different algorithms. In one design, the method includes changing the projection space and/or the projection dimension of the algorithm. The algorithm can be a HiPPO algorithm, as described.

In one embodiment, non-volatile memristive elements are used. These elements do not depend on an input control signal and do not need to be loaded from a separate memory, as would be the case with DRAM or SRAM. Energy is only consumed when needed when calculations or adjustments are carried out.

In one embodiment, each element of the matrix is present in duplicate. In particular, a first embodiment links the input signal to an integrated output signal of the matrix. In particular, a second embodiment links the inverted input signal to an inverted, integrated output signal of the matrix. In particular, both embodiments of a respective element of the matrix are connected to the same output. The inversion corresponds to a change in sign. This also makes it possible to technically implement negative values of the matrix. An inverter can be present to invert the results of the multiplication. The results of the multiplication can correspond to the output signal of the matrix.

An element of the matrix links a respective input signal with a respective output signal. This means that the respective input signal and the respective output signal are fed into the matrix and subjected to an operation, such as multiplication.

In one embodiment, the device comprises an integrator for temporally integrating the output signal of the matrix. In particular, an integrator is provided for each row of the matrix. In this way, each output signal of the output signal vector can be temporally integrated.

In one embodiment, the integrator includes an operational amplifier. An operational amplifier, also referred to as an op-amp for short, has the advantage of providing a virtual ground at the matrix output. This way, the matrix output or the output signal is not loaded. No voltage builds up that could lead to value corruption.

Some integrator designs, especially those with an operational amplifier, invert the signal. For this reason, the device may include an inverter to determine the coefficients from the integrated signal.

In particular, the device comprises an inverter for each row of the matrix. This allows a coefficient to be determined for each integrated signal of the vector of integrated signals. Typically, a vector of coefficients is thus determined.

A further aspect of the invention is a use of resistive elements, in particular memristive elements, for the continuous-time multiplication of an analog electrical input signal.

The resistive or memristive elements are used in particular to map or maintain a matrix, which can be multiplied by the input signal in this way. All features, advantages, and configurations of the method and device described above can apply analogously to the use, and vice versa.

Below, exemplary embodiments of the invention are explained in more detail with reference to the figures. Features of the exemplary embodiments can be combined individually or in multiples with the claimed subject matter, unless otherwise stated. The claimed scope of protection is not limited to the exemplary embodiments.

• 1: eine schematische Darstellung einer quadratischen Matrix;
• 2: eine schematische Darstellung einer erfindungsgemäßen Vorrichtung;
• 3: eine weitere schematische Darstellung einer erfindungsgemäßen Vorrichtung;
• 4: eine weitere schematische Darstellung einer erfindungsgemäßen Vorrichtung; sowie
• 5 bis 8: ein Beispiel einer erfindungsgemäßen Datenverarbeitung.

They show:

• 1 : a schematic representation of a square matrix;
• 2 : a schematic representation of a device according to the invention;
• 3 : a further schematic representation of a device according to the invention;
• 4 : a further schematic representation of a device according to the invention; and
• 5 to 8 : an example of data processing according to the invention.

1 shows a square matrix A. The square matrix A has 4 rows and 4 columns and therefore the dimension 4. The individual matrix elements are labeled w and the indices for the row and column.

In the illustrated technical implementation using a device for analog data processing, each matrix element can be represented by a memristive element 7. An exemplary basic structure of such a memristive element 7 is shown on the left using an enlarged circuit diagram. The memristive element 7 comprises an adjustable resistor and a transistor 12 or a selector, which, as shown, are connected to a word line 13, a selection line 14, and a bit line 15. The selection line 14 serves to initialize the square matrix A or to store values in the memristive element or resistor. The method comprises, in particular, the initialization of the square matrix A and/or the vector B.

Each matrix element can include or consist of a transistor 12 and a memristive element 7, as shown. Transistor 12 is required only for initializing (programming) the memristive elements and thus the matrix. During normal operation, transistors 12 are fully open via a gate voltage.

In addition to the square matrix A, the device according to the invention typically also comprises the vector B shown in the following figures. The elements of the vector B can also be represented by the memristive elements 7 shown and described here.

For data processing, voltages v with the respective indices are introduced into the individual rows of the square matrix A. Currents i with the respective indices result in the columns of the square matrix A.

2 shows schematically the structure of a device 1 for data processing. Top left is an enlarged view of the illustration from 1 shown, which corresponds to the square matrix A. To the left of the square matrix A in the main image is the vector B, which typically has the same number of elements as the number of rows and columns of the matrix. The square matrix A and vector B together form the matrix A, B. Because the square matrix has dimension 4, see above, the matrix A, B has dimension 4 × 5.

An input 2 of the device serves to input an analog electrical input signal 4 into the matrix A, B, here into the vector B of the matrix A, B. Signals from the vector B are fed into the square matrix A. In addition, a signal vector 6 is fed into the square matrix A, which will be discussed further below.

The output signals 5 of the matrix A, B are output from the output 3 of the device 1 and correspond to a temporary time derivative $\frac{\partial c}{\partial t}$ of coefficients c. These are integrated over time in an integrator 9 and then fed into the square matrix A as a signal vector 6. The integrated output signals 5 correspond to the coefficients c. The coefficients c are a projection of the input signal 4 into the high-dimensional function space and can be tapped, for example, for signal transmission, to reconstruct the input signal and/or to be digitized.

3 shows a concrete technical implementation of a device for data processing. The elements w of the matrix A, B are memristive elements according to 1 designed. In 3 Some elements w are marked as examples only.

The input signal 4, an analog voltage signal, is fed into the vector B. A signal from each element w of the vector B is fed into an element w of the first column of the square matrix A. In addition, the coefficients c are fed into the matrix B as signal vector 6. The signal vector 6 contains, in particular, electrical voltage signals. The currents add up in each row of the square matrix A and result in a vector of current signals as the output signal at the end of the matrix A or the square matrix A, B. This corresponds to the time derivative. $\frac{\partial c}{\partial t}$ the coefficients c. The elements of this vector are integrated over time using integrator 9. This results in a voltage vector containing the coefficients c.

Again 3 As can be seen, in the example shown here a circuit with an operational amplifier is used as integrator 9. There is one such integrator 9 for each row of the square matrix A. In order to determine the coefficients c from the signals inverted by the specific design of the integrator, an inverter 10 is used after each integrator 9. The voltage vector of the coefficients c is output from the inverters 10 and fed back into the square matrix A as feedback. The vector c can - depending on the design of the square matrix A - depend on the entire input signal processed so far, on components of the entire input signal that are weighted at different times, in particular exponentially, or on the input signal in a fixed period of time before the current time.

In 3 For each column of the matrix A, B, a selection terminal 8 is also shown, to which an access transistor can be connected. The selection terminals 8 are connected to the respective selection lines 14 (see 1 ) and are used to initialize the memristive elements of the matrix A, B, i.e. both the square matrix A and the vector B. In addition, an integrator reset 11 is shown, with which the integrators 9 can be reset before signal processing begins.

4 shows a slightly modified version. For clarity, a square matrix A of dimension 2 is shown here purely as an example. In contrast to 3 Here, each element w of the matrix A, B exists in duplicate. Two examples of an element are labelled w' and w''. In the first example, the Input signal 4' is inputted, and an inverted (negative) input signal 4'' is inputted into the second embodiment. For this purpose, the device may comprise an inverter.

The signal path of the first embodiment inputs the output signals integrated with integrator 9 and inverted with inverter 10, which correspond to the coefficients c. Here, too, the integrators 9 are based on operational amplifiers, so that the coefficients c are generated by a subsequent inverter 10. The signal path of the second embodiment inputs the output signals integrated with integrator 9 and not inverted again, which correspond to the inverted or negative coefficients -c.

This embodiment serves to account for the positive and negative values of the matrix in some embodiments. Resistive or memristive conductivities or resistances can only be positive. However, since elements of the matrix can also assume negative values, in this embodiment, each element of the matrix is implemented with two memristive elements w' and w'', so that the positive and negative values can be determined separately. In other words, the matrix or vector B and the square matrix A each comprise a positive submatrix and a negative submatrix, the difference of which corresponds to the original matrix. This can be represented by the following formula, where i and j are the indices of the square matrix, A ⁺ corresponds to the positive matrix element or memristive element, and A ^- corresponds to the negative matrix element or memristive element: $$\frac{\partial c_{ij}}{\partial t}=c_i*A_{ij}^{+}+\left(-c_i\right)*A_{ij}^{-}=c_i*\left(A_{ij}^{+}-A_{ij}^{-}\right)=c_i*A_{ij}.$$

The 5 to 8 show different data processing of a common input signal, namely a one-dimensional analog electrical input signal in the form of a mono audio signal. 5 shows the input signal. The value va is plotted over time, with individual time steps shown on the x-axis. The original O, which corresponds to the unprocessed input signal, is plotted in dark color, and the reconstruction R of the input signal is plotted in light color.

To calculate the reconstruction, the method described above and in the 3 or 4 The method according to the invention shown in Figure 1 was used. The input signal was then reconstructed or approximated from the coefficients. It can be seen that the reconstruction R deviates from the original O in such a way that a cumulative temporal offset builds up. This is not due to the method or algorithm, but rather to a programming error that has since been corrected. Furthermore, it is evident that there are only extremely small visible deviations between the original O and the reconstruction R.

6 shows a classic spectrogram created using a conventional fast Fourier transform (FFT). It plots the intensities of the different frequencies f over time. Time is plotted in non-specific time units. 7 shows the coefficients c determined continuously from the input signal according to the invention. The matrix was chosen to implement a Fourier FouT-HiPPO algorithm. Thus, a projection into a Fourier function space was performed.

8 shows a spectrogram obtained using the coefficients c from 7 was reconstructed. A frequency-resolved reconstruction of the signal was calculated based on the coefficients. As an example, two coefficients were determined, corresponding to a sine and a cosine function of the same frequency. The coefficients were combined by adding their squares.

It turns out that the spectrum obtained is very similar to the classical spectrogram from 6 The intensity in dB varies, but the features at specific times clearly have a similar pattern. It has been shown that a comparatively low resolution (< 16 bits) is sufficient for such a representation. The x-axis shows indefinite time units and has been adjusted to be consistent with the representation of 6 The x-axis of the coefficients c in 7 corresponds to the x-axis of the 8 .

List of reference symbols

1

device

2

Entrance

3

Exit

4, 4'

Input signal

4''

Inverted input signal

5

Output signal

6

Signal vector

7

Memristive element

8

Selective connection

9

Integrator

10

Inverter

11

Integrator reset

12

transistor

13

Wording

14

Selection management

15

Bit line

AWAY

matrix

A

square matrix

B

vector

c

coefficient

-c

Inverted coefficient

temporal derivation

w, w', w''

element

v

Tension

i

Electricity

va

Value

f

frequency

O

Original

R

reconstruction

Claims (15)

Method for data processing in which an analog electrical input signal (4) is multiplied continuously by a matrix (A, B). Method according to the preceding claim, characterized in that the matrix (A, B) comprises a vector (B) and a square matrix (A). Method according to the preceding claim, characterized in that the input signal (4) is multiplied by the vector (B). Method according to one of the two preceding claims, characterized in that a signal vector (6) is introduced into the square matrix (A). Method according to one of the preceding claims, characterized in that an output signal (5) of the matrix (A, B) is integrated over time. Method according to the two preceding claims, characterized in that the integrated output signal (5) of the matrix (A, B) is introduced into the square matrix (A) as a signal vector (6). Method according to one of the preceding claims, further comprising at least one of the following steps: - compressing an output signal (5) of the matrix (A, B), - sampling and/or digitizing an output signal (5) of the matrix (A, B), - reconstructing the input signal (4) from an output signal (5) of the matrix (A, B). Method according to one of the preceding claims, characterized in that a multi-dimensional input signal (4) is used and is multiplied continuously in time by a multi-dimensional matrix (A, B). Device (1) for data processing, comprising an input (2) for inputting an analog electrical input signal (4), a matrix (A, B) for the continuous-time processing of the input signal (4) by multiplication with the matrix (A, B) and an output (3) for outputting an output signal (5). Device (1) according to the preceding claim, wherein the matrix (A, B) comprises resistive elements. Device (1) according to one of the two preceding claims, wherein the matrix (A, B) comprises memristive elements (7). Device (1) according to one of the three preceding claims, characterized in that each element (w) of the matrix (A, B) is present in duplicate, a first version linking the input signal (4) to an integrated output signal (5) of the matrix (A, B) and a second version linking an inverted input signal (4) to an inverted, integrated output signal of the matrix (A, B). Device (1) according to one of the four preceding claims, characterized in that the device (1) has an integrator (9) for the temporal integration of the output signal (5) of the matrix (A, B). Device (1) according to the preceding claim, characterized in that the integrator (9) comprises an operational amplifier and/or that the device (1) comprises an inverter (10) in order to determine coefficients (c) from the integrated signal. Use of resistive elements, in particular memristive elements (7), for the continuous-time multiplication of an analog electrical input signal (4).