A deep oscillatory neural network based band pass filter

Abstract

The present invention generally relates to digital filters, more particularly, deep oscillatory neural network based band pass filters. The band pass filter comprises a first layer of neurons configured to process an input signal with a wide range of frequency components to amplify the essential signal components of the input signal. Further, a second layer of neural oscillators arranged in successive layers to the first layer, The each of the neural oscillators have a central frequency, and each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when the input signal is supplied to the second layer to extract Fourier coefficient representations of the input signal. Finally, a third layer is configured to generate a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer. The band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the input signal.

Description

[0001] Title: A DEEP OSCILLATORY NEURAL NETWORK BASED BAND PASS FILTER

[0002] TECHNICAL FIELD

[0003] The present invention relates generally to oscillatory neural networks, and more particularly to a deep oscillatory neural network-based band pass filter.

[0004] BACKGROUND

[0005] A digital filter may be implemented in hardware and / or software that operates on a digital input signal to produce a digital output signal for the purpose of achieving a filtering objective. Digital filters operate on digitized analog signals or just numbers, representing some variable, stored in a memory. The conventional technologies disclose a transfer function which represents Infinite Impulse Response (HR) filters. If the denominator is simply unity, it represents a Finite Impulse Response (FIR) filter. Based on the frequency bands they allow or reject, digital filters are classified as low pass, high pass, band pass and band stop filters. An ideal band pass filter (BPF) may allow all the frequencies between f and fu and suppress all the other frequencies. However, this cannot be implemented practically, since it is a non-causal system. So, the main challenge with designing digital filters is to achieve characteristics as close to the ideal filter as possible.

[0006] One of the conventional technologies designs digital filters using Parks-McClellan algorithm for designing efficient and optimal FIR filters which take the pass band, transition band and stop band ranges with the number of taps as input and uses an iterative approach to return the taps of the designed FIR filter. The Bilinear Transform is a standard method for designing HR filters by converting the desired analog filters into digital filters.

[0007] The information disclosed in this background of the disclosure section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.

[0008] SUMMARY

[0009] One or more shortcomings discussed above are overcome, and additional advantages and features are provided by the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered a part of the disclosure. In a non-limiting embodiment of the present disclosure, a deep oscillatory neural network-based band pass filter, the band pass filter comprises a first layer of neurons configured to process an input signal with a wide range of frequency components to amplify essential signal components of the input signal. Further, the deep oscillatory neural network comprises a second layer of neural oscillators arranged in successive layers to the first layer. The neural oscillators have a central frequency, and each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when the input signal is supplied to the second layer to extract Fourier coefficient representations of the signal. A third layer of the deep oscillatory neural network is configured to generate a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer. The band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the input signal.

[0010] In yet another non-limiting embodiment of the present disclosure, the neural oscillators of the second layer are Hopf oscillators. The neural oscillators are configured to operate in a critical or supercritical Hopf regime to achieve the resonance within the narrow frequency range around the central frequency. The Hopf regime to achieve the resonance within the narrow frequency is defined by: where a > 0, co is the angular frequency, 0 < 0, and I(t) is the output of the first layer. The solution of the differential equation is Zd(t).

[0011] In another non-limiting embodiment of the present disclosure, the nonlinear activation functions comprise Rectified Linear Unit (ReLU) activation function and hyperbolic tangent (tanh) activation function. The nonlinear activation functions are defined by:

[0012] Zs(t) = f(Re(Zd(t))) + if (Im(Zd(t))) where Zd(t) is the output of the neural oscillators, and Re and Im represent real and imaginary parts of the output of the neural oscillators, respectively.

[0013] In yet another non-limiting embodiment of the present disclosure, the deep oscillatory neural network based band pass filter is trained using a dataset of sinusoidal signals with varying frequencies and amplitudes to replicate magnitude response similar to digital filters. In yet another non-limiting embodiment of the present disclosure, the neural oscillators are configured to operate in a resonator mode.

[0014] In yet another non-limiting embodiment of the present disclosure, the central frequencies of the neural oscillators are adjustable in manner that a constant change in the central frequencies of all the neural oscillators results in a shift in pass band range of the band pass-filter.

[0015] In yet another non-limiting embodiment of the present disclosure, the method for processing an input signal in a deep oscillatory neural network based band pass filter. The method comprises receiving the input signal at the first layer of the deep oscillatory neural network based band pass filter. Further, processing the input signal to amplify signal components of the input signal. The method further comprises processing each of the signal components using a second layer of neural oscillators of the deep oscillatory neural network based band pass filter arranged in successive layer to the first layer, each of the neural oscillators have a central frequency, and each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when each of the frequency components of the input signal are supplied to the neural oscillators of the second layer for extracting Fourier coefficient representations of the signal. Finally, the method comprises generating a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer. The band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the input signal.

[0016] The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

[0017] BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

[0018] The embodiments of the disclosure itself, as well as a preferred mode of use, further objectives, and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying drawings. One or more embodiments are now described, by way of example only, with reference to the accompanying drawings in which: FIG. 1 illustrates oscillatory neural network architecture used for constructing digital filters., in accordance with one embodiment;

[0019] FIG. 2 shows a graph representation indication behavior of Hopf oscillator, in accordance with one embodiment;

[0020] FIG. 3 shows a graph representation indicating transfer functions of the original and shifted band pass filter, in accordance with one embodiment;

[0021] FIG. 4 shows a schematic diagram to describe the essential features of the DONN based BPF, in accordance with one embodiment; and

[0022] FIG. 5 illustrates a flowchart of a method of processing an input signal in a deep oscillatory neural network-based band pass filter, in accordance with one embodiment.

[0023] It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of the illustrative systems embodying the principles of the present subject matter. Similarly, it will be appreciated that any flowchart, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and executed by a computer or processor, whether or not such computer or processor is explicitly shown.

[0024] DETAILED DESCRIPTION

[0025] In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.

[0026] While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example in the drawings and will be described in detail below. It should be understood, however, that it is not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure.

[0027] The terms “comprises,” “comprising”, or any other variations thereof, are intended to cover a nonexclusive inclusion, such that a setup, device, or method that comprises a list of components or steps does not include only those components or steps but may include other components or steps not expressly listed or inherent to such setup or device or method. In other words, one or more elements in a system or apparatus preceded by “comprises... a” does not, without more constraints, preclude the existence of other elements or additional elements in the system or apparatus.

[0028] In the following detailed description of the embodiments of the disclosure, reference is made to the accompanying drawings that form a part hereof, and in which are shown by way of illustration specific embodiments in which the description may be practiced. These embodiments are described in sufficient detail to enable those skilled in art to practice the disclosure, and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present disclosure. The following description is, therefore, not to be taken in a limiting sense.

[0029] The terms like “at least one” and “one or more” may be used interchangeably throughout the description. The terms like “a plurality of’ and “multiple” may be used interchangeably throughout the description. The terms like “network” and “communication network” may be used interchangeably throughout the description.

[0030] A complex dynamic of interacting oscillators have recently been investigated as building blocks for computation, especially in Al applications. Further, a model which is a variant of oscillator-based methods, called Deep Oscillatory Neural Networks (DONN) shows state-of-the-art performance in many signal processing tasks. Thus, DONN may be used to learn digital filters. Thus, the present disclosure is not an alternative to traditional filter design methods, rather a result that shows that oscillatory neural networks can learn these digital filters and are a learnable end-to-end deep learning solution for the same.

[0031] A band-pass filter may be used to transmit signals in a certain band of frequencies and block signals of lower and higher frequencies. In other words, the basic function of a digital filter is to eliminate the noise and to extract the signal of interest from other signals. A digital filter is a basic device used in digital signal processing. There are several techniques available to design digital filters. Generally, while designing a digital filter, first an analog filter is designed and then it is converted into the corresponding digital filter. A filter is essentially a system or network that selectively changes the wave shape amplitude - frequency and / or phase - frequency characteristics of a signal in a desired manner. A digital filter may be implemented in hardware and / or software that operates on a digital input signal to produce a digital output signal for the purpose of achieving a filtering objective. Thus, the digital filters are used to enhance or suppress certain frequency bands of a signal. This ability to manipulate, separate and restore signals has made them essential building blocks in the field of digital signal processing.

[0032] FIG. 1 illustrates block architecture of a deep oscillatory neural network -based band pass filter, in accordance with one embodiment.

[0033] The present disclosure describes deep oscillatory neural network-based band pass filter 103 that may use Hopf oscillator as the oscillatory neuron model. The Hopf oscillator may be capable of synchronizing its oscillating frequency to any oscillatory input signals 101. The band pass filter 103 comprises a first layer of neurons configured to process an input signal 101 with a wide range of frequency components to amplify the essential signal components of the input signal 101. For instance, a sinusoidal signal of known frequencies may be passed through the first layer of neurons to observe the DFT plots of the input’s signals . The deep oscillatory neural network-based band pass filter 103 consists of successive layers of static dense or convolutional layers with nonlinear activation and dynamic Hopf oscillator layers. A general oscillator neural network is depicted in Fig. 1. There may be various forms in which an input may be presented to the oscillator layer i.e., as an external input which may also be referred to as resonator mode. In an alternative embodiment, an input signal 101 may also be presented as to the amplitude which is also referred as amplitude modulation or an input to the frequency which is defined also as frequency modulation.

[0034] In an embodiment, the band pass filter 103 comprises the second layer of neural oscillators arranged in successive layers to the first layer the neural oscillators have a central frequency. In the present disclosure, each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when the input signal 101 is supplied to the second layer to extract thereby extracting Fourier coefficient representations of the input signal. The neural oscillators of the second layer are Hopf oscillators. The neural oscillators are configured to operate in a critical or supercritical Hopf regime to achieve the resonance within the narrow frequency range around the central frequency. The Hopf oscillator is represented by a complex-valued differential equation:

[0035] Particularly, a > 0, co is the angular frequency, 0 < 0, and I(t) is the output of the first layer. The solution of the differential equation is Za(t). In general, the Hopf oscillators exhibits four distinct dynamical behaviors determined by the parameters (a, 0, y) but not limited to critical Hopf regime (a = 0, 0 < 0, y = 0), supercritical Hopf regime (a > 0, 0 < 0, y = 0), double limit cycle regime (a < 0, 0 > 0, y < 0).

[0036] To simplify, the neural oscillators which are configured to achieve resonance within a narrow frequency range around the central frequency, during this state the frequency of the input signal is equal to the frequency of the oscillator activation. The central frequencies of the neural oscillators are adjustable in the manner that a change in the central frequencies of the neural oscillators results in a shift in the pass band range of the band pass-filter. For instance, the resonance may occur specifically when the input follows the form I(t) = Ioel“Ot, and it depends on the frequency difference between the input and output. Thus, changing the intrinsic frequency of the oscillator allows us to shift the resonant curve to that frequency.

[0037] Further, the band pass filter 103 comprises a third layer configured to generate a band pass signal 105 by applying nonlinear activation functions pointwise in time to outputs of the second layer. The band pass signal 105 is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the input signal. The nonlinear activation functions comprise Rectified Linear Unit (ReLU) activation function and hyperbolic tangent (tanh) activation function, the nonlinear activation functions are defined by:

[0038] Zs(t) = f(Re(Zd(t))) + if (Im(Zd(t))) Here, Zd(t) is the output of the neural oscillators, and Re and Im represent real and imaginary parts of the output of the neural oscillators, respectively.

[0039] In an embodiment, the deep oscillatory neural network-based band pass filter 103 is trained using a dataset of sinusoidal signals with varying frequencies and amplitudes to replicate magnitude response similar to digital filters. Specifically, to train the network described in Figure 1 to behave like a digital filter, the present disclosure generates the training dataset based on the single frequency noisy sinusoidal signals as the input. s(t) = Acos(27tft) + n(t)

[0040] The amplitude A lies in the range [1, 2], frequency f lies in the range [1, 500] Hz and n(t) is additive white Gaussian noise (AWGN) with zero mean and 0.01 standard deviation. The signal is generated for 1 second with a sampling rate, fs = 1000 Hz. in the range [1, 500] Hz and n(t) is additive white Gaussian noise (AWGN) with zero mean and 0.01 standard deviation. The signal is generated for 1 second with a sampling rate, fs = 1000 Hz. For instance, in the present disclosure may use Finite Impulse Response (FIR) filter designed using the Parks McClellan algorithm and Infinite Impulse Response (HR) filter based on the Butterworth family of filters. Further, the above-mentioned filters are now applied to input sinusoids to generate the filtered output signals. In the present disclosure the SciPy library may be used for implementing the filters, however this should not be construed as the limitation as other library functions may be used to implement the filters. As a result, the output signals for the pass band frequencies are sinusoids similar to input signals. For instance, the initial input signal 101 is processed to remove, suppress and / or amplify certain frequency components. The input data is composed of synthetically generated sinusoidal signals with frequency in the range 5Hz to 300Hz (for example), and arbitrary phase delays and amplitudes. The signal may be generated for 1 second with a sampling rate, fs = 1000. The signal may be filtered using HR Butterworth filter using SciPy library, allowing frequencies in the range 50Hz to 100Hz to pass and attenuates others.

[0041] To simplify, the present disclosure comprises the oscillator frequencies of the nodes present in the neural oscillator layer (as seen in Figure 1), are shifted to represent some other pass band range. For instance, the deep oscillatory neural network may act as a band pass filter (BPF) for that shifted pass band range. Figure 3 shows the estimated transfer function of a BPF originally trained for 140-160 Hz which is then shifted to a pass band range of 240-260 Hz. In this case, re-training the shifted model reduced the MSE loss from 0.03 to 0.008.

[0042] Now, moving on to FIG 4. that illustrates a schematic of the present disclosure, to describe the construction of a band pass filter 103 to construct any arbitrary filter profile. The initial graph indicated (A) describes the resonance property of the Hopf Oscillator. Further, the graph (B) describes an Oscillator Resonator Block (ORB). The addition of the nonlinear activation layer results in a sharper tuned response for a band of frequency, with its center frequency f. Furthermore, the graph indicated as (C) discloses the combination of such ORBs that may be used to create a Band Pass Filter for a desired pass band. Further, the graph indicated as (D) describes shifting the pass band. In shifting the passband, a trained BPF may function as BPF for a new range of pass band frequencies by shifting the intrinsic frequencies of the oscillator by a desired frequency c, fi — > fi + c. The graph indicated as (E) describes the amplification of the pass band by a scaling parameter. Finally, the graph indicated as F describes any arbitrary filter profiles that may be constructed by a combination of this shifting and scaling property as described.

[0043] FIG 5. illustrates a method 500 for processing an input signal in a deep oscillatory neural network based band pass filter, in accordance with an embodiment of the present disclosure.

[0044] Although example method 500 depicts a particular sequence of operations, the sequence may be altered without departing from the scope of the present disclosure. For example, some of the operations depicted may be performed in parallel or in a different sequence that does not materially affect the function of method 500.

[0045] According to some examples, the at block 501 method 500 includes receiving the input signal at a first layer of the deep oscillatory neural network based band pass filter. The deep oscillatory neural network-based band pass filter is trained using a dataset of sinusoidal signals with varying frequencies and amplitudes to replicate magnitude response similar to digital filters.

[0046] According to some examples, at block 503, method 500 includes processing each of the signal components using a second layer of neural oscillators of the deep oscillatory neural network-based band pass filter arranged in successive layers to the first layer. The each of the neural oscillators have a central frequency, and each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when each of the frequency components of the input signal are supplied to the neural oscillators of the second layer to extract Fourier coefficient representation of the signals. The neural oscillators of the second layer are Hopf oscillators, and the neural oscillators are configured to operate in a supercritical Hopf regime to achieve the resonance within the narrow frequency range around the central frequency. The supercritical Hopf regime to achieve the resonance within the narrow frequency range are defined by: where a > 0, co is the angular frequency, 0 < 0, and I(t) is the output of the first layer. The solution of the differential equation is Zd(t). Further, the central frequencies of the neural oscillators are adjustable in the manner that a change in the central frequencies of the neural oscillators results in a shift in pass band range of the band pass-filter.

[0047] According to some examples, at block 505, method 500 generates a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer. The band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the input signal. The nonlinear activation functions comprise Rectified Linear Unit (ReLU) activation function and hyperbolic tangent (tanh) activation function. The the nonlinear activation functions are defined by:

[0048] Zs(t) = f(Re(Zd(t))) + if (Im(Zd(t))) where Zd(t) is the output of the neural oscillators, and Re and Im represent real and imaginary parts of the output of the neural oscillators, respectively.

[0049] Specifically, the present disclosure describes the ability of deep oscillatory neural networks to learn to behave like filters. These models are capable of showing behavior similar to both FIR and HR filters. The idea of shifting the frequencies, which is inherent to the Hopf oscillator node used as described above. Thus, the present disclosure describes how to obtain filters shifted to a different range of frequencies with minimal re-training of the model. By combining multiple such models to generate a wide variety of filters, it is also discussed and demonstrated. While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the detailed description.

[0050] The order in which the various operations of the methods are described is not intended to be construed as a limitation, and any number of the method described blocks can be combined in any order to implement the method. Additionally, individual blocks may be deleted from the methods without departing from the spirit and scope of the subject matter described herein. Furthermore, the methods can be implemented in any suitable hardware, software, firmware, or combination thereof.

[0051] It may be noted here that the subject matter of some or all embodiments described with reference to Figs. 1-5 may be relevant for the methods and the same is not repeated for the sake of brevity.

[0052] The various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and / or software component(s) and / or module(s), including, but not limited to a circuit, an application specific integrated circuit (ASIC), or processor. Generally, where there are operations illustrated in Figures, those operations may be performed by any suitable corresponding counterpart means-plus-function components.

[0053] Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., non-transitory. Examples include Random Access Memory (RAM), Read-Only Memory (ROM), volatile memory, nonvolatile memory, hard drives, Compact Disc (CD) ROMs, Digital Video Disc (DVDs), flash drives, disks, and any other known physical storage media. Certain aspects may comprise a computer program for performing the operations presented herein. For example, such a computer program product may comprise a computer readable media having instructions stored (and / or encoded) thereon, the instructions being executable by one or more processors to perform the operations described herein. For certain aspects, the computer program product may include packaging material.

[0054] Various components, modules, or units are described in this disclosure to emphasize functional aspects of devices configured to perform the disclosed techniques, but do not necessarily require realization by different hardware units. Rather, as described above, various units may be combined in a hardware unit or provided by a collection of intraoperative hardware units, including one or more processors as described above, in conjunction with suitable software and / or firmware.

[0055] As used herein, a phrase referring to “at least one” or “one or more” of a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c. The terms “a”, “an” and “the” mean “one or more”, unless expressly specified otherwise. The terms “including”, “comprising”, “having” and variations thereof, when used in a claim, is used in a non-exclusive sense that is not intended to exclude the presence of other elements or steps in a claimed structure or method, unless expressly specified otherwise.

[0056] Finally, the language used in the specification has been principally selected for readability and instructional purposes, and it may not have been selected to delineate or circumscribe the inventive subject matter. It is therefore intended that the scope of the invention be limited not by this detailed description, but rather by any claims that are issued on an application based here on. Accordingly, the embodiments of the present disclosure are intended to be illustrative, but not limiting, of the scope of the invention, which is set forth in the appended claims.

Claims

We Claim:

1. A deep oscillatory neural network based band pass filter, the band pass filter comprises: a first layer of neurons configured to process an input signal with a wide range of frequency components to amplify essential signal components of the input signal; a second layer of neural oscillators arranged in successive layer to the first layer, wherein each of the neural oscillators have a central frequency, and wherein each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when the input signal is supplied to the second layer to extract Fourier coefficient representations of the input signal; and a third layer configured to generate a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer, wherein the band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the inputs signal.

2. The band pass filter as claimed in claim 1 , wherein the neural oscillators of the second layer are Hopf oscillators, and wherein the neural oscillators are configured to operate in a critical or supercritical Hopf regime to achieve the resonance within the narrow frequency range around the central frequency; and wherein the supercritical Hopf regime to achieve the resonance within the narrow frequency range are defined by -where a > 0, co is the angular frequency, 0 < 0, and I(t) is the output of the first layer. The solution of the differential equation is Zd(t).

3. The band pass-filter as claimed in claim 1 , wherein the nonlinear activation functions comprise Rectified Linear Unit (ReLU) activation function and hyperbolic tangent (tanh) activation function, and wherein the nonlinear activation functions are defined by:Zs(t) = f(Re(Zd(t))) + if (Im(Zd(t)))where Zd(t) is the output of the neural oscillators, and Re and Im represent real and imaginary parts of the output of the neural oscillators, respectively.

4. The band pass-filter as claimed in claim 1 , wherein the deep oscillatory neural network-based band pass filter is trained using a dataset of sinusoidal signals with varying frequencies and amplitudes to replicate magnitude response similar to digital filters.

5. The band pass-filter as claimed in claim 1, wherein the neural oscillators are configured to operate in a resonator mode.

6. The band pass-filter as claimed in claim 1, wherein the central frequencies of the neural oscillators are adjustable in manner that a change in the central frequencies of the neural oscillators results in a shift in pass band range of the band pass-filter7. A method of processing an input signal in a deep oscillatory neural network based band pass filter, the method comprising: receiving the input signal at a first layer of the deep oscillatory neural network based band pass filter; processing the input signal to amplify signal components of the input signal; processing each of the signal components using a second layer of neural oscillators of the deep oscillatory neural network based band pass filter arranged in successive layer to the first layer, wherein each of the neural oscillators have a central frequency, and wherein each of the neural oscillators is configured to achieve resonance within a narrow frequency range around the central frequency when each of the frequency components of the input signal are supplied to the neural oscillators of the second layer for extracting Fourier coefficient representations of the signal; and generating a band pass signal by applying nonlinear activation functions pointwise in time to outputs of the second layer, wherein the band pass signal is generated by combining the outputs of the neural oscillators of the second layer which achieves resonance upon applying the inputs signal.

8. The method as claimed in claim 7, wherein the neural oscillators of the second layer are Hopf oscillators, and wherein the neural oscillators are configured to operate in a supercritical Hopf regime to achieve the resonance within the narrow frequency range around the central frequency; and wherein the supercritical Hopf regime to achieve the resonance within the narrow frequency rangedefined bywhere a > 0, co is the angular frequency, 0 < 0, and I(t) is the output of the first layer. The solution of the differential equation is Za(t).

9. The method as claimed in claim 7, wherein the central frequencies of the neural oscillators are adjustable in manner that a change in the central frequencies of the neural oscillators results in a shift in pass band range of the band pass-filter.

10. The method as claimed in claim 7, wherein the deep oscillatory neural network based band pass filter is trained using a dataset of sinusoidal signals with varying frequencies and amplitudes to replicate magnitude response similar to digital filters.Dated this 03rdday of December 2024Mayank Sood OF K & S PARTNERS AGENT FOR THE APPLICANT(S) IN / PA-1850

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