Research On Memristor Crossbar Based Discrete-time FIR Filter Design

Memristor is a non-linear passive two-terminal electrical component with non-volatile memory property and is similar to an adjustable resistor in circuit.Its resistance is solely related to its internal states.Studies have shown that memristors can store and process data in circuits.FIR filters can obtain linear phase easily.Therefore,it is important to study FIR filters based on memristors.In this paper,a memristor crossbar based FIR filter structure is presented based on previous studies.In this structure,the coefficients of the FIR filter are stored in the memristor crossbar in the form of memristor resistance.Firstly,a sample-delay circuit formed by switched-capacitor circuit samples the input signal and various delays of discretized signal are generated.Then,the sampled signal and its discretized delays are weighted by memristor and summed by an output module,which is form by cascade of inverting summing circuits.Thus,FIR filter function is realized.The asynchronous sample-delay circuit used in previous studies has the problem of sequence misalignment and parameter selection,so the memristor-based FIR filter length that can be achieved is very small.In this paper,a synchronous sample-delay circuit is proposed,which can fully delay the input signal and its discretized delayed signals with sampling period at the same time,and compared to asynchronous sample-delay circuit delayed signals no longer overlap.A single signal can be used for control,and it is no longer necessary to delay the control signal for transmission,eliminating the delay circuit of the control signal.By solving the problem of asynchronous sample-delay circuit in the sequence misalignment and parameter selection,sampling and filtering performs is greatly improved and theoretically memristor crossbar based FIR filters with any length can be realized.An output module composed of cascaded inverting summing circuits is proposed,and the memristor crossbar based FIR filter structure is completed.In the original memristor-based FIR filter design,the coefficients can only have the same symbol,which results in the inability to implement most FIR filters.By using the cascade inverting summing circuit to form the output module,the memristor resistance value can be used to represent real FIR filter coefficients,which solves the symbol limitation in the preliminary design.Combining it with the synchronous sample-delay circuit can form a relatively complete memristor crossbar based FIR filter structure.Theoretically any arbitrary memristor crossbar based FIR filters can be implemented using the direct method with it.Accordingly,to prove the feasibility of the structure,a detailed analysis and verification of a 30-order memristor crossbar based FIR low-pass filter is carried out in this paper.The proposed structure does not use processors or A/D converters,and is fully implemented using analog devices,thus is free of round-off error and have a higher processing speed.In addition,because the FIR filter coefficients are stored in memristor crossbar,FIR filters based on structure proposed in this paper can be easily modified or redesigned.Parallel,cascade and combined structures of the memristor crossbar based FIR filter are proposed.Due to the use of the crossbar structure and the cascaded inverting summing circuits,signal can be multiplexed and multiple signals can be processed at the same time.The parallel structure can be realized by re-inputting the output signals from the crossbar into the crossbar again,and the output signals can be input into another delay circuit to realize the cascade structure.When the output signals are input into the delay circuit and then input into the crossbar,the combined structure can be realized.This feature can be flexibly used to realize more complex structure of memristor crossbar based FIR filters.While verifying this design,the coefficient multiplexing is accomplished by the equivalence of the output module and the adder circuit.Feedback is also introduced into the memristor crossbar based FIR filter in combined structure and memristor crossbar based IIR filter is formed in this way.Based on the foregoing research,a memristor crossbar based EIR(Extrapolated Impulse Response)filter is proposed.Because of the flexibility of the structure,memristor crossbar based FIR filters can implement other filter design methods.As a proof,this paper expands the aforementioned 30-order memristor crossbar based FIR low-pass filter to A memristor crossbar based EIR filter.By using one set of feature vector and two sets of feature vectors for extrapolation,and implementing their circuit structures and simulation experiments,it is proved that memristor crossbar based FIR filters can achieve some complex structural adjustments and perform filtering in the form of a plurality of sub-filters in combination,and can get the theoretical performance.Based on the extension of EIR filter,the implementation of filter bank and response masking filter based on the structure of this paper is discussed.The parallel of filters is used to generate the complementary filter of the memristor crossbar based FIR filter.At the same time,the coefficient interpolation is completed by inserting extra delay circuits without changing the position and resistance of the memristor.This proves the feasibility of using the proposed structure to implement frequency response masking filter.