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Tunable front-end filters are necessary in wireless systems that support multiple frequency bands. N-path filters have the potential for wide tuning ranges, but require multiple high-frequency mixing clocks and suffer from harmonic responses. Another option is digital filtering. However, this requires high-speed analog-to-digital converters and the time complexity to perform Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT) operations using conventional digital computers is O(N 2 ). Conversely, memristor crossbars have experimentally demonstrated the ability to perform various signal processing tasks, including Discrete Cosine Transform (DCT), in one time-step. In this work, this has been taken a step further by presenting full DFT and IDFT operations using memristive crossbars and proposes the implementation of novel continuous-time tunable analog filters by applying filter coefficients in between these DFT and IDFT crossbars. This highly scalable new method of filtering leverages advantages found both in conventional digital and analog filters and allows any digital filter to be implemented in the analog domain with a filter order as large as half the utilized crossbar size. The proposed architecture allows for the generation of arbitrary filter functions with tunable corner (or center) frequencies and bandwidths from 0.2-20GHz. Stopband attenuation greater than 40dB is achieved with as low as 2bit memristor precision, while close to 80dB is possible with 8-bit precision. The filter system consumes 106mW to support the 20GHz frequency range, resulting in a 5.3mW/GHz energy metric.

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