In this paper, a fixed-point finite impulse response adaptive filter is proposed using approximate distributed arithmetic (DA) circuits. In this design, the radix-8 Booth algorithm is used to reduce the number of partial products in the DA architecture, although no multiplication is explicitly performed. In addition, the partial products are approximately generated by truncating the input data with an error compensation. To further reduce hardware costs, an approximate Wallace tree is considered for the accumulation of partial products. As a result, the delay, area, and power consumption of the proposed design are significantly reduced. The application of system identification using a 48-Tap bandpass filter and a 103-Tap high-pass filter shows that the approximate design achieves a similar accuracy as its accurate counterpart. Compared with the state-of-The-Art adaptive filter using bit-level pruning in the adder tree (referred to as the delayed least mean square (DLMS) design), it has a lower steady-state mean squared error and a smaller normalized misalignment. Synthesis results show that the proposed design attains on average a 55% reduction in energy per operation (EPO) and a 3.2\times throughput per area compared with an accurate design. Moreover, the proposed design achieves 45%-61% lower EPO compared with the DLMS design. A saccadic system using the proposed approximate adaptive filter-based cerebellar model achieves a similar retinal slip as using an accurate filter. These results are promising for the large-scale integration of approximate circuits into high-performance and energy-efficient systems for error-resilient applications.

This paper proposes the design of an adaptive filter in stochastic circuits. The proposed circuit requires lower area and power than a conventional stochastic implementation. In the proposed design, the stochastic multiplier is implemented by an XNOR gate, as in a conventional scheme. However, the stochastic adder based on a multiplexer is not a very efficient implementation due to the three required stochastic number generators (SNGs) and the iterative operation required in the adaptive filter. Thus, a novel stochastic adder using a counter and a post processing unit is proposed. This adder avoids the use of SNGs, therefore it incurs a smaller area and power, while operating faster than the conventional (multiplexer-based) stochastic adder. In terms of accuracy and hardware efficiency, simulation results show that the adaptive filter using the proposed stochastic design outperforms the conventional stochastic implementation using linear feedback shift register (LFSR) based SNGs. Specifically, the proposed design consumes 35.81% less dynamic power and 21.34% less area than an LFSR-based implementation at a slightly higher accuracy.