Evaluation of Stochastic Cascaded IIR Filters

Stochastic cascaded IIR filters are used for area-efficient complicated filters in hardware, such as gammatone and gammachirp filters, but the effectiveness of the cascaded form has not been studied in stochastic computation. To evaluate the performance of the stochastic cascaded IIR filters, stochastic direct-form IIR filters are also designed as a baseline filter. The performance of both stochastic filters are simulated in MATLAB and compared with floating-point results in different orders and different stochastic bit lengths. The simulation results show that the cascaded form reduces errors in comparison with the direct form in stochastic IIR filters as well as the well-known effectiveness of the cascaded form in digital IIR filters. In addition, some interesting features of the stochastic IIR filters such as oscillations are exhibited, which are discussed based on spectral analysis.