Stochastic FIR filter using SC

\label{stochastic-fir-filter-using-sc}
FIR filter which has a number of useful properties ( require no feedback, be stable, easily be designed) is an interesting problem in signal processing. It has been recently considered as an important application in SC [6], denoted Stochastic FIR filter. In this design, besides an appropriate number of SNGs, it equally requires to employ the inner–product unit which includes the XOR gates and a multiplexer. An M –order stochastic FIR filter can be illustrated as Fig.4.1.
D
x(n-1)
D
x(n-2)
seed0
seed1
h(0)
h(1)
Inner-product unit

y(n)
D
x(n-M)
seedM

h(M)
1/K
Figure 4.1: Implementation of M–order FIR filter using SC
In this architecture, the filter’s output can be mathematically given as