y [n] = . h [k] x [n
− k] (4.1)
k=0
where x, h, y are input signal, filter coefficient,
output signal, respectively, and M designates filter order. Note
that after passing the delay component D, each element of signal
x is mapped to stochastic sequence by using individual SNG in
oder to reduce the correlation of stochastic sequences. Therefore,
M SNGs will be investigated in this design.
In this simulation, an input x mixed from 5 sinusoidal signals
with different frequencies is employed.
Fig.4.2 shows the input signal,
filter’s frequency response and output signal when using conventional
computing on FIR filter, or ideal filter. It will be used as a standard
to evaluate the accuracy of our stochastic FIR filter. Now, stochastic
implementation using the bit sequence of length as 1024 and Leap–Ahead
LFSR based SNGs is carried out. It can be observed in
Fig.4.2 that the spectrum of the
stochastic filter is very close to that of the conventional filter.
Consequently, it can be concluded that stochastic technique assures as
well as conventional method the function of FIR filter.