Signals and Systems - Electrical Engineering

496 C H A P T E R 8: Discrete-Time Signals and Systems

0 20 40 60 80 100

(a)

(b)

120 140 160 180

0 20 40 60 80 100 120 140 160 180

− 1

−0.5

0

0.5

1

y[

n],

z[

n]

y[

n],

z^1

[n

]

− 1

−0.5

0

0.5

1

n

FIGURE 8.12

Averaging filtering with filters of order (a)M= 3 and of order (b)M= 15 result used to get rid of Gaussian noise

added to a sinusoidx[n]=cos(πn/ 16 ). Solid line corresponds to the noisy signal, while the dashed line is for the

filtered signal. The filtered signal is very much like the noisy signal (a) whenM= 3 is the order of the filter, while

the filtered signal looks like the sinusoid, but shifted, (b) whenM= 15. The plotting in this figure is done using

plotinstead ofstemto allow a better visualization of the filtering results.

a nonlinear filter, and a comparison of the results is shown in Figure 8.13. In this case the nonlinear

filter is able to denoise the signal much better than the linear filter.

%%%%%%%%%%%%%%%%%%%

% Nonlinear filtering

%%%%%%%%%%%%%%%%%%%

clear all; clf

N = 200;n = 0:N−1;

% impulsive noise

for m = 1:N,

d = rand(1, 1);

if d>= 0.95,

noise(m) =−1.5;

else

noise(m) = 0;

end

end