Signals and Systems - Electrical Engineering

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

FIGURE 8.11

First-order

autoregressive filter

impulse responseh[n]

and responsey[n]due

tox[n]=u[n]−

u[n−3].

0 5 10 15 20

0

0.5

1

h[

n]

n

n

0 2 4 6 8 10 12

0

0.5

1

1.5

2

y

[n

]

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% Example 8.24

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a = [1−0.5]; b = 1; % coefficients of the difference equation

d = [1 zeros(1, 99)]; % approximate delta function

h = filter(b, a, d); % impulse response

x = [ones(1, 3) zeros(1, 10)]; % input

y = filter(b, a, x); % output from filter function

y1 = conv(h, x); y1 = y1(1:length(y)) % output from conv

n

8.3.4 Linear and Nonlinear Filtering with MATLAB..............................

One is not always able to get rid of undesirable components of a signal by means of linear filtering.

In this section we will illustrate the possible advantages of using nonlinear filters.

Linear Filtering

To illustrate the way a linear filter works, consider getting rid of a random disturbanceη[n], which we

model as Gaussian noise (this is one of the possible noise signals MATLAB provides) that has been

added to a sinusoidx[n]=cos(πn/ 16 ). Lety[n]=x[n]+η[n]. We will use an averaging filter having

an input–output equation

z[n]=

1

M

M∑− 1

k= 0

y[n−k]