Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 281

1

x ()

+

y(n)

1.

− 1

+

xn ( − 1 )

− 1

0 36 .

xn ( − 2 )

FIGURE 7.40

FIR filter realization for Example 7.18.

Program 7.12. MATLAB program for Example 7.18.
% Sample MATLAB code
sample ¼ 1:1:10; % Input test array

x ¼ [ 0 0 0];

% Input buffer [x(n) x(n-1) . ]

y ¼ [0];

%output buffer [y(n) y(n-1) . ]

b ¼ [1.0 1.2 0.36]; % FIR filter coefficients [b0 b1 ]

.

KK length(b);

for n

¼

¼ 1:1:length(sample) % Loop processing

for k ¼ KK:-1:2 % Shift input by one sample

x(k) ¼ x(k-1);

end
x(1) ¼ sample(n); % Get new sample

y(1) ¼ 0; % Perform FIR filtering

for k ¼ 1:1:KK
y(1) ¼ y(1) þ b(k)*x(k);
end
out(n) ¼ y(1); %send filtered sample to the output array
end
out

7.7.2 Linear Phase Form
We illustrate the linear phase structure using the following simple example.
Consider the following transfer function with 5 taps obtained from the design:

HðzÞ¼b 0 þ b 1 z 1 þ b 2 z 2 þ b 1 z 3 þ b 0 z 4 (7.39)

We can see that the coefficients are symmetrical and the difference equation is

yðnÞ¼b 0 xðnÞþb 1 xðn 1 Þþb 2 xðn 2 Þþb 1 xðn 3 Þþb 0 xðn 4 Þ

This DSP equation can further be combined to yield

yðnÞ¼b 0 ðxðnÞþxðn 4 ÞÞ þ b 1 ðxðn 1 Þþxðn 3 ÞÞ þ b 2 xðn 2 Þ

Then we obtain the realization structure in a linear phase form as shown in Figure 7.41 .