Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 265

Table 7.11 Illustrative Usage for MATLAB Function firfs(N, Hk)

function B ¼ firfs(N,Hk)

%B firls(N,Hk)

% FIR filter design using the frequency sampling method.
% Input parameters:
% N: the number of filter coefficients.
% note: N must be odd number.
% Hk: sampled frequency response for k

¼

¼ 0,1,2, ,M ¼ (N-1)/2.

.

% Output:
% B: FIR filter coefficients.

(number of taps) and a vector Hk containing the specified magnitude values H k , k ¼ 0; 1; / ; M. Finally, the
MATLAB function will return the calculated FIR filter coefficients.

EXAMPLE 7.13
a. Design a linear phase lowpass FIR filter with 25 coefficients using the frequency sampling method. Let the
cutoff frequency be 2,000 Hz and assume a sampling frequency of 8,000 Hz.
b. Plot the frequency responses.
c. List the FIR filter coefficients.
Solution:
a. The normalized cutoff frequency for the lowpass filter is U c ¼ uT ¼ 2p2000=8000 ¼ 0:5p radi-
ans, N ¼ 2M þ 1 ¼ 25, and the specified values of the sampled frequency response are chosen to be

H k ¼½1111111000000

MATLAB Program 7.8 produces the design results.
Program 7.8. MATLAB program for Example 7.13.
% Figure 7.31 (Example 7.13)
% MATLAB program to create Figure 7.31
fs

¼ 8000; % Sampling frequency

H1 [1 1 1 1 1 1 1 0 0 0 0 0 0]; % Magnitude specifications

B1 ¼ firfs(25,H1); % Design filter
[h1,f] ¼ freqz(B1,1,512,fs); % Calculate magnitude frequency response
H2 ¼ [1 1 1 1 1 1 1 0.5 0 0 0 0 0]; % Magnitude specifications
B2 ¼ firfs(25,H2);

¼

% Frequency response

[h2,f] ¼ freqz(B2,1,512,fs); % Calculate magnitude frequency response

p1 ¼ 180*unwrap(angle(h1))/pi;
p2 ¼ 180*unwrap(angle(h2))/pi
subplot(2,1,1); plot(f,20*log10(abs(h1)), ' -. ' ,f,20*log10(abs(h2)));grid
axis([0 fs/2 -80 10]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Magnitude Response (dB) ' );
subplot(2,1,2); plot(f,p1, ' -. ' ,f,p2);grid
xlabel( ' Frequency (Hz) ' ); ylabel( ' Phase (degrees) ' );