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Summary: (Blank Abstract)
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To analyze or design linearphase FIR filters, we need to know
the characteristics of the amplitude response
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The frequency response
Suppose the FIR filter
For Type III and Type IV FIR filters, we have
In this example, the filter is a Type I FIR filter of length
7. An accurate plot of
The following Matlab code fragment for the plot of
h = [3 4 5 6 5 4 3]/30;
N = 7;
M = (N1)/2;
L = 512;
H = fft([h zeros(1,LN)]);
k = 0:L1;
W = exp(j*2*pi/L);
A = H .* W.^(M*k);
A = real(A);
figure(1)
w = [0:L1]*2*pi/(L1);
subplot(2,1,1)
plot(w/pi,abs(H))
ylabel('H(\omega) = A(\omega)')
xlabel('\omega/\pi')
subplot(2,1,2)
plot(w/pi,A)
ylabel('A(\omega)')
xlabel('\omega/\pi')
print deps type1
The command A = real(A)
removes the
imaginary part which is equal to zero to within computer
precision. Without this command, Matlab takes
A
to be a complex vector and the
following plot command will not be right.
Observe the symmetry of
The following Matlab code fragment produces a plot of
h = [3 5 6 7 7 6 5 3]/42;
N = 8;
M = (N1)/2;
L = 512;
H = fft([h zeros(1,LN)]);
k = 0:L1;
W = exp(j*2*pi/L);
A = H .* W.^(M*k);
A = real(A);
figure(1)
w = [0:L1]*2*pi/(L1);
subplot(2,1,1)
plot(w/pi,abs(H))
ylabel('H(\omega) = A(\omega)')
xlabel('\omega/\pi')
subplot(2,1,2)
plot(w/pi,A)
ylabel('A(\omega)')
xlabel('\omega/\pi')
print deps type2
The imaginary part of the amplitude is zero. Notice that
An exercise for the student: Describe how to obtain samples
of