全通滤波器对声音的影响

Effects of All-Pass Filtering on Speech
One area in which digital signal processing has enjoyed widespread use is in the field of speech processing. In this project, we consider issues relating to applying digital filtering to speech. Specifically, we consider the effect of all-pass filtering on speech.
A common “folk theorem ” states that the ear is insensitive to phase, i.e., that for audio, phase distortion is inaudible. If that is correct, then processing audio with an all-pass filter should not result in perceived distortion. This project tests this conjecture. The all-pass filter that we consider is of the form
()()()()()611306111011N
N k k k k k k k k k k k z e z e b z H z e z e z a z -*--=-*--==⎡⎤⎡⎤--⎢⎥⎢⎥==--⎢⎥⎢⎥⎣⎦⎣⎦∑∏∑ The data file project.mat will need to be first loaded into MATLAB. Then you copy it into your MATLAB working directory and type load project. The k b and k a coefficients are stored in the variables b and a respectively. (Note that ()1k b k b +=, and ()1k a k a +=.)
a) Implement the all-pass filter for 1N = and show plots of the impulse response
(the first 100 samples), the magnitude of the frequency response, and the group delay.
b) Plot the pole-zero diagram.
c) Process the speech file, stored as the variable speech (sampled at rate fs =
11025Hz), using the command filter to run the filter implemented in a). Listen to the result and comment specifically on whether there is audible distortion. (You may need to use the function sound to play the speech data back to sound ).
d) Implement the filter for 50N = and again show plots of the impulse response
(the first 5000 samples), the magnitude of the frequency response, and the group delay.
e) Repeat c). In your report, comment specifically on how you would subjectively
describe the distortion and on what aspect of the filter is it ’s primary cause.
Code ：
load project
N=input('input the N:=');
if N~=1
a1=a;
b1=b;
for k=2:N
b1=conv(b1,b);
a1=conv(a1,a);
end
end
figure
if N~=50
[h1,t1]=impz(b1,a1,100);
stem(t1,h1);
title(' impulse response (the first 100 samples)');
xlabel('n');
ylabel('Magnitude');
grid
else
[h1,t1]=impz(b1,a1,5000);
stem(t1,h1);
title(' impulse response (the first 5000 samples)');
xlabel('n');
ylabel('Magnitude');
grid
end
figure
[h2,w2]=freqz(b1,a1);
plot(w2/pi,20*log10(abs(h2)));
title('the magnitude of the frequency response');
xlabel('\omega/\pi');
ylabel('Magnitude/dB');
grid;
figure
[gd3,w3]=grpdelay(b1,a1,100);
plot(w3/pi,gd3);
title('the group delay');
xlabel('\omega/\pi');
ylabel('Group delay(100 samples)');
grid;
figure
zplane(b1,a1);
title(' the pole-zero diagram');
grid
y=filter(b,a,speech);
sound(y,fs);
a)
input the N:=1
The impulse response:
the magnitude of the frequency response:
The group delay:
b) the pole-zero diagram:
c)
运行project.m，input the N:=1; d)
input the N:= 50
the impulse response :
The magnitude of the frequency response:
The group delay:。