how can i integrate an array with respect to frequency w (omega)? the command "integral" requires function 'fun' to be declared as function of omega. how can i do this?

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Saiankita Anand
Saiankita Anand 2016-6-26
评论： Star Strider 2016-6-30
FB and W are frequency responses of two FIR filters fb and w. This is essentially what I am doing:
numer1=(abs(FBW-W)).^2; fun=@(omega) numer1; numer=integral(fun,0,pi,'ArrayValued',true);

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Star Strider
Star Strider 2016-6-26
What you believe you’re doing is not what you’re actually doing.
I’m just guessing here because I don’t have either ‘FB’ or ‘W’:
FBW = @(omega) ... SOMETHING ...;
W = @(omega) ... SOMETHING ELSE ...;
numer1 = @(omega) (abs(FBW(omega)-W(omega))).^2;
fun=@(omega) numer1(omega);
numer=integral(fun,0,pi,'ArrayValued',true);
Also, squaring abs is redundant (unless the argument is complex), because the square will be positive.
NOTE — This is obviously UNTESTED CODE. You may have to experiment with it to get it to work in your application.
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Saiankita Anand
Saiankita Anand 2016-6-30
Thank you, Star Strider. You were right. I went back to the documentation of freqz and realized that the frequency vector it returns is in radians/sample and that the frequencies are b/w 0 and pi. My sampling frequency is 16 kHz here but I reckon there is no need for it in this snippet of code as I want to integrate wrt to omega from 0 to pi. Appreciate your help.
Star Strider
Star Strider 2016-6-30
My pleasure.
The equation you posted specifically states integrating on the interval [0,pi], so your code is correct.

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