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?

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);

Answer 1

[Star Strider]

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.

[Saiankita Anand]

Thank you so very much for the help Star Strider. The file attached below is the entire equation that I am trying to simulate and then plot as "misalignment". fb is the FIR filter and w is the adaptive filter which will estimate fb. the code below is what I am doing:

%%code
fb=fir1(50,[0.2500 0.8750]); % w is fir filter also of order 50
 %%Misalignment
FBW = @(omega) freqz(fb,1,65536);%taking fourier transform as function of frequency omega
W = @(omega) freqz(w,1,65536);

%numerator
numer1 = @(omega) (abs(FBW(omega)-W(omega))).^2;
fun=@(omega) numer1(omega);
numer=integral(fun,0,pi,'ArrayValued',true);

%denominator
denom1=@(omega) (abs(FBW(omega))).^2;
fun2=@(omega) denom1(omega);
denom=integral(fun2,0,pi,'ArrayValued',true);

%misalignment
misalignment=10*log10(numer./denom);
figure;plot(misalignment);

[Star Strider]

My pleasure.

The freqz function will not produce a function you can use to integrate with the integral function. It will produce a vector of a complex transfer function and associated frequencies that you can integrate with the cumtrapz function. (See the documentation for freqz.) That would probably produce the misalignment metric you want to calculate. The frequencies of both filters that freqz returns have to be the same.

[Saiankita Anand]

I tried with cumtrapz as you suggested. I still have a doubt.

%I am trying to simulate the equation in the file equation2.jpg
%attached above
%fb, w are FIR filters of order 50

[a1,b1]=freqz(fb,1,65536);
  [a2,b2]=freqz(w,1,65536);
  num1=abs(a1-a2).^2; %numerator in equation 2
  num2=cumtrapz(b1,num1);% integrates num1 with respect to frequency vector b1
%both frequency vectors b1 and b2 are the same

My doubt is that how can I integrate num1 with respect to b1 from 0 to pi using _ cumtrapz_. I don't see anything in the documentation about that.

[Star Strider]

I don’t understand.

Without specifying a sampling frequency (you aren’t), the default frequency vector (here ‘b1’ and ‘b2’) will be on the interval [0,pi]. Your code looks correct to me to perform the integration you want.

[Saiankita Anand]

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]

My pleasure.

The equation you posted specifically states integrating on the interval [0,pi], so your code is correct.