How do I calculate frequency response of multi-stage CIC interpolation filter?

Here is the code, two stages differetiator, and two stage integrator.
It's very common but how do I plot the frequency response?

TIA!


d = cos(2*pi*(1:1e3)/1e2);
e = zeros(length(d)*10, 1);

db = [1 0 -1];
da = [1];

c0 = filter(db, da, d);
c1 = filter(db, da, c0);

ib = [1];
ia = [1 -1];

e(1:10:end) = c1;

c2 = filter(ib, ia, e);
c3 = filter(ib, ia, c2)/10/10;

figure;
subplot(2,1,1); plot(d);
subplot(2,1,2); plot(c3);

Matlab's "fvtool" should do the job for any z-domain filter.
If you have multiple stages, use conv() to multiply numerators and
denominators of several stages into one.

-mn

"mnentwig" <mnentwig@elisanet.fi> wrote in message 
news:pOudneiwrNay8mfbnZ2dnUVZ_qelnZ2d@giganews.com...
> Matlab's "fvtool" should do the job for any z-domain filter.
> If you have multiple stages, use conv() to multiply numerators and
> denominators of several stages into one.
>
> -mn

Thank you I was aware of conv and multi stage filter in fixed sampling rate.
But in CIC interpolation, the sampling rate is not fixed, so I am not sure 
how
to use conv/freqz stuff to plot it.

Right...
I think you can write out the whole chain at the highest sampling rate
(i.e. insert all zero samples at the input, space out filter coefficients
of each stage according to the rate, and carry all decimated samples to
the output).
At least I believe that's the approach I have used occasionally.

Maybe someone else can comment?

-mn

On Wed, 26 Sep 2007 22:24:29 +0800, "G Iveco" <G.Iveco@google.com>
wrote:

>Here is the code, two stages differetiator, and two stage integrator.
>It's very common but how do I plot the frequency response?
>
>TIA!
>
>
>d = cos(2*pi*(1:1e3)/1e2);
>e = zeros(length(d)*10, 1);
>
>db = [1 0 -1];
>da = [1];
>
>c0 = filter(db, da, d);
>c1 = filter(db, da, c0);
>
>ib = [1];
>ia = [1 -1];
>
>e(1:10:end) = c1;
>
>c2 = filter(ib, ia, e);
>c3 = filter(ib, ia, c2)/10/10;
>
>figure;
>subplot(2,1,1); plot(d);
>subplot(2,1,2); plot(c3);

Hi,
  how about this:

B = [1, 0, 0, 0, 0, 0, -1]; A = [1, -1]; %  CIC filter coeffs
[ImpResp1, T] = impz(B, A, 20); % Single CIC imp. resp.
ImpResp2 = conv(ImpResp1, ImpResp1); % Two-stage CIC imp. resp.

[FreqResp1, W] = freqz(ImpResp1, 1, 512);
FreqMagResp1 = abs(FreqResp1);
[FreqResp2, W] = freqz(ImpResp2, 1, 512);
FreqMagResp2 = abs(FreqResp2);

figure(1)
subplot(3,1,1)
plot(ImpResp1, '-bo')
grid on, zoom on
subplot(3,1,2)
plot(ImpResp2, '-ro')
grid on, zoom on

subplot(3,1,3)
plot(FreqMagResp1, '-b')
hold on
plot(FreqMagResp2, '-r')
hold off, grid on, zoom on

G Iveco,
The DC gain of the first CIC filter is 6.
The DC gain of two cascaded CIC filters is 36.

Good Luck,
[-Rick-]