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z-transform of sin(w*t) - Matlab

Started by bmalp January 3, 2007
Hi,

below I have two methods to calculate the frequency response of a
z-transformed sine signal. Neither of them gives the correct amplitude -
why?

Thanks,
Bmalp

function zdemo

format compact
syms w Ts  n  z phi t

Ts  = 1
w   = 0.1
phi = 0

vz = simplify(ztrans(sin(w*n*Ts+phi)))

if 0
    [num,den] = numden(simplify(vz));
    num = collect(num,'z')
    den = collect(den,'z')
    num1 = sym2poly(num)
    den1 = sym2poly(den)
    [h,w] = freqz(num1,den1,512,'whole');
else
    fs = 1;
    f = linspace(0,fs,256); 
    w = 2*pi*f;
    ss = sqrt(-1)*w;
    Z = exp(ss/fs);
    h = double(subs(vz,z,Z));
end
plot(w,abs(h))

bmalp wrote:

> Hi, > > below I have two methods to calculate the frequency response of a > z-transformed sine signal. Neither of them gives the correct amplitude - > why?
The z-transform of a sampled sine wave has a pole pair at exp(+ / - j w0), where w0 is the frequency of the sine wave. Perhaps Matlab has difficulties returning the value Infinity? Regards, Andor
bmalp wrote:

> Hi, > > below I have two methods to calculate the frequency response of a > z-transformed sine signal. Neither of them gives the correct amplitude - > why? > > Thanks, > Bmalp >
First and foremost, because a signal cannot have a response. Systems have responses, but systems are not responses. Responses are signals, not systems. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
>First and foremost, because a signal cannot have a response. > >Systems have responses, but systems are not responses. Responses are >signals, not systems. >
By definition - yes. But generally Matlabs freqz returns the Bode plot correctly. The symbolic solution of the z-transform is correct also. So I suspect more the evaluation of the signal or "response". I will compare with a sampled signal instead of a symbolic one.