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))

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

Started by ●January 3, 2007

Reply by ●January 3, 20072007-01-03

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

Reply by ●January 3, 20072007-01-03

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

Reply by ●January 3, 20072007-01-03

>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.