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## Main Question or Discussion Point

Hi,

I try to visualize a sine wave, z-transformed in a Bode plot. The frequency shows up correctly, but the amplitude is way off - why?

Thanks for your comments.

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))) % correct

if 0 % method 1

[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 % method 2

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)) % amplitude way too big

I try to visualize a sine wave, z-transformed in a Bode plot. The frequency shows up correctly, but the amplitude is way off - why?

Thanks for your comments.

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))) % correct

if 0 % method 1

[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 % method 2

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)) % amplitude way too big