Amplitude scaling applying fft of iddata object

When I compute fft of a signal manually, I get amplitudes of the signal correct, but if I create an iddata object and compute fft(iddata), then the amplitudes are somehow scaled. Does anyone know to get the correctly scaled amplitudes using fft(iddata)?

Here an example:

freq=100; %Hz
Period=1/freq;
Ts = 0.05*Period;             % Sampling time
Fs = 1/Ts;            % Sampling frequency
t=0:Ts:11*Period;
t(end)=[];
L = length(t);             % Length of signal
S=10+cos(2*pi*freq*t+44/180*pi); % signal generation
figure
plot(t,S)
hold on
xlabel('t (s)')
ylabel('S(t)')

Computing fft() of the signal I get amplitudes 10 @0 Hz and 1 @100 Hz, which perfectly matches with the generated signal:

Y = fft(S);
P2=Y/L;
P1=P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
figure
subplot(211)
plot(f,abs(P1))
title('Single-Sided Amplitude Spectrum of S(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')
grid on
subplot(212)
plot(f,angle(P1)/pi*180)
title('Phase S(t)')
xlabel('f (Hz)')
ylabel('Angle (deg)')
grid on

Using the iddata object, I get different amplitudes ~148 @0 Hz and ~7.42 @100 Hz:

data=iddata(S(:),[],Ts);
figure
plot(fft(data))

Answer 1

[Soumya]

Hi @Alexander Avdonin,

When the ‘fft’ function is applied to a time domain ‘iddata’ object, the FFTs are normalized by dividing each transform by the square root of the signal length to preserve the signal power and noise level. As a result, the amplitude values obtained using ‘fft(iddata)’ differ from those produced by the standard ‘fft’ function. If you want the amplitudes to match those calculated using the ‘fft’ function, extract the signal from the ‘iddata’ object and then apply the ‘fft’:

extractData = data.OutputData; 

Y = fft(extractData); 

The following documentation provides more information on ‘iddata’ object and its properties:

• https://www.mathworks.com/help/ident/ref/iddata.html
• https://www.mathworks.com/help/ident/ref/iddata.fft.html

I hope this helps!