Getting a perfect ifft for an input time series

Hi,

I have an input time series which needs to be converted to output time series by applying a transfer function. In order to do that, I need to do fft of my input time series, get its one sided amplitude spectrum, multiply the transfer function (frequency dependent) by it, and then get the one-sided output spectrum. Now the output spectrum needs to be converted to output time series using ifft function. However, the output I receive is not even close to what is expected.

I face two major issues:

(1) The ifft function is not doing inverse transform in the right manner. Somehow the conjugates and the complex number is making it weird

(2) Since the transfer function is multiplied by one-sided amplitude spectrum of the input, hence the output spectrum is also one-sided, which is making the output time series one-half of the length of input time series. How to resolve this?

Code:

X: input time series

L: Length of the time series

Fw: frequency dependent transfer function

One-sided spectrum is obtained using:

Y = fft(X);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L;

plot(f,P1)

title('Single-Sided Amplitude Spectrum of X(t)')

xlabel('f (Hz)')

ylabel('|P1(f)|')

% Transfer function multiplication

Outputspectrum= Fw.* P1;

Outputseries=ifft(Outputspectrum);

Can any of us please suggest in this manner?

Answer 1

[Mathieu NOE]

hello

the output spectrum must be augmented from single sided to double sided fft (make a symetrical of it and concatenate both vectors)

example below (only the output spectrum here is not affected by a transfer function)

clc
clearvars

x = randn(100,1);
N = length(x);
time = (0:N-1);


Y = fft(x,N);               % double sided fft vector

n2 = floor(N/2) + 1;        % indices for one sided fft
h=Y(1:n2);                  % one sidded fft vector
h_flipped = h(n2-1:-1:2)    % symetrical of one sidded fft vector
hh = [h ; conj(h_flipped)]; % concatenation of both vectors to re-create the double sided spectrum

acc_ifft1=ifft(Y,N);        % works fine (reference)
acc_ifft2=ifft(hh,N);       % works fine too

plot(time,x,'.-b',time,acc_ifft1,'dr',time,acc_ifft2,'*k');

[Ayushi Tiwari]

This works perfectly fine for even-valued L (when the length of the signal is even). Doesn't work for odd-length signal. Two questions also:

1. Should the transfer function be multiplied by hh here (like with the double sided spectrum or with the Y function?

2. Should the one-sided spectrum be obtained as the absolute value of Y or the absolute value of Y/L or is it fine just the way it is written?

[Ayushi Tiwari]

Transfer-function is frequency dependent!!

[Sujaan Kumar]

Any updates? Were you able to solve this?