Thread Subject: ifft from fft (Retrieving signal from a fourier transform using ifft)

I am trying to retrieve the signal back from an fft. According to the
help files, ifft(fft(S)) should yield the signal S, with some rounding
error. I have tried this numerous times, and get back a time series
not even remotely resembling the original time series. The ifft is
also yielding complex numbers as part of the time series, which were
never part of the original signal. I have tried using the ifft only
on the first have of the mirror fft spectrum, but this didn't correct
the problem. Am I missing a step, or is this a bug in the ifft
routine? Please help.

Hi Dru

    The IFFT and FFT should work fine at restoring the SAMPLED signal.

 » y=rand(2^8,1);
» yy=ifft(fft(y));
» max_real_err = max(abs(real(y-yy)))

max_real_err =

  7.4420e-016

» max_imag_err = max(abs(imag(y-yy)))

max_imag_err =

  1.9255e-016

» mean(y)

ans =

    0.4913


Compared to the average value around 0.5 the error above is only a couple
of bits out of the 53 mantissa bits that an IEEE double gives.

To kill the small imaginary part, just do

yy=real(ifft(fft(y)));


I don't know why your restored signal doesn't look like your original
SAMPLED signal. If you are comparing, an UN-sampled version of your
original signal with the restored version, then you may be seeing apparent
differences due to aliasing. However, the restored signal should still
agree with the SAMPLED signal even if aliasing occured.

Andy Bartlett

The trick is to plot the real part:

N = 200; %Number of samples
fs = 10; %Sampling rate
a = [1 .25]; %Amplitudes
f = [.05 ; 5]; %Frequencies
t = (0:N-1)/fs; %Time base
x = a*cos(2*pi*f*t); %Signal without noise
subplot(211);
plot(t,x);
subplot(212)
X = real(ifft(fft(x)));
plot(t,X)

Happy New Year!

--Jad

dru shockley (dru22@mindspring.com) wrote:
: I am trying to retrieve the signal back from an fft. According to the
: help files, ifft(fft(S)) should yield the signal S, with some rounding
: error. I have tried this numerous times, and get back a time series
: not even remotely resembling the original time series. The ifft is
: also yielding complex numbers as part of the time series, which were
: never part of the original signal. I have tried using the ifft only
: on the first have of the mirror fft spectrum, but this didn't correct
: the problem. Am I missing a step, or is this a bug in the ifft
: routine? Please help.

dru22@mindspring.com (dru shockley) wrote in message <34aa967c.7313103@news.mindspring.com>...
> I am trying to retrieve the signal back from an fft. According to the
> help files, ifft(fft(S)) should yield the signal S, with some rounding
> error. I have tried this numerous times, and get back a time series
> not even remotely resembling the original time series. The ifft is
> also yielding complex numbers as part of the time series, which were
> never part of the original signal. I have tried using the ifft only
> on the first have of the mirror fft spectrum, but this didn't correct
> the problem. Am I missing a step, or is this a bug in the ifft
> routine? Please help.

hi...
I am using matlab for first time. I want to retrieve back my original time domain signal using ifft and then plot it. Plotting is neglecting the small imaginary part, how can I avoid this and plot this imaginary part together?

Dipasree Som wrote:

> I am using matlab for first time. I want to retrieve back my original
> time domain signal using ifft and then plot it. Plotting is neglecting
> the small imaginary part, how can I avoid this and plot this imaginary
> part together?

plot(x,real(y),'r',x,imag(y),'g')

timesignal = sin(1:100);
freqsignal = fft(timesignal);
rectimesignal = real(ifft(freqsignal));
here time signal and rectimesignal are same.....

On Aug 1, 10:53 am, "Dipasree Som" <somdip...@gmail.com> wrote:
> hi...
> I am using matlab for first time. I want to retrieve back my original time domain signal using ifft and then plot it. Plotting is neglecting the small imaginary part, how can I avoid this and plot this imaginary part together?

In general, you could use a polar plot

figure
plot(x,'o')
xlabel('Real Part')
ylabel('Imaginary Part')

However, in this case you need different scales

figure
subplot(211)
plot(real(x))
subplot(212)
plot(imag(x))

I'll let you provide the details

Hope this helps.

Greg

On Aug 1, 1:34 pm, "Senthil " <senthilponku...@yahoo.co.in> wrote:
> timesignal  = sin(1:100);
> freqsignal = fft(timesignal);
> rectimesignal = real(ifft(freqsignal));
> here time signal and rectimesignal are same.....

No they aren't:

x = sin(1:100);
X = fft(x);
recx = real(ifft(X));

% In the context of this thread, recx and x
% are NOT the same.....

err = recx-x;
minmaxerr = minmax(err)

>>
minmaxerr =

 -5.8287e-016 5.5511e-016

Hope this helps.

Greg