Hi all,

Suppose my signal is a complex valued signal, and it is complex conjugated 
with respect to the center t=0.

That's to say f(-t)=f(t)*, where "*" denotes the complex conjugate.

Suppose now I do the truncation of above signal into between [-B, B),

and I sample it using stepsize dB,

then in Matlab, the sampling points are cfs=[-B:dB:B-dB],

which has 2B/dB data points, e.g. -B, -B+dB, -B+2*dB, ... , 0, dB, 2*dB, ... 
B-dB.

Let's assume 2B is divisable by dB.

I found out that I have to do fftshift(cfs) before feeding into fft 
function, then I will obtain my desired output:

so,

output = fft(fftshift(cfs)),

and the output are all real numbers. This is our desired output.

Now I want to ask: is there some trick in FFT that I can use to further 
reduce computations?

Let's say, since my output is going to be real, and my input is complex 
conjugate, is there a way to throw away the real part, and only do the FFT 
on the real part, or something like that? I saw somewhere on the web that 
there is a special program for real input and real output FFT which can be 
even faster than a standard complex FFT.

Moreover, my input is complex conjugate, is there a way that I can throw 
away the f(t)'s for t<0, and thus only do fft on half of the orginal data 
sequence?

Thanks a lot! 

<SNIP>
> Suppose my signal is a complex valued signal, and it is 
complex conjugated 
> with respect to the center t=0.
> 
> and the output are all real numbers. This is our desired 
output.
> 
> Now I want to ask: is there some trick in FFT that I can 
use to further 
> reduce computations?

Probably! 

What you seem to be saying is that The real part of your 
signal is even, and the imaginary part is odd, so when you 
transfer it into the frequency domain, you get a real only 
spectrum.

Suppose you multiply your next signal by -i (-j) so this 
will have an odd real part, and a even imaginary part, then 
add this to your first signal (fft is a linear process). 
Passing the summed signal into the FFT you will end up 
doing exactly the same calculation that you did before, but 
now the spectrum you will get out will be complex - but 
note that the real component will be the spectrum of signal 
1 and the imaginary part will be the spectrum of signal 2 
(albeit multiplied by -i (-j)) So you will now be able to 
almost double the performance of your algorithm.

Hope that this is of some help.

Regards

Dave Robinson

On Aug 9, 4:34 am, "Dave Robinson" <dave.robin...@somewhere.biz>
wrote:
> <SNIP>
>
> > Suppose my signal is a complex valued signal, and it is
> complex conjugated
> > with respect to the center t=0.
>
> > and the output are all real numbers. This is our desired
> output.
>
> > Now I want to ask: is there some trick in FFT that I can
> use to further
> > reduce computations?
>
> Probably!
>
> What you seem to be saying is that The real part of your
> signal is even, and the imaginary part is odd, so when you
> transfer it into the frequency domain, you get a real only
> spectrum.
>
> Suppose you multiply your next signal by -i (-j) so this
> will have an odd real part, and a even imaginary part, then
> add this to your first signal (fft is a linear process).
> Passing the summed signal into the FFT you will end up
> doing exactly the same calculation that you did before, but
> now the spectrum you will get out will be complex - but
> note that the real component will be the spectrum of signal
> 1 and the imaginary part will be the spectrum of signal 2
> (albeit multiplied by -i (-j)) So you will now be able to
> almost double the performance of your algorithm.
>
> Hope that this is of some help.
>
> Regards
>
> Dave Robinson

Thanks Dave....I don't see how does it double my performance?

> Thanks Dave....I don't see how does it double my 
performance?
> 

Lets say you are currently doing a 1024 point complex FFT
it takes time t to calculate it to generate your answer.

What I am suggesting is that you take two of these 
waveforms and add them together via the complex 
manipulation I told you about. You still have a 1024 point 
waveform that you FFT, but instead of getting a real answer 
you get a complex answer in which the real part is the 
spectrum of signal 1 and the imaginary part is spectrum 2; 
still in time t.

So you are getting 2 signals calculated in the same time 
(nearly) that it previously took to do 1.

Sounds mighty close to doubling your performance to me.

Mark you I guess the method, as it stands is no good if you 
only have one waveform.

Regards

Dave Robinson

Regards

Dave Robinson