Re: Real-data DFT in Octave

[Sergei Steshenko]

----- Original Message -----
> From: Torbjörn Rathsman <address@hidden>
> To: Sergei Steshenko <address@hidden>
> Cc: "address@hidden" <address@hidden>
> Sent: Saturday, October 6, 2012 5:28 PM
> Subject: Re: Real-data DFT in Octave
> 
> Sergei Steshenko skrev 2012-10-06 15:35:
>> 
>> 
>> 
>>  ----- Original Message -----
>>>  From: Torbjörn Rathsman <address@hidden>
>>>  To: address@hidden
>>>  Cc:
>>>  Sent: Saturday, October 6, 2012 3:18 PM
>>>  Subject: Real-data DFT in Octave
>>> 
>>>  Is it possible to without much effort call the real to complex dft 
> routins from
>>>  octave. It is easier to manipulate the spectrum that way, since i am 
> guarantied
>>>  that the mirror part becomes correct. The purpose in this case is to 
> compute
>>>  filtered derivative of second order.
>>>  _______________________________________________
>>>  Help-octave mailing list
>>>  address@hidden
>>>  https://mailman.cae.wisc.edu/listinfo/help-octave
>> 
>>  I am not sure what the problem is, but dealing with real input data I use 
> 'conj' and 'fliplr' in the end when I need to produce mirrored 
> spoectrum for inverse FFT.
>> 
>>  Regards,
>>     Sergei.
>> 
>> 
> Do you mean
> 
>     Y=fft(y)';
>     for k=1:length(Y)
>         if(k<=1024)
>             Y(k)=(k-1)*(k-1)*Y(k)/N;
>         else
>             Y(k)=0;
>         end
>     end
> 
>     Y=Y+conj( fliplr(Y) );
> ? cannot get it work.


Let's for simplicity assume N is even and let's assume 'signal' is 1:N real 
vector. Let's also assume 'filter' is 1:N/2 complex vector. Then:

spectrum = fft(signal);
filtered_spectrum = spectrum(1:N/2) .* filter;
filtered_signal = real(ifft([filtered_spectrum 
conj(fliplr(filtered_spectrum))]));

- the above is the idiom I'm using everywhere for real input signals.

Regards,
  Sergei.







>