Re: Real-data DFT in Octave

[Torbjörn Rathsman]

Doug Stewart skrev 2012-10-06 19:08:

On Sat, Oct 6, 2012 at 12:50 PM, Sergei Steshenko <address@hidden> wrote:

----- 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.

>
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To help us understand each other, I have a question.

Do you understand that the N/2 up to N results from the FFT are really the negative frequency results?

--

DAS

https://linuxcounter.net/user/206392.html

Yes. And for real input it is exacly the same but cojugated. FFTW claims that it can improve performance by taking advantage of this property: http://www.fftw.org/fftw3_doc/One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data