Re: Real-data DFT in Octave

[Torbjörn Rathsman]

Sergei Steshenko skrev 2012-10-06 20:06:
> ----- Original Message -----
> > From: Torbjörn Rathsman <address@hidden>
> > To: Sergei Steshenko <address@hidden>
> > Cc:
> > Sent: Saturday, October 6, 2012 7:36 PM
> > Subject: Re: Real-data DFT in Octave
> [snip]
> > I get imaginary part that is in the same order of magnitude as the real
> > part. Note: my N is odd, but that should only result in a discarded
> > sample or?
> For odd N you do the following:
>
> 1) leave (N+1)/2 frequency bin intact;
> 2) take the first (N-1)/2 frequency bins and mirror them around (N+1)/2 
> frequency bin.
>
> In such a manner nothing is lost/discarded, everything is mathematically 
> strictly invertible.
>
> E.g. for N=5 you have in Octave terms:
>
> 1 2 3 2' 1'
>
> where "'" means complex conjugate; since '1' is DC 1' == 1, but who cares, i.e. 
> it's easier to write mirroring not taking this into account - complex conjugate of a real 
> component is still the same real.
>
> Regards,
>    Sergei.
Even N also gives me wrong result.

    Y=fft(y);
    length(y) %31047
    Y=Y(1:floor(length(Y)/2));
    length(Y) %15523
    for k=1:length(Y)
        if(k<=1024)
            Y(k)=(k-1)*(k-1)*Y(k)/N; %diffrentiate twice
        else
            Y(k)=0;
        end
    end
    Y=[Y; conj(flipud(Y))];
    y=ifft(y);
    plot(real(y),imag(y));

reim.png
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