Re: Real-data DFT in Octave

[Torbjörn Rathsman]

Sergei Steshenko skrev 2012-10-06 20:47:
> ----- Original Message -----
> > From: Torbjörn Rathsman <address@hidden>
> > To: Sergei Steshenko <address@hidden>; "address@hidden" <address@hidden>
> > Cc:
> > Sent: Saturday, October 6, 2012 8:25 PM
> > Subject: Re: Real-data DFT in Octave
> >
> > 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));
>
> What are you trying to achieve ? If you have spectrum, why won't use it to 
> calculate derivative ?
>
>
> Regards,
>    Sergei.
I am trying to apply a filter that is k*k for k<1024 which is somewhat 
equivalent to diffrentiate the input twice for low frequencies. Also I 
want to get rid of high frequency noise. However, the filter does not work

Now y is of even length:

    Y=fft(y);
    length(y)
    Y=Y(1:floor(length(Y)/2));
    length(Y)

    Y=[Y; conj(flipud(Y))];
    y=ifft(Y); %I missed capital Y here but
    plot(real(y),imag(y)); %still huge imaginary part.

reim.png
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