> With a double band (256 points undersampling), the final signal is
> coherent with attempted one. The fact is that I kept the whole useful
> signal (that is the 128 first & last points of my 16384pts FFTsignal),
> instead of 1 point out of 2.
> But I don't understand why this does not work with 128 points
> however....(is there an explanation?)
The 128 non-zero bins at each end of the large FFT represent positive
and negative aspects of 128 frequencies. For proper sampling, you need
to sample twice as fast as the highest of those. That works out to a
sample for each bin -- positive and negative -- of the result. Fewer
samples wouldn't have enough information to determine the values of 256
bins.
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by bastide●December 13, 20062006-12-13
With a double band (256 points undersampling), the final signal is
coherent with attempted one. The fact is that I kept the whole useful
signal (that is the 128 first & last points of my 16384pts FFTsignal),
instead of 1 point out of 2.
But I don't understand why this does not work with 128 points
however....(is there an explanation?)
Thanks for your answer Jerry
Bast.
Jerry Avins a =E9crit :
> bastide wrote:
> > Hello,
> >
> > I have a problem with my fftw complex transform (1d) when I want to
> > undersample my signal.
> > I start with initial signal (Dimension 16384points), and get the FFT of
> > this signal in complex with fftw_plan_dft_1d (result is a 16384points
> > dimension too). This signal has 128 first non-zero values and last 128
> > points non zero values. Between, all is close to 0 (10e-15).
> >
> > I want to undersample this signal, and get only 128 points in useful
> > signal (get only 1 point of 2 within 128 first points and 128 last)).
> > The FFT-1 of this 128-undersampled signal is is uncoherent with the
> > initial one. I attempted to get the same shape that my 16384pts initial
> > signal.
> >
> > Is that a physical problem (I've heard about Shannon law) or a bug in
> > fftw ?
> > How can I get a coherent undersampled 128pts-signal ?
>
> If I understand what you're doing, the first and last points represent
> positive and negative frequencies. Your signal seems to have no higher
> frequencies. If that is indeed the case, then you can sample at a lower
> rate. 256 samples taken over the same time should suffice.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
> Hello,
>
> I have a problem with my fftw complex transform (1d) when I want to
> undersample my signal.
> I start with initial signal (Dimension 16384points), and get the FFT of
> this signal in complex with fftw_plan_dft_1d (result is a 16384points
> dimension too). This signal has 128 first non-zero values and last 128
> points non zero values. Between, all is close to 0 (10e-15).
>
> I want to undersample this signal, and get only 128 points in useful
> signal (get only 1 point of 2 within 128 first points and 128 last)).
> The FFT-1 of this 128-undersampled signal is is uncoherent with the
> initial one. I attempted to get the same shape that my 16384pts initial
> signal.
>
> Is that a physical problem (I've heard about Shannon law) or a bug in
> fftw ?
> How can I get a coherent undersampled 128pts-signal ?
If I understand what you're doing, the first and last points represent
positive and negative frequencies. Your signal seems to have no higher
frequencies. If that is indeed the case, then you can sample at a lower
rate. 256 samples taken over the same time should suffice.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by bastide●December 12, 20062006-12-12
Hello,
I have a problem with my fftw complex transform (1d) when I want to
undersample my signal.
I start with initial signal (Dimension 16384points), and get the FFT of
this signal in complex with fftw_plan_dft_1d (result is a 16384points
dimension too). This signal has 128 first non-zero values and last 128
points non zero values. Between, all is close to 0 (10e-15).
I want to undersample this signal, and get only 128 points in useful
signal (get only 1 point of 2 within 128 first points and 128 last)).
The FFT-1 of this 128-undersampled signal is is uncoherent with the
initial one. I attempted to get the same shape that my 16384pts initial
signal.
Is that a physical problem (I've heard about Shannon law) or a bug in
fftw ?
How can I get a coherent undersampled 128pts-signal ?
Thanks in advance
B.