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## [Discuss-gnuradio] Re: Resampling in the frequency domain

 From: Alberto di Bene Subject: [Discuss-gnuradio] Re: Resampling in the frequency domain Date: Sat, 19 Feb 2005 17:08:11 +0100 User-agent: Mozilla Thunderbird 1.0 (Windows/20041206)

```Bob,

thanks for your answer. Yes, what you say is quite clear. So you suggest
to do the downsampling in the time domain, after the IFFT. I had hoped that
```
limiting somehow the portion of the spectrum given as input to the IFFT, after the circular shift and the lowpass filtering, this would result in an automatic
```downsampling. Isn't this the technique used in Linrad ?   TNX.

Alberto
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Robert McGwier wrote:

```
```Alberto:

Glad to know you are here.

I would not revert to the time domain.  "Rename" the complex
bins of your fft by performing a simple circular shift until
the right bin is on zero.  Apply the low pass filter in the
frequency domain,  IFFT and then downsample.  Since these
frequencies or bins are discrete, you might need to retune
BUT this can now be done on the decimated signal.

REMEMBER,  fft is a circular convolution.  So if you use
a N tap filter, you will probably want to use an
roof(log_2(N))+1 long FFT and then do overlap save or
add to turn it into a linear convolution.

If this was not clear, please say so.

Cheers,
Bob

-----Original Message-----
Of Alberto di Bene
Sent: Saturday, February 19, 2005 3:13 PM
Subject: [Discuss-gnuradio] Resampling in the frequency domain

A question for all the DSP gurus lurking here.
Suppose I have the spectrum of a signal, obtained via an FFT, and
I want to isolate a portion of it, bring it to baseband and downsample it.
The first idea that comes to mind is to do it in the time domain, first
multiplying the signal by a complex exponential, then lowpass it,
then decimate it.
Would it be possible to simply translate the spectrum by the needed
amount (thus bringing the wanted portion at baseband) and then resample
it so to have a lower sampling rate when the signal is brought back into
the time domain? It looks doable, but I am sure there are issues to
be taken into account (aliasing? windowing? etc.).
Which are the caveats in doing such a process which looks on paper much
faster than working in the time domain?   Thanks in advance.

Alberto

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