Re: [Discuss-gnuradio] Frequency discriminator using a frequency to voltage converter

[Daniele Nicolodi]

On 06/11/15 19:01, madengr wrote:
> Marcus Müller-3 wrote
>> Hi Lou,
>>
>> that's a pretty good application of the spectrum, I agree. One could
>> certainly modify the freq_sink to do that, however, as it is now, the
>> PSD calculation (based on the fft result) is done in a single VOLK
>> kernel, 32fc_s32f_x2_power_spectral_density_32, which probably has some
>> performance advantages, so changing that would mean to either abandon
>> that benefit or introduce a new "processing path" inside the frequency
>> sink.
>>
>> I'm a bit confused, though: The DFT is a linear operation. So averaging
>> k FFT vectors (linear operation) before or after the DFT wouldn't make a
>> difference, because
>>
>> $\sum_{n=1}^k \mathrm{DFT}(x_n) = \mathrm{DFT}(\sum_{n=1}^k x_n)$, with
>> $x_n$ being our DFT length-sized input sample vectors.
>>
>> You should be able to do $\sum_{n=1}^k x_n$ with a stream to vector->add
>> block combination in front of the normal frequency sink.
>
> Hmm.. maybe it is.  I have done it in (shudder) LabView and it's nice since
> noise reduces at 1/N instead of 1/sqrt(N); N is number of averages.  Maybe
> I'll try it tonight with just discrete blocks to compare them side by side. 
> Just something that can't be done with a normal spectrum analyzer.

Why does that hold true?

I don't think it is possible, at least in the general case.

Cheers,
Daniele