[TangerineSDR] Question on bandwidth versus sample rate: can they be independently set?

[Scotty Cowling]

Hi Bill,

To answer your first questions first...

The reason that we have to run multiple channels at the same sample rate 
is due to the fact that we are interleaving multiple virtual receivers' 
data in the same packet. Although theoretically we *could* interleave 
them at different rates, Digital RF would probably not like it.

However, we have the capability to create multiple single-receiver data 
streams (maybe not in phase 1), and these would not have to be related 
in any way (sample rate or bandwidth).

The frequency precision or resolution bandwidth is related to the number 
of bins and the time interval. If you want 10 milli-hertz resolution, 
you must sample for 100 seconds (1/0.010Hz=100sec). The sample rate will 
determine the length your FFT needs to be. If you are over-sampling at 
122.88Msps and want 10 milli-Hertz resolution bandwidth, you must still 
sample for 100 seconds. Thus you would need an FFT of length 
100*122.88*10^6, which is kind of long. :-) Of course, you would get 
12,288,000,000 bins, each 10milli-Hz wide. You would then use the 10 or 
20 bins centered on 2.5MHz to determine WWV's doppler shift, throwing 
away the other 12,287,999,980 frequency bins

It makes more sense to filter and decimate to something more reasonable, 
like 10sps (+/- 5Hz) and do an FFT of length 1000 to get 1000 bins of 10 
milli-Hz each. Especially since filtering to a 5Hz bandwidth without 
decimating is exceptionally hard. Reducing the bandwidth with combined 
filtering and decimation is a common technique for DSP, which may be why 
you often see sample rates and filter bandwidths track.

Think of it this way. If I give you 48ksps sample rate, do you really 
want more than 48kHz of bandwidth? Anything above 48kHz of bandwidth 
will alias back into your baseband. I could give you less (say 24kHz), 
but then why not reduce the sample rate to 24kHz and reduce the load on 
your DSP code running on the PC/SBC?

So to answer your first question, yes, we can arrange it so the you can 
independently set the sample rate and bandwidth, but I don't see much 
reason to do it, and in extreme cases it makes the filtering difficult 
inside the FPGA.

To answer your second question, yes, the way Tom describes it is exactly 
how the FPGA will process the raw data before sending it to you.  All we 
have to do is to make sure that we support the sampling rates that you 
require. If you need +/- 5Hz, then we will do it. In many ways, lower 
sampling rates are easier to implement. They certainly take up less 
bandwidth on the wire than sending over full bandwidth data. :-)

9 virtual receivers at 10sps won't take up very much bandwidth. Even a 
RPi might be able to do 9 FFTs of 1024 samples each in a reasonable 
amount of time. If not, then maybe you would have to develop the 
algorithm to do the calculations in the time domain.

Hope that this makes some sense, along with Tom's excellent explanation.

73,
Scotty WA2DFI


On 4/14/2020 12:50 PM, Engelke, Bill wrote:
> Tom – thanks for the analysis on that.  (I must admit, I will have to study this a bit to really grasp it)…
> But now, let me pose a couple of questions for Scotty & Nathaniel –
>
>
>    *   Scotty – could we enable the DE to be able to do what Tom describes below?
>    *   Nathaniel – regarding the precision & sample rate – for science results, is this the right trade-off between precision and how often we get a sample?  Or is there another, better way to do it?
>
> -73- Bill, AB4EJ
>
> From: Tom McDermott <tom.n5eg at gmail.com>
> Sent: Tuesday, April 14, 2020 1:27 PM
> To: TAPR TangerineSDR Modular Software Defined Radio <tangerinesdr at lists.tapr.org>
> Cc: Engelke, Bill <bill.engelke at ua.edu>
> Subject: Re: [TangerineSDR] Question on bandwidth versus sample rate: can they be independently set?
>
> Hi Bill - generally the bandwidth and sample rate are locked together.  The Nyquist criteria is that the
> sample rate be at least twice the highest frequency component.  When using I+Q samples, we are able
> to distinguish negative from positive frequencies, so the range of usable frequencies goes from
>   -fsamp/2 to +fsamp/2.    Nyquist means that in theory no information is discarded at lower than half the sample
> rate ** - even very fractional Hertz stuff is in there and can be recovered, but it might take a long time.
>
> As an example:
> In order to receive a 10 Hertz wide spectrum slice (+/- 5 Hz) the receiver would need to first
> lowpass filter the signal to < 5 Hz. (i.e. from -5 to +5) then decimate and change the sample rate, then send those to you.
> You could then for example implement a Complex FFT of size=1024.  This would yield bin sizes of
> 10 / 1024,  or 9.8 milliHertz.   Beware however that at a 10 Hz sample rate, that FFT process needs 102.4 seconds worth
> of data per FFT.
>
> Does this clarify?
>
> -- Tom, N5EG
>
> ** Except that due to imperfect LPF filter roll-off, ADC quantization, etc.
>
>
>
> On Tue, Apr 14, 2020 at 10:17 AM Engelke, Bill via TangerineSDR <tangerinesdr at lists.tapr.org<mailto:tangerinesdr at lists.tapr.org>> wrote:
> This question is sort of directed to Scotty, but I am posting it here because I’m sure others will have useful thoughts on this matter.
>
> As you may recall, in TangerineSDR when we collect IQ data for multiple channels, we have to run them all at the same sample rate (at least, for Phase 1). The main reason for this is that Digital RF is optimized for handling data that way, and we need to roll with that rather than struggle against it, so that we can have something ready and tested in the time frame. We can add more complexity later if we want.
>
> I am puzzling over something, however – probably because I still have a lot to learn about digital signal processing.  The frequency precision of an FFT is related to the number of bins (i.e., when I do the FFT with 2048 samples, I get more precision than if I do it with 1024 samples). In several conversations, the sample rate and the bandwidth have been almost interchangeable; however, is that mandatory?
>
> Specifically, let’s say that I want to closely watch the carrier frequency of WWV at 10 MHz.   We know that the most it moves due to doppler shift is a fraction of a Hz, so I only want to handle a few Hz of bandwidth – but I want to do it to a precision of 0.01 Hz.  This precision would seem to dictate a very high sample rate, but the bandwidth I want to process is only 2 to 3 Hz.
>
> The QUESTION then is this:  when configuring the channels for the DE to run, is it feasible for me to be able to independently set the sample rate and bandwidth?   If so, is there a major downside to doing this?
>
> -73- Bill AB4EJ
> --
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