Re: [Discuss-gnuradio] resample ratio for fractional_resampler

[Yang Liu]

HI Marcus,

Thank you so much for your help!

Since there's one iteration per output sample and the number of taps of filtering is 8 (fixed), the time it takes to do one iteration is fixed no matter what resampling ratio I set. What slows things down is: as the resampling ratio increase, the number of iteration increases given a fixed number of input items. I just want to make sure I understand things correctly :)

I set the resampling ratio to be (1/67.5) at transmitter, I noticed that (1/67.5) doesn't work as good as the integer (1/64.0), does it mean fractional part will also slow things down?

Thanks,

Yang

On Mon, Oct 23, 2017 at 5:47 AM, Marcus Müller <address@hidden> wrote:

Hi Yang,

for questions of performance, it's usually best to consult the source code itself. By the way, fractional_resampler_** has been renamed mmse_resampler_** on git's "next" branch.

You'll notice the code in {mmse_|fractional_}resampler_cc_impl.cc is:

        while(oo < noutput_items) {
          out[oo++] = d_resamp->interpolate(&in[ii], d_mu);

          double s = d_mu + d_mu_inc;
          double f = floor(s);
          int incr = (int)f;
          d_mu = s - f;
          ii += incr;
        }

        consume_each(ii);
        return noutput_items;

Which means there's one iteration per output sample, invariably, no matter what your resampling ratio is.
What would increase the performance is reducing NTAPS in {mmse_|fractional_}interpolator, but since that is already only 8, which, with a bit of SIMD, your CPU does in a single instruction, I don't seem that much room for improvement there.
The other thing would be reducing NSTEPS, but it's already but a 7 bit quantization of the q in rᵣₑₛₐₘₚₗₑ = n + q, n∈ℕ₀, 0≤q∈ℚ, so I'm not convinced you'd want to do that; the jitter you get for a b bit quantization (i.e. b=log₂ NSTEPS) has a variance of (-20b log₁₀ 2-10 log₁₀ 12) dB ≈ -(6b + 10.8) dB (hoping that I do the math right). If I juggle Cauchy's mean value theorem correctly in my head, that means you basically get that (times the signal power) as the worst-case power in the phase noise introduced by the timing approximation with a critically sampled signal. If I'm right (really, haven't taken the time to write this down), then that means e.g. for NSTEPS=128, that you get -52.8 dB phase noise, whereas a reduction to let's say NSTEPS=16 gives you 24 dB more noise – and -28.8 dB phase noise isn't all that great.

What are the resampling ratios you're working with?

Best regards,
Marcus

On 2017-10-23 05:31, Yang Liu wrote:

Dear all, 

I used fractional resampler(gr::filter::fractional_resampler_cc) at transmitter side to help up sample the signal to the device sample rate before sending it out. In the experiment, I found that this resampler works well for some resample ratio (in terms of speed), and the performance (speed) doesn't necessarily improve as the resample ratio decreases.

Therefore, I am wondering whether this resampling block indeed works better for some sets of resampling ratio? If yes, what are these sets? Knowing this will help me to set the parameters at tx properly especially when the sample rate is high :)

Thanks a lot for your help.

Best, 

Yang

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