Resampling with small integer ratios can be pretty staightforward, like a rate change of 3/2, upsample by 3 -> LPF -> dec by 2. However, it's not as simple when it's a ratio of large integers or some arbitrary new sample rate. I started to read this document on resampling: http://ccrma-www.stanford.edu/~jos/resample/ Is this how others are implementing (in hardware), resampling for these cases? Multiplying the input samples with a windowed, weighted sinc at the new sample frequency? Thanks for any insights, Brady

# Resampling irrational or large rational ratios?

Started by ●July 8, 2005

Reply by ●July 8, 20052005-07-08

<bgaughan@airnetcom.com> wrote in message news:1120851001.817454.131680@g14g2000cwa.googlegroups.com...> Resampling with small integer ratios can be pretty staightforward, like > > a rate change of 3/2, upsample by 3 -> LPF -> dec by 2. However, it's > not as simple when it's a ratio of large integers or some arbitrary new > > sample rate. > > I started to read this document on resampling: > http://ccrma-www.stanford.edu/~jos/resample/ > > Is this how others are implementing (in hardware), resampling for these > cases? Multiplying the input samples with a windowed, weighted sinc at > the new sample frequency? > > Thanks for any insights, > Brady >Hello Brady, Yes, the basic synopsis (in the above link) is essentially correct. The difficulty with sinc() interpolation is the requirement of trying to perfectly interpolate all the way up to one half of the sampling rate. If your system has any oversampling at all, then more efficient interpolation functions may be used. The sinc() function has assymptoticly 1/x tails which provide for very slow convergence. If you remember your calculus, the error in summing an alternating series (1st n terms) is less than the magnitude of the 1st omitted term. Think about how many terms are needed to achieve 90 dB of signal to noise! Window functions, such as Kaiser (adjustable) feature tails with faster than 1/x rolloff and are still nearly flat in the passband. Some have even used Hermite polys for interpolation. It just depends on the required accuracy. Since most look (resampling in the signal processing world with discrete signals) at interpolation errors in the frequency domain, the window methods provide a very simple means to which to bound your interpolation errors. Of course with human perception, tolerance levels of interpolation errors may be a little hard to quantify. But you can always overkill it a bit. IHTH, Clay

Reply by ●July 11, 20052005-07-11

Sorry, Brady. I expected that you'd get a lot more answers here on comp.dsp than you did on comp.arch.fpga. But I guess most people are on vacation or something. Greg Berchin

Reply by ●July 11, 20052005-07-11

bgaughan@airnetcom.com wrote:> > Resampling with small integer ratios can be pretty staightforward, like > > a rate change of 3/2, upsample by 3 -> LPF -> dec by 2. However, it's > not as simple when it's a ratio of large integers or some arbitrary new > > sample rate. > > I started to read this document on resampling: > http://ccrma-www.stanford.edu/~jos/resample/ > > Is this how others are implementing (in hardware), resampling for these > cases? Multiplying the input samples with a windowed, weighted sinc at > the new sample frequency?Sorry, missed this post first time round. I'm not really an exprt on resampling on hardware, but from memory, the technique people use in hardware is called the Farrow interpolator. The advantage of the Farrow technique over JOS's technique is that it uses a much smaller table of coefficients. Erik -- +-----------------------------------------------------------+ Erik de Castro Lopo nospam@mega-nerd.com (Yes it's valid) +-----------------------------------------------------------+ "Hey, I've re-dorkulated." -- Prof. Frink (The Simpsons)