[Discuss-gnuradio] Rational Resampler

[Robert McGwier]

The rational resampler is functional and has been checked in by Eric.  I 
learned a valuable lesson which I will pass on.  Like everyone who does 
a lot of different coding these days,  the first place to go is to 
Google for the time saving code.  Julius O. Smith of CCRMA did a very 
good study of resampling technology and shared code.  
http://ccrma.stanford.edu/~jos/resample/resample.html

Rather than doing the smart thing  for the required Kaiser window 
derived filter, I used the "top of the list" kaiser window calculation 
code.  I have subsequently discovered, after Matt and I confirmed that 
it is hosed,  that it was taken directly (without attribution by the 
way) from Numerical Recipes.  JUST SAY NO.  Their modified bessel 
function of order zero is broken.  In JOS pages on this, he points to 
code for  his resampling code and in it, he uses the recursion relation 
and allows it to proceed iteratively until the update is very small.  
The Kaiser window derived filters now look spectacular.  We chose to 
have a fixed "Beta" allowing for the first lobe to be 50 dB down from 
the "main lobe" in the frequency response of the Kaiser window. 

Do not be alarmed by the huge size of the FIR filter designed if, for 
example,  you have a 32000 or 48000 sample per second input and you 
chose to output 11025 samples per second.  The size of the filter is 
determined by number of taps at the output frequency if the default 
filter is 0.4 cutoff and 0.5 being Nyquist.  The closer you push the 
cutoff towards Nyquist, the longer it will get.  Let's take the exampler 
of 48000 and 11025 as the input and output sample rates respectively.  
The lcm of 48000 and 11025 is 7056000 so the first step is to 
interpolate up by 147 times and then decimate by 640.  So the filter 
will be about huge for this.  However, the amount of computational load 
is the on the order of the decimation of the filter.  HOWEVER:  You will 
have a problem with this code if you have a cache free machine.  The 
Sempron and the Celeron are not great signal processing chips because of 
their cache challenged state!

This is round one of this.  Enjoy.

Bob

--
Laziness is the number one inspiration for ingenuity.  Guilty as charged!