Multirate Progress

[Jay Kickliter]

Here's a notebook showing some rough multirate filter routines I've been working on. So far there's a interpolator and rational resampling. I haven't written a decimation function, but it would be similar to the other two. I should have usable stateless filtering pretty soon. I'm going to take my time with state-preserving code, since it'll require composite types. Eventually I'd like to implement arbitrary sample rate conversion, but I still don't understand it.

I'll post again when I think I have some code worthy of a pull-request to DSP.jl.

[Jay Kickliter]

I now have both one-off and stateful versions of single rate, interpolation, decimation, and rational resampling. The hardest part was getting stateful resampling working the I wanted it. I didn't want the user to have to think about the size of the data they are feeding the filters. If you feed one of the filters a single sample, and it doesn't have enough to calculate a new input, it will store the sample in the delay line. Or if you feed enough samples to return some results, but it still has some samples leftover, it will store those leftovers in the delay line until you call it again.

I'm not totally happy withe all my design choices. Currently, I have the state preserving version of filt calling the stateless functions decimate, interpolate, and resample. In order to get some of them to work that way, I had to add arguments indicating what x index to start at, the initial phase of the filter bank, and the delay line. I think I should do the reverse, where if you call a filtering operation without filter object, one is created in the background. There is a little overhead for very short filter lengths, but it is probably insignificant for long input vectors. There a bunch of early design choices that I now realize weren't great, so I'll be fixing those.

Here's an example of the rational resampler:

julia> ratio = 3//5;

julia> h = [1.0:9.0];

julia> x = [1.0:20.0];

julia> resampler = FIRFilter( h, ratio )
FIRFilter{FIRRational}(FIRRational(3x3 Array{Float64,2}:
 1.0  2.0  3.0
 4.0  5.0  6.0
 7.0  8.0  9.0,3//5,1),[0.0,0.0],2)

julia> filt( resampler, x[1:1] )
1-element Array{Float64,1}:
 1.0

julia> filt( resampler, x[2:2] )
1-element Array{Float64,1}:
 12.0

julia> filt( resampler, x[3:3] )
0-element Array{Float64,1}

julia> filt( resampler, x[4:4] )
1-element Array{Float64,1}:
 39.0

julia> filt( resampler, x[5:9] )
3-element Array{Float64,1}:
  54.0
 102.0
 114.0

julia> filt( resampler, x[10:end] )
6-element Array{Float64,1}:
 114.0
 192.0
 189.0
 174.0
 282.0
 264.0