Decimation

h1. Summary of results

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h2. What we're looking at

Here we're only looking at causal methods, so no forward/backward filtering. The question in my head is really whether faster IIR filters are still so much faster as to be worth using in preference to linear-phase methods with better (?) theoretical quality. Of course that would always depend on the application, but it's interesting to compare. 

We compared

 * @decimate@: the "Decimator":http://code.soundsoftware.ac.uk/projects/qm-dsp/embedded/classDecimator.html implementation in the "qm-dsp":/projects/qm-dsp library, which uses an IIR lowpass filter (perhaps an elliptical filter?) with 8 coefficient pairs;

 * @decimate_b@: the "DecimatorB":http://code.soundsoftware.ac.uk/projects/qm-dsp/embedded/classDecimatorB.html class in the "qm-dsp":/projects/qm-dsp library, which uses a Butterworth IIR lowpass filter of order 6;

 * @resample_hq@, @resample_mq@, @resample_lq@: the "Resampler":http://code.soundsoftware.ac.uk/projects/qm-dsp/embedded/classResampler.html implementation in the "qm-dsp":/projects/qm-dsp library, which uses a lengthy Kaiser-windowed sinc filter, at three different quality settings;

 * @src@: the sndfile-resample program which uses "libsamplerate":http://mega-nerd.com/SRC/, a well trusted resampler also using a Kaiser-windowed sinc implementation, at its default quality setting;

 * @zoh@: the sndfile-resample zero-order hold resampler, which just takes every Nth sample without any filtering, serving as a baseline.

h2. Speed

For 5292000 input frames on a Core i3-3229Y low-voltage CPU. (Frames-per-second values are for input frames.)

All code is 64-bit. The qm-dsp implementations (resample_* and decimate) were compiled with -O3 -ffast-math while the libsamplerate implementations (src and zoh) were standard Ubuntu packages, so probably -O2. This is likely to make a very significant difference, so these results are more useful for comparison among the qm-dsp implementations than between qm-dsp and libsamplerate.

The decimate implementation supports factors up to 8 only, so 16x, 32x and 64x are handled in two passes.

All implementations use libsndfile for audio file I/O, so that should not be a factor in overall speed.

These frames-per-second figures look terribly precise, but I imagine there's a good 10% margin of error (run to run or whatever).

h3. Implementations by decimation factor

For 11520000 input frames.

h4. Factor 02

|Kfps|Clock time|Implementation|

|      61604|0.187|zoh|

|      52602|0.219|decimate_b|

|      52363|0.220|decimate|

|      17668|0.652|resample_lq|

|       9365|1.230|resample_mq|

|       4768|2.416|resample_hq|

|       2176|5.294|src|

h4. Factor 04

|Kfps|Clock time|Implementation|

|      93658|0.123|zoh|

|      58181|0.198|decimate|

|      47213|0.244|decimate_b|

|      19896|0.579|resample_lq|

|       9982|1.154|resample_mq|

|       4965|2.320|resample_hq|

|       2292|5.026|src|

h4. Factor 08

|Kfps|Clock time|Implementation|

|     128000|0.090|zoh|

|      60952|0.189|decimate|

|      44651|0.258|decimate_b|

|      21215|0.543|resample_lq|

|      10331|1.115|resample_mq|

|       3480|3.310|resample_hq|

|       2361|4.879|src|

h4. Factor 16

|Kfps|Clock time|Implementation|

|     160000|0.072|zoh|

|      46080|0.250|decimate|

|      43636|0.264|decimate_b|

|      22068|0.522|resample_lq|

|       7700|1.496|resample_mq|

|       3529|3.264|resample_hq|

|       2119|5.435|src|

h4. Factor 32

|Kfps|Clock time|Implementation|

|     182857|0.063|zoh|

|      53333|0.216|decimate|

|      42825|0.269|decimate_b|

|      21021|0.548|resample_lq|

|       7379|1.561|resample_mq|

|       3443|3.345|resample_hq|

|       2179|5.286|src|

h4. Factor 64

|Kfps|Clock time|Implementation|

|     188852|0.061|zoh|

|      53581|0.215|decimate|

|      42666|0.270|decimate_b|

|      16202|0.711|resample_lq|

|       7417|1.553|resample_mq|

|       3489|3.301|resample_hq|

|       2423|4.753|src|

h3. Decimation factors by implementation

For 11520000 input frames.

h4. Implementation zoh

|Kfps|Clock time|Factor|

|     188852|0.061|64|

|     182857|0.063|32|

|     160000|0.072|16|

|     128000|0.090|08|

|      93658|0.123|04|

|      61604|0.187|02|

h4. Implementation decimate

|Kfps|Clock time|Factor|

|      60952|0.189|08|

|      58181|0.198|04|

|      53581|0.215|64|

|      53333|0.216|32|

|      52363|0.220|02|

|      46080|0.250|16|

h4. Implementation decimate_b

|Kfps|Clock time|Factor|

|      52602|0.219|02|

|      47213|0.244|04|

|      44651|0.258|08|

|      43636|0.264|16|

|      42825|0.269|32|

|      42666|0.270|64|

h4. Implementation resample_hq

|Kfps|Clock time|Factor|

|       4965|2.320|04|

|       4768|2.416|02|

|       3529|3.264|16|

|       3489|3.301|64|

|       3480|3.310|08|

|       3443|3.345|32|

h4. Implementation resample_mq

|Kfps|Clock time|Factor|

|      10331|1.115|08|

|       9982|1.154|04|

|       9365|1.230|02|

|       7700|1.496|16|

|       7417|1.553|64|

|       7379|1.561|32|

h4. Implementation resample_lq

|Kfps|Clock time|Factor|

|      22068|0.522|16|

|      21215|0.543|08|

|      21021|0.548|32|

|      19896|0.579|04|

|      17668|0.652|02|

|      16202|0.711|64|

h4. Implementation src

|Kfps|Clock time|Factor|

|       2423|4.753|64|

|       2361|4.879|08|

|       2292|5.026|04|

|       2179|5.286|32|

|       2176|5.294|02|

|       2119|5.435|16|

h3. Resampler filter lengths

Filter lengths the qm-dsp Resamplers decided to use:

|Factor|Length (hq)|Length (mq)|Length (lq)|

|2|643|291|119|

|4|1285|579|237|

|8|2567|1155|471|

|16|5131|2307|939|

|32|10261|4613|1877|

|64|20519|9223|3751|