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[Y, Zf] = FILTER(A, B, X, Zi) is a very fundamental function. Therefore I assumed that it is implemented efficiently.
The function FILTFILT (filter in forward and reverse direction to get a zero phase shift) splits input matrices to vectors and call itself recursively, although the underlying FILTER can handle matrices as input directly. Therefore I've written a patch for FILTFILT, which enables the direct processing of matrices. In addition the initial and final phase for reducing edge effects are calculated separately instead of joining the artificial signals to the original data. This reduces the used temporary memory and I got a 25% to 90% faster version using only standard Matlab methods.
Finally reverting the signal two times was the bottleneck and I've implemented a naive direct form II transposed filter (as described in "doc filter"), which works in reverse direction. To my deep surprise it was about 3 times faster than Matlab's built-in FILTER function.
Using this and avoiding the reversing of the signal my new FILTFILT is 5 to 25 times faster than the original.
I did not apply any SSE or assembler tricks, just some loop-unrolling for small parameter vectors. I did not omit the necessary checks for the inputs, of course. The output equals the original function exactly.
Therefore I do not have the faintest idea why the original FILTER can run so much slower. Has it been created as M-code and converted by the old compiler to run even on 386 processors?!
However, I tested it with Matlab until 2009a only. FILTER of 2011a has been multi-threaded (in opposite to my function) - has it been accelerated by factor 3 for vectors also? I'd be very happy if a user of a modern Matlab version could post a speed comparison:
In addition I decided to use DOUBLEs for the internal accumulators in case of input (and output) in SINGLE format. This is not remarkably slower, but more accurate than FILTER, which seems to use SINGLEs internally. Especially for filters with a high order the additional stability is important - but the results are slightly different to Matlab's FILTER due to the reduction of rounding errors.
I will encourage the TMW team to brush-up the core functions, if they are time-consuming.
Sorry for the self-advertisment. My implementations are naive, such that they cannot make me proud. I'd be really glad if the filtering in 2011a is faster (most of all I could save the time for building a multi-threaded version!). Otherwise this function might be helpful for others to save time...
Kind regards, Jan
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