Eric Niebler wrote:
Anyway, from Wikipedia, I see that convolution is "the integral of the product of the two functions after one is reversed and shifted." Seems straightforward. There already is a shift adapter. I could add a reverse adapter.
If you add a reversed adapter then you can implement convolution and correlation (correlation is the same algorithm without the reversal) in terms of the same primitives. To apply an arbitrary filter (such as the sinc filter mentioned by Janek) you simply convolve a time series consisting of the values of the function (truncated) with the original series. When decimating you obviously only need to evaluate the result at the output rate, not for every sample point at the input rate. The sinc filter is a good choice for decimation because it is the (truncated) time series representation of a "brick wall" filter (ie a hard cutoff in the frequency domain). As many filters of interest are symmetrical, you don't actually need the reverse step anyway.
(Reversed relative to what time t? Should it be a parameter to the adapter?)
I don't think the origin of the reversal belongs in reverse. For the decimation or smoothing filters you want to have 0 delay so you would construct your filter sequence to be symmetrical about t=0. A way to apply a time offset to an existing sequence would seem like a reasonable thing to have (and be trivial to implement as an adapter I would think).
Series multiplication is already implemented, as is an integrate() function. So maybe it's almost already there.
The multiply and integrate can/should be combined and optimized as multiply-accumulate. It seems you have something very close to a good set of primitives already. A few examples of how to combine/use them (especially if those examples actually provided needed functionality like decimation and interpolation) would help a lot I think. Regards Darryl.