Normal
Re: FIR filtersOne way to think of it is that the OLA and OLS convolution methods - links above - aren't really frequency domain methods. They just exploit properties of the Fourier transform (and it's fast implementation, the FFT) to reduce the number of multiplies it takes to compute the convolution. Direct convolution costs ~N multiplies per sample, where N is the FIR filter length. OLA and OLS transform methods take roughly log2(N) multiplies per sample. For a 512 length FIR, that's 512 multiplies per sample versus ~9 multiplies. For a processor (and ignoring parallel operations) that's about 25 mega cycles per second versus ~0.5 mega cps (and versus ~0.25 mega cps for a biquad) - all for ~48 kHz audio. (Adds and memory moves move these numbers around a bit but they're roughly in the ball park.)As for examples of using transforms for convolution in audio, many convolutional reverbs use them, as does some signal processing in TV's, AVR's, portable devices....Cheers,----Edit: Numbers corrected above.
Re: FIR filters
One way to think of it is that the OLA and OLS convolution methods - links above - aren't really frequency domain methods. They just exploit properties of the Fourier transform (and it's fast implementation, the FFT) to reduce the number of multiplies it takes to compute the convolution. Direct convolution costs ~N multiplies per sample, where N is the FIR filter length. OLA and OLS transform methods take roughly log2(N) multiplies per sample. For a 512 length FIR, that's 512 multiplies per sample versus ~9 multiplies. For a processor (and ignoring parallel operations) that's about 25 mega cycles per second versus ~0.5 mega cps (and versus ~0.25 mega cps for a biquad) - all for ~48 kHz audio. (Adds and memory moves move these numbers around a bit but they're roughly in the ball park.)
As for examples of using transforms for convolution in audio, many convolutional reverbs use them, as does some signal processing in TV's, AVR's, portable devices....
Cheers,
----
Edit: Numbers corrected above.
