How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?

Question

I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect.

I've been reading up on partitioned convolution reverb, and it seems to operate on the principle that you just accumulate samples until you have enough to convolve a short block of the impulse while the rest of the input comes in, getting bigger and bigger every chunk. How does this work if I can only start working on the input once it's all accumulated? How do convolution reverb plugins in DAWs work with this limitation (buffer sizes are usually lower, but never single-sample)?

For example, my impulse is 16384 samples long. I partition it into 480 + 32, then 480 + 64, 480 + 128, 480 + 256 (rounded up to 1024), etc. All the partitions add up to a length longer than it would have been if I'd just done 16384 + 480 samples (rounded up to 32768).

In my specific case, the source audio is a sample being played back at variable speed so I guess I could apply the reverb as each sample is being added to the buffer or even bake the reverb if I don't mind the room characteristics shifting with the pitch, but I'd like to understand how others do it first.

Answer 1

This is typically done using a segmented overlap add method or sometimes also refered to as a block convolver.

Let's assume your block size if 512 (makes the numbers a little easier).

1. Chop up your impulse response into 32 blocks of 512 samples each. Zero pad each block to 1024 samples and FFT. You know have 32 filters $H_0(z) ... H_{31}(z)$
2. On each new input block: zero pad to 1024 samples and FFT. Keep the most recent 32 signal spectra around, so you have $X_N(z), X_{N-1}, ... X_{N-31}(z)$
3. Multiply the spectra and sum them, $Y(z) = \sum_{k=0}^{31} H_k(z) \cdot X_{N-k}(z)$
4. Inverse FFT the result: you get 1024 time samples. The last 512 are the "overlap". Store for the next block.
5. Take the first 512 samples of your inverse FFT and add the overlap from the previous block. That's your output.

Repeat steps 2-5 for each new block.