The latency, or delay, through the PHL depends on several interrelated parameters. This post shows how latency is affected by changing the configuration of a typical multiband compressor based on Short Term Fourier Transform (STFT) using overlapp and add processing. The ‘simple-compressor.cfg’ program used in other posts is the starting point for the examples here.
As described in the documentation for the overlapadd plugin, the signal is windowed then usually zero padded before going through the FFT. The window is advanced by fragment size and the process is repeated.
M: Window size
N: FFT size
P: Frag size
The delay due to the signal processing is then
M + (N-M)/2
In addition to this delay, there is a significant delay associated with the data buffering of the Linux operating system.
In terms of practical implementations, there are some general constraints:
- The window size M is usually a multiple of the frag size P (P=2*M, P=4*M, etc.)
- Zero padding is necessary to prevent aliasing in practical systems. This means N>M, and the length of the zero padding limits the length of the impulse response of the effective filter formed by different band gains.
- The length of the FFT can affect its computational efficiency. It doesn’t need to be a power of two, but it’s probably best to keep it a product of small prime numbers. For example, 2^5 * 3 = 96.
- At a certain point the CPU will run out of cycles when the configuration as a whole proves too much. Sampling rate, fragment size, FFT size and overall algorithm complexity all play a role here.
- And of course, a smaller FFT size results in less frequency resolution for a given sample rate (given the usual zero padding caveats). This may or may not be much of an issue, depending on how your bands are structured.
Delay examples
The delay through the PHL was measured for different parameter configurations and the results are shown below. The electronic measurement used a soundcard to generate an impulse that was routed through the PHL using the Line input/output connectors. All of these configurations used the same sampling rate, 24kHz, for ease of comparison.
| M | N | P | Delay | |
|---|---|---|---|---|
| 1 | 128 | 256 | 64 | 13ms |
| 2 | 64 | 128 | 32 | 7ms |
| 3 | 48 | 96 | 24 | 6ms |
| 4* | 110 | 162 | 55 | 10ms |
Example 1 uses the parameters in the original ‘simple-compressor.cfg’ program. Examples 2 and 3 show how the delay decreases as the FFT size and corresponding parameters are made smaller. Example 4* was measured using the default hearing aid program that comes installed on the PHL.
Example 3 was also attempted using a sampling rate of 32kHz and the measured delay was 4.5ms, but the processor couldn’t keep up and this caused a very audible sporadic clicking.