#### Envelope Compression

Once we have our data in the form of amplitude and frequency envelopes for each filter-bank channel, we can compress them by a large factor. If there are channels, we nominally expect to be able to downsample by a factor of , as discussed initially in Chapter 9 and more extensively in Chapter 11.In early computer music [97,186], amplitude and frequency envelopes were ``downsampled'' by means of

*piecewise linear approximation*. That is, a set of

*breakpoints*were defined in time between which linear segments were used. These breakpoints correspond to ``knot points'' in the context of polynomial spline interpolation [286]. Piecewise linear approximation yielded large compression ratios for relatively steady tonal signals.

^{G.10}For example, compression ratios of 100:1 were not uncommon for isolated ``toots'' on tonal orchestral instruments [97]. A more straightforward method is to simply downsample each envelope by some factor. Since each subband is bandlimited to the channel bandwidth, we expect a downsampling factor on the order of the number of channels in the filter bank. Using a hop size in the STFT results in downsampling by the factor (as discussed in §9.8). If channels are downsampled by , then the total number of samples coming out of the filter bank equals the number of samples going into the filter bank. This may be called

*critical downsampling*, which is invariably used in filter banks for

*audio compression*, as discussed further in Chapter 11. A benefit of converting a signal to critically sampled filter-bank form is that bits can be allocated based on the amount of energy in each subband relative to the psychoacoustic masking threshold in that band. Bit-allocation is typically different for tonal and noise signals in a band [113,25,16].

**Next Section:**

Vocoder-Based Additive-Synthesis Limitations

**Previous Section:**

Frequency Envelopes