On 16/07/2015, Peter S <peter.schoffhau...@gmail.com> wrote: > Quantization, interpolation and other numerical errors > will add a slight uncertainity to your entropy estimate; in practice, > things are very rarely "exact".
Another view at looking at this - for any real-world signal, there is typically some noise in the signal. When it is not dithered, there's quantization error, resulting in quantization noise. When it is dithered, there's noise from the dithering. When you interpolate it, there is error from the interpolation, and possibly noise from the numerical errors. When the signal is sampled from analog, then there's a noise floor from the A/D converter, the microphone, or whatever equipment was used to produce it. So whatever the real-world sampled periodic signal is, irregardless of how it was derived, unless the cycle length is integer, periods will not be bit-by-bit identical, but rather, have some small noise and error with a certain distribution. So irregardless of method, the measured entropy will never reach zero (unless it's special corner case), because these various forms of noise will always add some slight level of unpredictability to the signal. Dither noise and the noise floor of an A/D converter or a microphone are fully uncorrelated, so those will always add some unpredictability and thus (perceived) entropy to the signal, even when it's fully periodic. Quantization noise is not trivial to model either. Hence, unless it is a constant signal, measured entropy will typically never be zero, as there is almost always some slight "noise" in a sampled signal. -P -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
