turk@apple.UUCP (Ken "Turk" Turkowski) (11/04/86)
In article <116@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: >(2) winnie!brad (Brad Garton) writes: >> ... When I consider the digitized versions of analog >> signals we deal with over here <computer music>, it seems that we >> approximate more and more closely the analog signal with the >> digital one as we increase the sampling rate. There is a difference between sampled signals and digital signals. A digital signals is not only sampled, but is also quantized. One can have an analog sampled signal, as with CCD filters. As a practical consideration, all analog signals are band-limited. By the Sampling Theorem, there is a sampling rate at which a bandlimited signal can be perfectly reconstructed. *Increasing the sampling rate beyond this "Nyquist rate" cannot result in higher fidelity*. What can affect the fidelity, however, is the quantization of the samples: the more bits used to represent each sample, the more accurately the signal is represented. This brings us to the subject of Signal Theory. A particular class of signal that is both time- and band-limited (all real-world signals) can be represented by a linear combination of a finite number of basis functions. This is related to the dimensionality of the signal, which is approximately 2WT, where W is the bandwidth of the signal, and T is the duration of the signal. >> ... This process reminds >> me of Mandelbrot's original "How Long is the Coastline of Britain" >> article dealing with fractals. Perhaps "analog" could be thought >> of as the outer limit of some fractal set, with various "digital" >> representations being inner cutoffs. Fractals have a 1/f frequency distribution, and hence are not band-limited. >> In article <105@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: >> I'm not convinced. Common ways of transmitting analog signals all >> *do* lose at least some of the signal, irretrievably... Let's not forget noise. It is impossible to keep noise out of analog channels and signal processing, but it can be removed in digital channels and can be controlled (roundoff errors) in digital signal processing. >> ... Losses of information in processing analog signals tend to >> be worse, and for an analog transformation to be exactly invertible, it >> *must* preserve all the information in its input. Including the exclusion of noise. Once noise is introduced, the signal cannot be exactly inverted. -- Ken Turkowski @ Apple Computer, Inc., Cupertino, CA UUCP: {sun,nsc}!apple!turk CSNET: turk@Apple.CSNET ARPA: turk%Apple@csnet-relay.ARPA