jj@alice.UUCP (01/24/85)
>A perfect sine wave could be recovered if sampled at 2X plus epsilon, >but this would require a perfect filter. (Sampling at exactly 2X won't >work, for example, all the samples might be zero.) Well, the now infamous theorem you refer to talks about "information", and a continuous sine wave doesn't have any information. Now, then, if you CHANGE the amplitude, you introduce information (such as if you start it and stop it, and then the RINGING of the filter, if it's good enough, will introduce the CORRECT information into the A/D <Hard to believe, but true...> >... >the reconstruction filters on playback, but these filters have a less >difficult role, especially on players with two DACs where the digital >waveform before filtering is a staircase and not a collection of pulses. Now, hooooold on here, what DOES the staircase vs. pulse do? What it does is change the shape of the signal's spectrum, both in band and out of band. If you have nearly a pulse you have a flat signal in-band. If you DON'T have a pulse, but rather a staircase, you DO have less aliasing energy, BUT you also have a 4dB drop in signal level at Fs/2, which has to be compensated for (it's called sin(x)/x compensation, not too surprisingly) in the filter. THIS makes the filter more complex (!) because you have to put emphasis in the filter, and then go from the emphasized part to the fastest rolloff. Since a response of x/sin(x) isn't easily realized, you also have considerable phase distortion introduced. Of course, you CAN correct the phase, and add MORE filter stages... >The advantage of digital filters is primarily one of implementation; the >critical parameters of the steep filter can be implemented more precisely. >In addition it is possible to build linear-phase digital filters, but these >may not be the answer since they have amplitude ripple in the passband. Analog filters of the sort that are sharp enough to be used for anti-aliasing filters have ripple in the passband, too. Look at any cauer elliptic function and see. In fact, the passband and stopband are equiripple, which is necessary for the most effective filter. (The PB and SB do NOT have the same MAGNITUDE of ripple in either the linear phase or FIR implementation. That's also normal and expected and true of all kinds...) The ONLY difference when using oversampling is that THEN you can use a good analog filter, too, and have no significant phase problems. (everything reduces to a delay, equal in both channels) It works better, both in theory, and to my ear. >As long as theoretical arguments are going to be applied where practical >arguments should be used, consider this: the only causal signal which is >bandlimited is the zero signal. Such a signal could be processed perfectly >by a digital recorder, but would only be useful to reproduce a single piece >of music (by John Cage). Oh, spare me the emotional rhetoric, will you. Your statement regarding bandlimiting is true, your statement about "theoretical" is mere prejudice. > Tony Lauck > > ...decvax!decwrl!rhea!bergil!lauck sigh, back to the textbooks, please. -- TEDDY BEARS PROTECT PENGUINS FROM WALRUSES "I wish I was home again, back home in my heart again, it's been such a time since my heart's home to me. ..." (allegra,harpo,ulysses)!alice!jj