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From: tom@syssoft.com (Rodentia)
Newsgroups: comp.dsp
Subject: Re: 48k to 44.1k sample rate conversion
Message-ID: <1991May29.204046.12494@syssoft.com>
Date: 29 May 91 20:40:46 GMT
References: <5826@media-lab.media.mit.edu.MEDIA.MIT.EDU> <457@valid.valid.com> <42200@ucbvax.BERKELEY.EDU> <498@valid.valid.com> <42250@ucbvax.BERKELEY.EDU> <502@valid.valid.com>
Reply-To: tom@syssoft.com (Rodentia)
Organization: Systems & Software, Inc., Irvine, CA
Lines: 44

I have been following this discussion for some time, and I have a few 
comments and questions.  Warning:  I am not a DSP engineer by trade, but 
I suspect there are many readers with my level of expertise.

1)  How bad is interpolation?  Clearly, the signal probably did not look
    like the linear interpolation of the samples (I know, look is not
    important; hear or dB is), but it seems to be a "reasonable" 
    approximation.  Roughly how much dB or % distortion is added?
    I have read here that a linear interpolation is a special form of
    low pass filter.  Is its problem that it doesn't have high or band
    pass characteristics as well?

2)  How good is digital filtering?  Does the filtered signal actually 
    include the sample points, or can the filter turn a V into a U 
    (imagine a U that doesn't go down as far) at a high frequency 
    area?  Is this considered distortion or just a loss of amplitude
    (that can be compensated by rescaling)?

3)  It appears that a filters instantaneous response is based on its
    current internal state (charge on the capacitors, etc.) and the
    input signal.  It seems that it should be possible to construct
    equations that continuously reflect the output of a filter between
    samples.  It also seems that these equations would be exponential 
    or perhaps 2nd-order or greater.

    I know that this would involve more complex math and perhaps numeric
    errors (underflow, etc.), but it seems to have the advantage of 
    generating only those samples needed (as opposed to a high i
    intermediate frequency).  Has anyone compared this more mathematical
    approach to the current number-crunching mac (multipy-accumulate)
    approach?  Is the theoretical distortion any different?  Are computers
    just so much better at the simpler math (with the increased possibilty
    of pipelining) that the more mathematical approach has been discarded  
    for the time being?

Sorry if that dragged on a bit.  Please respond by followup as I truly
believe this to be of interest, for historical reasons if nothing else
(you see, I have reinvented some of the greatest solutions to problems
of all times, and this is probably just another of them ;-{) ).
-- 
Thomas Roden                                      | tom@syssoft.com
Systems and Software, Inc.                        | Voice: (714) 833-1700 x454 
"If the Beagle had sailed here, Darwin would have | FAX:   (714) 833-1900
come up with a different theory altogether." - me |