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From: whit@milton.u.washington.edu (John Whitmore)
Newsgroups: sci.electronics
Subject: Re: ..but what about _output_ filtering for D/A's?
Summary: It's pretty standard filtering (like in all the books)...
Keywords: D/A, filter
Message-ID: <9284@milton.u.washington.edu>
Date: 15 Oct 90 21:44:34 GMT
References: <1319@beguine.UUCP>
Organization: University of Washington, Seattle
Lines: 49

In article <1319@beguine.UUCP> Jeff.Miller@samba.acs.unc.edu (Jeff Miller) writes:

>Of course the first thing any treatment of digital audio and A/D converters
>geos into is the Nyquist frequency and the crucial need for effective input
>filtering to avoid aliasing. That I've got covered.
> 
>But I don't recall any treatment of the need and mathematics of filtering
>the output of a D/A converter. I would imagine at CD or DAT frequencies
>it wouldn't be too critical as any harmonics would be ultrasonic (or would
>they? 

	Yes, they'd be ultrasonic, BUT that doesn't mean the sound
reproducing equipment will ignore them.  A classic problem arose when
the early FM tuners were connected to tape recorders; the harmonics
of the (19 kHz?) stereo pilot signal beat against the (circa 60 kHz)
record bias oscillator to generate a horrendous howl (which wavered
because the bias oscillator frequency wasn't terribly stable).

>And  I've always wondered: can two ultrasonic sounds or an ultrasonic
>and audible sound beat to create an audible tone?

	Obviously, yes.
> but at lower frequencies,
>I would think that aproximating a sine wave with stepped squares would sound
>bad. 

	For this reason, many top-end CD players mask the low-amplitude
'warble' that a low-amplitude signal becomes when played back on a
digital system (the problem here is that there's 96 dB signal/noise
for LOUD signals, but a quiet passage, 80 dB down from the peak
power in a given opus, will only have 16 dB signal/noise).  Typical
treatment is to mask the artifact with some pink noise (yes, there
are noise generators in good CD players).
>
> Would mathematically interpolating a few output
>levels between each input sample help, and deos that technique have a name
>I should look out for?

	A generalized interpolation scheme is to consider each point in
time to be a linear combination of the nearby sampled points; this
is called a Finite Impulse Response filter (FIR).  Such a scheme
is a filter because it can be chosen (by twiddling the coefficients)
to generate zero output amplitude of the first harmonic interval
(which is called a '2X oversampling digital filter'), or of the
first two harmonic intervals ('4X oversampling digital filter').
	These so-called 'digital filters' are a hot topic; I don't
know, offhand, what would be a good reference. 

		John Whitmore