Re: FIR Filter limitation (or not?)

rover8898 wrote: 
Hello,


It's not the digital filters -- it's the digitizing process of an
analog signal what requires this filtering;  it's not always done
with analog signals;  some times it's easier to sample the signal
at a far higher rate, then apply a digital low-pass filter, and
then "sample" the resulting signal  (since it is already in the
digital domain, we're talking simply about keeping one every N
samples, or "downsample" by a factor of N)



The filtering can be done with a [oversampling at higher sample rate] +
[digital low pass filter] +[downsampling] scheme, I guess. But if the
input signal (prior to A/D) has frequency components beyond the
[oversampling rate/2] threshold, then there will aliasing, digital
lowpass filter or not. Is there a reason why a precautionary ~broad
analog filter cannot be placed ahead of the A/D (aside from cost and
maybe gadget size)  ?


The technique of sampling at a much higher frequency and then do
a low-pass digital filtering does not replace the analog filter;
it just makes the analog filter trivial -- if you know that your
signal has valuable spectral contents up to 20 kHz and want to
sample at 44.1 kHz, the analog filter required would have to be
very precise and very "wall-like" -- it would be quite hard to
design an analog filter with such a "wall" frequency response
and without truly ugly phase distorsion (mostly at frequencies
near the cutoff).

So, instead, if you sample at, say, 8 times the intended rate
(i.e., at 8 x 44.1 kHz), then a very simple, perhaps first-
order RC filter with cutoff at 50 kHz would do a more-than-
excellent job, since now you only need to worry to eliminate
frequencies above 4x44.1, or approx. 170 kHz -- that's trivial,
since the RC already has a good attenuation at that point,
and also, the audio signal really has very low contents at
those ultra-high frequencies.

The part that you really were worried about -- a wall-like
cutoff above 20 but below 22, that you get with a digital
filter with nice phase response.

Notice, however, that I'm not describing a universal technique
that is applied unconditionally in every design -- it's just
that it may be very practical and easy, so you do encounter it
quite often -- for speech, for instance, where you want a
sampling rate of 8 kHz (typically), it's quite easy to do the
sampling at a higher rate and then bring it down after it is
in the digital domain.

HTH,

Carlos
--
.

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