Re: Can a LPF have linear phase when the impuse response is not symmetric?

DBD wrote:
On Mar 30, 5:31 pm, Rick Lyons <R.Lyons@xxxxxxxxxxxxxxx> wrote:





On Sat, 29 Mar 2008 10:45:29 -0700 (PDT), dbd <d...@xxxxxxxx> wrote:

  (Snipped by Lyons)

What is broken is your substitution of "exhibit symmetry I can see"
for the possession symmetry. The symmetries you have learned to  "see"
at this point are symmetries about a sample point or a point half-way
between samples. But a uniform sampling (satisfying Nyquist) of a
symmetric waveform is still symmetric. You just haven't learned to
"see" these symmetries. The set you know and have learned to "see" as
symmetric doesn't span the concept.

As Wil Rogers once said, "The problem isn't what we don't know so much
as what we know that ain't so."

Dale B Dalrymple
Hi Dale,
  Are you saying that if we use the sequence
represented by the dots in Figure 5-35(c) as
the coefficients of a tapped-delay line FIR
filter, that this filter will have linear phase?

[-Rick-]

I don't see a 5-35(c) so let me say it another way.

I suggest that if you want to associate 'symmetry' with linear phase
it might be convenient to consider any -sequence- that samples a
symmetric continuous waveform sufficiently to reconstruct the
symmetric waveform to be 'symmetric' whether the samples themselves
are symmetric or not.

That's true - this phenomena explains the causal, linear-phase IIR
filters.

However, for FIR filters with real coefficients, symmetry or anti-
symmetry are necessary and sufficient for the filter to have linear
phase response. Summing a symmetric and an anti-symmetric FIR filter
does not lead to a linear-phase response (except for a delay, wich is
symmetric and anti-symmetric), as you suggested in this thread.

Regards,
Andor
.

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