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

On Mar 31, 4:27 am, Greg Berchin <gberc...@xxxxxxxxxxxxxxxxxxx> wrote:
On Mar 30, 9:05 pm, "Ron N." <rhnlo...@xxxxxxxxx> wrote:

If the sequence is a uniform sampling of a symmetric waveform
which is bandlimited to below the new sampling rate represented
by the dots, then, according to reconstruction theory, yes.
However, remember that this perfectly bandlimited waveform
can't be time limited as well, therefore any finite length FIR
filter is really a truncated approximation of some symmetric
infinite impulse response.

I was thumbing through my DSP books last night, refreshing my memory
of this topic. I noted that discussions of linear phase were
introduced in the context of sequences, rather than of FIR filters. A
sequence is just a sequence; other considerations such as Nyquist,
windowing, band-limiting, etc., only become important in a specific
implementation (such as a FIR filter).

The criterion for determining whether a sequence was linear phase was
whether it could be made zero phase by time-shifting. A zero phase
sequence has to be symmetric, so that its spectrum is either purely
real or purely imaginary.

If you are talking about pure sequences, without respect
to windowing, Nyquist and bandlimiting, then how can you
also talk about the spectrum and phase of that spectrum
without ambiguity? Once you allow usable definitions of
spectrum and phase for your pure sequence, then you also
allow modifications of that spectrum and phase which which
might be represented as a fractional time shift that could
produce a spectrum which is either purely even or odd.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
.

Relevant Pages

  • Re: Is an upsampled Maximum Length Sequence also an MLS?
    ... N has the effect of compressing the sequence into 1/N of the original ... If you then apply this to an LTI system, ... spectrum, which is probably not what you were hoping to achieve. ... I've been very happy to learn from this thread that simply increasing the length and the sampling rate of the original sequence, it is more than possible to measure the frequency response of a bandlimited system. ...
    (comp.dsp)
  • Re: Spectral analysis
    ... always apply a window. ... the data is on infinite extent. ... data sequence x'(the prime indcating that the sequence is the ... but it has the benefit of providing a discrete spectrum: ...
    (comp.dsp)
  • Re: rf design
    ... > The outline of a pulse spectrum is just the harmonics in the pulse, ... > lobes get narrower and denser, and when it increases, the lobes get ... With the psuedo-random LFSR sequence, ...
    (sci.electronics.design)
  • Re: conjugate symmetric & mirror image of the spectrum
    ... Yes it should be obvious you can calculate the spectrum from half the ... points in your sequence. ... and whether mirror image is same as conjugate symmetric. ... It is just symmetric - the symmetry of your sequence should produce no ...
    (comp.dsp)