Filter design with 'freqsamp' method?
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From: robert bristow-johnson on 4 Jul 2010 20:30 On Jul 4, 1:35 pm, Greg Berchin <gberc...(a)comicast.net.invalid> wrote: > On Sun, 4 Jul 2010 16:15:35 +0000 (UTC), spop...(a)speedymail.org (Steve Pope) > wrote: > > >So as to save you guys some googling I have uploaded Ibnkahla's > >definition of RMS delay spread to the following link which > >I will leave in place for a few days. > > >Hopefully this makes things less ambiguous. might be if i knew what P(t) is. > >http://www.rahul.net/spp/IbnkahlaDelaySpread.bmp > > I only gave it a cursory look, but comparing that with the discussion of moments > that I put into US Patent 5375067, Ibnkahla's definition of RMS delay spread > appears to be the same as RMS Duration. can you define that in terms of impulse response, h(t)? otherwise i'm still confused. r b-j
From: Steve Pope on 4 Jul 2010 20:50 robert bristow-johnson <rbj(a)audioimagination.com> wrote: >> On Sun, 4 Jul 2010 16:15:35 +0000 (UTC), spop...(a)speedymail.org (Steve Pope) >> >So as to save you guys some googling I have uploaded Ibnkahla's >> >definition of RMS delay spread to the following link which >> >I will leave in place for a few days. >> >Hopefully this makes things less ambiguous. >might be if i knew what P(t) is. For the full details, enough of Ibnakahla's text (see my previous post) is on Google books to extract those. I think he wants P(tau) to be the power delay profile, but another possibility is the just magnitude of the impulse response. (So, yes, still ambiguous.) S.
From: Greg Berchin on 4 Jul 2010 21:03 On Sun, 4 Jul 2010 17:30:48 -0700 (PDT), robert bristow-johnson <rbj(a)audioimagination.com> wrote: >can you define that in terms of impulse response, h(t)? In the case of the RMS Duration, it is simply the normalized second moment of a generic time domain waveform, so h(t) will do nicely. In the case of Ibnkahla's RMS delay spread, I interpreted P(tau) to be something like h(t-tau), where tau is the temporal centroid. If P(t) is something else, then I don't know. Greg
From: Fred Marshall on 5 Jul 2010 12:54 Fred Marshall wrote: > robert bristow-johnson wrote: >> On Jul 1, 10:59 am, Fred Marshall <fmarshallx(a)remove_the_xacm.org> >> wrote: >>> r b-j, >>> >>> Well, maybe I've had it wrong all these years but I'd say that the >>> windowing method starts with N frequency samples where N is the length >>> of the filter you want. >> >> so then, since the DFT and iDFT are bijective (i love using fancy- >> pants words), why window? if h[n] has N samples and N degrees of >> freedom, so does H[k]. you specify your N frequency samples and you >> can hit it perfectly with no windowing. >> >> so, that seems curious to me. >> >> r b-j > > You window because the frequency response between those points can be > nasty. Either you don't window and convolve those samples with a > matching sinc er.. Dirichlet or you window and convolve those samples > with something else. > > The trade is that the Dirichlet matches all the samples exactly. Other > windows don't. Some match them all except the adjacent two as in the > 1/2 1 1/2 sum of adjacent Dirichlets. It still has zeros in the sum > at all the other sample points - so the convolution doesn't perturb > their values. And, the values between points are better behaved. > > And making N larger to begin with doesn't affect any of this in my way > of looking at it. > > Fred And, I'm sure you know .. If you use the basis 1/2 1 1/2 sum of Dirichlets (raised cosine in time) which I will refer to as "RC" then you do have to convolve and can't solve a system of equations that matches the samples exactly at each point. If you did that, then it would revert to using a single Dirichlet I do believe. Since the stopbands are zero then all you get in them are the fast-decaying tails of RC components from the passbands by 1/f^3 [rather than 1/f for a single Dirichlet]. Fred
From: robert bristow-johnson on 5 Jul 2010 13:18
On Jul 3, 6:21 pm, Fred Marshall <fmarshallx(a)remove_the_xacm.org> wrote: > robert bristow-johnson wrote: > > On Jul 1, 10:59 am, Fred Marshall <fmarshallx(a)remove_the_xacm.org> > > wrote: > >> r b-j, > > >> Well, maybe I've had it wrong all these years but I'd say that the > >> windowing method starts with N frequency samples where N is the length > >> of the filter you want. > > > so then, since the DFT and iDFT are bijective (i love using fancy- > > pants words), why window? if h[n] has N samples and N degrees of > > freedom, so does H[k]. you specify your N frequency samples and you > > can hit it perfectly with no windowing. > > > so, that seems curious to me. > > > r b-j > > You window because the frequency response between those points can be > nasty. Either you don't window and convolve those samples with a > matching sinc er.. Dirichlet or you window and convolve those samples > with something else. you're always windowing it (unless your impulse response is an infinitely-repeating periodic function. you draw your N (or more) discrete points in the frequency domain, you iDFT it and what you have there is still a periodic sequence. if you use just one cycle of that (and zero the rest, as you would for an FIR), then you've applied the rectangular window. > The trade is that the Dirichlet matches all the samples exactly. Other > windows don't. Some match them all except the adjacent two as in the > 1/2 1 1/2 sum of adjacent Dirichlets. It still has zeros in the sum > at all the other sample points - so the convolution doesn't perturb > their values. And, the values between points are better behaved. the values between points exhibit less "high frequency" behavior or are less smooth. that's normally thought of as "better". and the reason is that in the other domain (where the window is applied), you've reduced the amplitude of the points further from h[0] (the "high frequency" points, but they're really the high time-displacement points that fuel the "high frequency" wiggling in the frequency domain. > And making N larger to begin with doesn't affect any of this in my way > of looking at it. it allows you to draw the frequency response more densely. so you can explicitly specify how "wiggly" you want it between the sparser points you have with your smaller "N". but to do so, the impulse response is very large, too large. so you have to shorten it and that is windowing. then, starting with the ideal (but too long) impulse response, you can try shortening it in a variety of different ways (using different windows) and see how well you do. you can also try shortening it to different lengths (using whatever window that looks best) to make a tradeoff decision on FIR length and its performance. it's very similar in philosophy to what we do with the windowed-sinc LPF design. start with the ideal (which is too long) and see what happens when you settle for something shorter. r b-j |