jim wrote:> > Bob Cain wrote: > >>jim wrote: >> >> >>>You were doing well up to now. Your filter is not differentiation >>>regardless of a popular belief that it is. A simple yes to the question >>>would have been a better answer. >> >>Care to elaborate? > > > Not really but here goes. The correct answer to the question is it > linear was yes. It's an FIR filter why wouldn't it be linear. Whether > differentiation is linear or not is irrelevant.Gee, thanks. That helped a whole lot. IOW, never mind. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein

# FIR notch filters using the Windowing method

Started by ●April 13, 2005

Reply by ●April 16, 20052005-04-16

Reply by ●April 16, 20052005-04-16

jim wrote:>> >> Jerry Avins wrote: >> >> I've long (a little longer than I've been hanging around here) taken >> it for granted that in order to affect a frequency significantly, a >> filter's significant impulse response needs to last in the order of >> that frequencies reciprocal. >>Just to clarify. I think I know what Jerry is getting at in the above maxim (something like - potential of a filter to discriminate between frequencies). But the counter example given makes it clear this is not the way to state it. The counter example is the shortest meaningful filter possible yet the longer the wavelength fed to this filter the greater it will be affected. -jim ----== Posted via Newsfeeds.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----

Reply by ●April 16, 20052005-04-16

jim wrote:> > jim wrote: > > >>>Jerry Avins wrote: >>> >>>I've long (a little longer than I've been hanging around here) taken >>>it for granted that in order to affect a frequency significantly, a >>>filter's significant impulse response needs to last in the order of >>>that frequencies reciprocal. >>> > > > Just to clarify. I think I know what Jerry is getting at in the above > maxim (something like - potential of a filter to discriminate between > frequencies). But the counter example given makes it clear this is not > the way to state it. The counter example is the shortest meaningful > filter possible yet the longer the wavelength fed to this filter the > greater it will be affected. > > -jimYour filter is indeed proof that my rule of thumb suffers from extreme brachydactylia. In other words, it is way too short. While it is a perfect counterexample to the short statement, ii is on the edge, not at the heart, of what I had in mind. Its maximum slope is 6 dB/decade; the gain of frequencies an octave apart differ by at most 2:1. Moreover, no particular low frequency is singled out and its significant frequency, the corner frequency below which the response drops, is near enough to Fs to be "in the order of" the sampling rate itself. That's in keeping with the spirit of my rule, even though it was stated too briefly. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●April 16, 20052005-04-16

Jerry Avins wrote:> Your filter is indeed proof that my rule of thumb suffers from extreme > brachydactylia. In other words, it is way too short. While it is a > perfect counterexample to the short statement, ii is on the edge, not at > the heart, of what I had in mind.Understood, Jerry. That's why I put a smiley at the end. Any "interesting" filter will likely obey your simple rule. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein

Reply by ●April 17, 20052005-04-17

On Wed, 13 Apr 2005 11:33:43 -0700, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:> >"Greer" <Greer.GRAY@oxinst.co.uk> wrote in message >news:q5WdnZYwX6dsysDfRVn-sw@giganews.com... >> Hi, >> >> I am trying to obtain a FIR notch filter which is very narrow. For >> example, a 50 Hz notch filter to remove mains noise from a 1250Hz signal >> say. >> > Many thanks, > Greer(snipped) Hello Greer, I just went through an analysis of narrowband notch FIR filters and discovered that we can build a computationally-efficient 3-tap narrowband FIR notch filter. The FIR filter's coefficients are [1, b, 1]. The value for "b" is equal to: b = -2cos(4*pi*Fnotch/Fs) where Fnotch is the center freq of the filter's notch in Hz, and Fs is the sample rate in Hz. Good Luck, [-Rick-] You friendly neighborhood DSP junkie.

Reply by ●April 17, 20052005-04-17

Rick Lyons wrote: ...> I just went through an analysis of narrowband notch FIR > filters and discovered that we can build a > computationally-efficient 3-tap narrowband FIR notch filter. > > The FIR filter's coefficients are [1, b, 1]. > The value for "b" is equal to: > > b = -2cos(4*pi*Fnotch/Fs) > > where Fnotch is the center freq of the filter's notch > in Hz, and Fs is the sample rate in Hz.WOW! Zowie! This I have to plot! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●April 17, 20052005-04-17

On Sat, 16 Apr 2005 23:21:38 -0400, Jerry Avins <jya@ieee.org> wrote:>Rick Lyons wrote: > > ... > >> I just went through an analysis of narrowband notch FIR >> filters and discovered that we can build a >> computationally-efficient 3-tap narrowband FIR notch filter. >> >> The FIR filter's coefficients are [1, b, 1]. >> The value for "b" is equal to: >> >> b = -2cos(4*pi*Fnotch/Fs) >> >> where Fnotch is the center freq of the filter's notch >> in Hz, and Fs is the sample rate in Hz. > >WOW! Zowie! This I have to plot! >Ah ha. This is good. I'd be tickled if your independent analysis gives the same results as mine. That way I'd be more confident that the above expression for "B" is correct. See Ya' Jer, [-Rick-]

Reply by ●April 17, 20052005-04-17

Rick Lyons wrote:> > > >> I just went through an analysis of narrowband notch FIR > >> filters and discovered that we can build a > >> computationally-efficient 3-tap narrowband FIR notch filter. > >> > >> The FIR filter's coefficients are [1, b, 1]. > >> The value for "b" is equal to: > >> > >> b = -2cos(4*pi*Fnotch/Fs) > >> > >> where Fnotch is the center freq of the filter's notch > >> in Hz, and Fs is the sample rate in Hz. > > > >WOW! Zowie! This I have to plot! > > > > Ah ha. This is good. I'd be tickled if your > independent analysis gives the same results as mine. > That way I'd be more confident that > the above expression for "B" is correct.shouldn't it be: b = -2cos(2*pi*Fnotch/Fs) f DC fs/4 fs/2 b -2 0 2 -jim ----== Posted via Newsfeeds.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----

Reply by ●April 17, 20052005-04-17

On Sat, 16 Apr 2005 23:21:38 -0400, Jerry Avins <jya@ieee.org> wrote:>Rick Lyons wrote: > > ... > >> I just went through an analysis of narrowband notch FIR >> filters and discovered that we can build a >> computationally-efficient 3-tap narrowband FIR notch filter. >> >> The FIR filter's coefficients are [1, b, 1]. >> The value for "b" is equal to: >> >> b = -2cos(4*pi*Fnotch/Fs) >> >> where Fnotch is the center freq of the filter's notch >> in Hz, and Fs is the sample rate in Hz. > >WOW! Zowie! This I have to plot! >OOoops! Hey Jerry, I just realized: I gave you the wrong form of the equation for coeff "b". My incorrect form came from an AM demod circuit I'm trying to understand. In any case, the correct formula for "b" is: b = -2cos(2*pi*Fnotch/Fs) My original "4*pi* should be "2*pi". Sheece! Sorry 'bout that. [-Rick-]

Reply by ●April 17, 20052005-04-17

On Sun, 17 Apr 2005 11:47:45 -0500, jim <"N0sp"@m.sjedging@mwt.net> wrote:> > >Rick Lyons wrote: > >> > >> >> I just went through an analysis of narrowband notch FIR >> >> filters and discovered that we can build a >> >> computationally-efficient 3-tap narrowband FIR notch filter. >> >> >> >> The FIR filter's coefficients are [1, b, 1]. >> >> The value for "b" is equal to: >> >> >> >> b = -2cos(4*pi*Fnotch/Fs) >> >> >> >> where Fnotch is the center freq of the filter's notch >> >> in Hz, and Fs is the sample rate in Hz. >> > >> >WOW! Zowie! This I have to plot! >> > >> >> Ah ha. This is good. I'd be tickled if your >> independent analysis gives the same results as mine. >> That way I'd be more confident that >> the above expression for "B" is correct. > >shouldn't it be: > > b = -2cos(2*pi*Fnotch/Fs) > >f DC fs/4 fs/2 >b -2 0 2 > >-jimHi Jim, yep. you are correct. You caught my error before I did. Good catch Jim! Ya know what's interesting. I tried to derive the equation for the "b" coefficient for an FM demod problem on which I was working. I went through a z-transform derivation (brute-force & clumsy) and ended up with an equation to compute the "b" coefficient. But my equation involved square roots and tangent-squared stuff. Messy, but it was correct. Then a few days ago I ran into a equation on the Internet (in the context of an AM demodulation discussion) that also computed the "b" coefficient, but this equation was the very simple cosine expression that I originally posted. I thought to myself, "Now how did that guy come up with with such a clean simple expression for the "b" coefficient. Then it hit me. We can use the discrete-time Fourier transform (DTFT) to arrive at the simpler "cosine" expression for "b". So in terms of the "Fnotch" frequency I had an equation for coeff "b". OK, neat. Then this afternoon, I'm not joking, this afternoon I'm diggin' through a DSP book for info on another subject and I ran into the author's discussion of "Here's a simple 3-tap FIR notch filter, and here's how to compute the center "b" filter coefficient"!!! It seems that every time I discover something that I think is mildly clever and "not so well-known", later I see that it's already been described in some clever guy's DSP book!! See Ya', [-Rick-]