Complex FIR coefficients
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From: Randy Yates on 30 Mar 2010 12:10 HardySpicer <gyansorova(a)gmail.com> writes: > So I suppose it is complex because the imaginary part also has > frequency-selective properties as well as real. Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency response isn't Hermitian symmetric. Note I use "*" here to denote conjugation. -- Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven. Digital Signal Labs % She love the way Puccini lays down a tune, and mailto://yates(a)ieee.org % Verdi's always creepin' from her room." http://www.digitalsignallabs.com % "Rockaria", *A New World Record*, ELO
From: Tim Wescott on 30 Mar 2010 12:24 Randy Yates wrote: > HardySpicer <gyansorova(a)gmail.com> writes: > >> So I suppose it is complex because the imaginary part also has >> frequency-selective properties as well as real. > > Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency > response isn't Hermitian symmetric. Note I use "*" here to denote > conjugation. That's not a _physical_ interpretation, because no physical system has a frequency response that isn't Hermitian symmetric. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Tim Wescott on 30 Mar 2010 12:28 HardySpicer wrote: > On Mar 29, 1:38 pm, Tim Wescott <t...(a)seemywebsite.now> wrote: >> HardySpicer wrote: >>> What is the physical significance of having an impulse response with >>> complex coefficients ie >>> {h0,h1,h2...hn} where the h values are complex. >> That your system, as described, is impossible to implement physically. >> >> You've asked a question with an absurd answer, and you're not dim. So >> what are you _really_ doing? >> >> The two biggest reasons I could think that you may see this happen are: >> >> (1) you've calculated an impulse response from a frequency response >> using an FFT and you've either not paid proper attention to phase, or >> you have the inevitable numerical inaccuracies and you haven't noticed >> that the imaginary parts are minuscule >> >> (2) you're modeling a system that's operating on I/Q data, and you've >> modeled quadrature as imaginary. > > Oh I saw a paper with an example in it that has complex data points, > actually it is matrices but the same principle holds. > It was for Quarternary-Quam. So I suppose it is complex because the > imaginary part also has frequency-selective properties as well as > real. Well, you were asking for physical significance. The physical significance is what I outlined in (2) above: the system being modeled is doing I/Q demodulation down to baseband, and the quadrature channel is modeled as imaginary. The spectrum of the _physical_ signal is a pair of identical, Hermitian-symmetrical spectra reflected around f = 0; in choosing to treat the quadrature channel as imaginary you're essentially just doing the math on the frequency-positive half of the spectrum. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Randy Yates on 30 Mar 2010 12:38 Tim Wescott <tim(a)seemywebsite.now> writes: > Randy Yates wrote: >> HardySpicer <gyansorova(a)gmail.com> writes: >> >>> So I suppose it is complex because the imaginary part also has >>> frequency-selective properties as well as real. >> >> Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency >> response isn't Hermitian symmetric. Note I use "*" here to denote >> conjugation. > > That's not a _physical_ interpretation, because no physical system has > a frequency response that isn't Hermitian symmetric. You are correct by strict interpretation. I was trying to answer what I thought his real question was. It takes two to communicate. -- Randy Yates % "Though you ride on the wheels of tomorrow, Digital Signal Labs % you still wander the fields of your mailto://yates(a)ieee.org % sorrow." http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO
From: Tim Wescott on 30 Mar 2010 13:10
Randy Yates wrote: > Tim Wescott <tim(a)seemywebsite.now> writes: > >> Randy Yates wrote: >>> HardySpicer <gyansorova(a)gmail.com> writes: >>> >>>> So I suppose it is complex because the imaginary part also has >>>> frequency-selective properties as well as real. >>> Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency >>> response isn't Hermitian symmetric. Note I use "*" here to denote >>> conjugation. >> That's not a _physical_ interpretation, because no physical system has >> a frequency response that isn't Hermitian symmetric. > > You are correct by strict interpretation. I was trying to answer what I > thought his real question was. > > It takes two to communicate. I shall find my swagger stick, and polish my monocle and my German accent. Tee hee! Schnort! Hopefully between the two of us we've managed to satisfy Hardy. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com |