What is the physical significance of having an impulse response with complex coefficients ie {h0,h1,h2...hn} where the h values are complex. Hardy

# Complex FIR coefficients

Started by ●March 28, 2010

Reply by ●March 28, 20102010-03-28

On 29 Mar, 00:14, HardySpicer <gyansor...@gmail.com> wrote:> What is the physical significance of having an impulse response with > complex coefficientsDoes there have to be one? Rune

Reply by ●March 28, 20102010-03-28

HardySpicer <gyansorova@gmail.com> writes:> What is the physical significance of having an impulse response with > complex coefficients ie > > {h0,h1,h2...hn} where the h values are complex.Hi, You know that the the frequency response of an FIR filter is the Discrete Fourier Transform (DFT) of its impulse response, right? What are the properties of the DFT when the inputs are real versus complex? -- Randy Yates % "Maybe one day I'll feel her cold embrace, Digital Signal Labs % and kiss her interface, mailto://yates@ieee.org % til then, I'll leave her alone." http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

Reply by ●March 28, 20102010-03-28

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. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com

Reply by ●March 29, 20102010-03-29

On Mar 29, 1:38�pm, Tim Wescott <t...@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. > > -- > Tim Wescott > Control system and signal processing consultingwww.wescottdesign.comOh 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. Hardy

Reply by ●March 30, 20102010-03-30

HardySpicer <gyansorova@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@ieee.org % Verdi's always creepin' from her room." http://www.digitalsignallabs.com % "Rockaria", *A New World Record*, ELO

Reply by ●March 30, 20102010-03-30

Randy Yates wrote:> HardySpicer <gyansorova@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

Reply by ●March 30, 20102010-03-30

HardySpicer wrote:> On Mar 29, 1:38 pm, Tim Wescott <t...@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

Reply by ●March 30, 20102010-03-30

Tim Wescott <tim@seemywebsite.now> writes:> Randy Yates wrote: >> HardySpicer <gyansorova@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@ieee.org % sorrow." http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO

Reply by ●March 30, 20102010-03-30

Randy Yates wrote:> Tim Wescott <tim@seemywebsite.now> writes: > >> Randy Yates wrote: >>> HardySpicer <gyansorova@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