I've been reading Lyons' Chapters 4&5 (FIR and IIR filters). Some questions crossed my mind triggered by what I read. They didn't correspond to where Rick wants to take the reader ;) 1. What "kind(s)" of filter(s) would have a strictly real valued impulse response. 2. Starting with the IIR topology of Fig 6-3, what "kind(s)" of filter response(s) would result from strictly real values for the feedback and feedforward coefficients a(n) and b(n)?
Newbie type "What if's"
Started by ●July 16, 2008
Reply by ●July 16, 20082008-07-16
On 16 Jul, 20:00, Richard Owlett <rowl...@atlascomm.net> wrote:> I've been reading Lyons' Chapters 4&5 (FIR and IIR filters). > Some questions crossed my mind triggered by what I read. > They didn't correspond to where Rick wants to take the reader ;) > > 1. What "kind(s)" of filter(s) would have a strictly real valued impulse > response. > > 2. Starting with the IIR topology of Fig 6-3, what "kind(s)" of filter > response(s) would result from strictly real values for the feedback and > feedforward coefficients a(n) and b(n)?The answer to both your questions is that most people will never see a case where the coeffcients are *complex*. Even when complex coefficients might be useful, most people use real IQ filters. Rune
Reply by ●July 17, 20082008-07-17
Rune Allnor wrote:> On 16 Jul, 20:00, Richard Owlett <rowl...@atlascomm.net> wrote: > >>I've been reading Lyons' Chapters 4&5 (FIR and IIR filters). >>Some questions crossed my mind triggered by what I read. >>They didn't correspond to where Rick wants to take the reader ;) >> >>1. What "kind(s)" of filter(s) would have a strictly real valued impulse >>response. >> >>2. Starting with the IIR topology of Fig 6-3, what "kind(s)" of filter >>response(s) would result from strictly real values for the feedback and >>feedforward coefficients a(n) and b(n)? > > > The answer to both your questions is that most people will never see > a case where the coeffcients are *complex*. Even when complex > coefficients > might be useful, most people use real IQ filters. > > RuneMaybe I have a better feel for "how things are" than I thought. As to the first question, I was reasoning along the line that there should be a duality between a time delay and a phase angle. I had also been reading that to realize an arbitrarily shaped frequency response yo Fourier Transform it to get the required impulse response. I'll experiment with the frequency responses that interest me, keep only the real part of the resulting impulse response and see if the result is "good enough" To what does "real IQ filters" refer. I don't find any thing in index of either rick Lyons' or Steve Smith's books. Google was no help. The closest I came was a quaduture modulation technique.
Reply by ●July 17, 20082008-07-17
On 17 Jul, 12:14, Richard Owlett <rowl...@atlascomm.net> wrote:> Rune Allnor wrote: > > On 16 Jul, 20:00, Richard Owlett <rowl...@atlascomm.net> wrote: > > >>I've been reading Lyons' Chapters 4&5 (FIR and IIR filters). > >>Some questions crossed my mind triggered by what I read. > >>They didn't correspond to where Rick wants to take the reader ;) > > >>1. What "kind(s)" of filter(s) would have a strictly real valued impulse > >>response. > > >>2. Starting with the IIR topology of Fig 6-3, what "kind(s)" of filter > >>response(s) would result from strictly real values for the feedback and > >>feedforward coefficients a(n) and b(n)? > > > The answer to both your questions is that most people will never see > > a case where the coeffcients are *complex*. Even when complex > > coefficients > > might be useful, most people use real IQ filters. > > > Rune > > Maybe I have a better feel for "how things are" than I thought. As to > the first question, I was reasoning along the line that there should be > a duality between a time delay and a phase angle. I had also been > reading that to realize an arbitrarily shaped frequency response yo > Fourier Transform it to get the required impulse response. I'll > experiment with the frequency responses that interest me, keep only the > real part of the resulting impulse response and see if the result is > "good enough"When you IFFT a (complex) spectrum that formally gives a real impulse response, be aware that the numerics will yield an imaginary part form the computations. The numbers in this imaginary part will be very small, though, the realtive accuracy (i.e. the ratio abs(imaginary part)/abs(real part)) on the order of 1e-15 if you use double-precision floating point numbers. Rune
Reply by ●July 17, 20082008-07-17
Rune Allnor wrote:> ... most people use real IQ filters. >I'm lost ;/ What's an "IQ filter"? As Rune specifically did not answer the question before, I assume it's not too relavant too the questions I originally posed.
Reply by ●July 17, 20082008-07-17
Richard Owlett wrote:> Rune Allnor wrote: >> ... most people use real IQ filters. >> > > I'm lost ;/ > What's an "IQ filter"? > As Rune specifically did not answer the question before, > I assume it's not too relavant too the questions I originally posed.He meant, "Instead of using one filter that takes a complex input and has complex coefficients, most people use two filters with real coefficients and real inputs; one for the in-phase (I) part, and the other for the quadrature(Q) part." Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 18, 20082008-07-18
Jerry Avins wrote:> Richard Owlett wrote: > >> Rune Allnor wrote: >> >>> ... most people use real IQ filters. >>> >> >> I'm lost ;/ >> What's an "IQ filter"? >> As Rune specifically did not answer the question before, >> I assume it's not too relavant too the questions I originally posed. > > > He meant, "Instead of using one filter that takes a complex input and > has complex coefficients, most people use two filters with real > coefficients and real inputs; one for the in-phase (I) part, and the > other for the quadrature(Q) part." > > JerryOK, that makes sense. It also joggles my brain on what triggered my interest in DSP originally, examining voiced phonemes. The model of speech I use PRESUMES the information is in the power envelope of each of the formants. [I'd not want to go out on any limbs claiming it has any correlation to current theory/practice.] I assume further that the vocal cords are not frequency stable and the characteristic time of the power variation is 10 to 100 times slower than the frequency of the sound. Since I'm interested in power over a band of frequencies, is it justifiable to filter by convolving the input with ONLY the real part of the impulse response of my filter?
Reply by ●July 18, 20082008-07-18
Richard Owlett wrote:> Rune Allnor wrote: > > ... �most people use real IQ filters. > > I'm lost ;/ > What's an "IQ filter"?Usenet works like an IQ filter: People come here, mysteriously lose their IQ and start writing all kinds of nonsense ... :-)
Reply by ●July 18, 20082008-07-18
Richard Owlett wrote:> Jerry Avins wrote: >> Richard Owlett wrote: >> >>> Rune Allnor wrote: >>> >>>> ... most people use real IQ filters. >>>> >>> >>> I'm lost ;/ >>> What's an "IQ filter"? >>> As Rune specifically did not answer the question before, >>> I assume it's not too relavant too the questions I originally posed. >> >> >> He meant, "Instead of using one filter that takes a complex input and >> has complex coefficients, most people use two filters with real >> coefficients and real inputs; one for the in-phase (I) part, and the >> other for the quadrature(Q) part." >> >> Jerry > > OK, that makes sense. > It also joggles my brain on what triggered my interest in DSP > originally, examining voiced phonemes. > > The model of speech I use PRESUMES the information is in the power > envelope of each of the formants. [I'd not want to go out on any limbs > claiming it has any correlation to current theory/practice.] > > I assume further that the vocal cords are not frequency stable and the > characteristic time of the power variation is 10 to 100 times slower > than the frequency of the sound. > > Since I'm interested in power over a band of frequencies, is it > justifiable to filter by convolving the input with ONLY the real part of > the impulse response of my filter?What kinds of filters have a complex impulse response? A complex signal that is not modulated onto a carrier needs two wires (plus ground). Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 18, 20082008-07-18
Jerry Avins wrote:> Richard Owlett wrote: > >> Jerry Avins wrote: >> >>> Richard Owlett wrote: >>> >>>> Rune Allnor wrote: >>>> >>>>> ... most people use real IQ filters. >>>>> >>>> >>>> I'm lost ;/ >>>> What's an "IQ filter"? >>>> As Rune specifically did not answer the question before, >>>> I assume it's not too relavant too the questions I originally posed. >>> >>> >>> >>> He meant, "Instead of using one filter that takes a complex input and >>> has complex coefficients, most people use two filters with real >>> coefficients and real inputs; one for the in-phase (I) part, and the >>> other for the quadrature(Q) part." >>> >>> Jerry >> >> >> OK, that makes sense. >> It also joggles my brain on what triggered my interest in DSP >> originally, examining voiced phonemes. >> >> The model of speech I use PRESUMES the information is in the power >> envelope of each of the formants. [I'd not want to go out on any limbs >> claiming it has any correlation to current theory/practice.] >> >> I assume further that the vocal cords are not frequency stable and the >> characteristic time of the power variation is 10 to 100 times slower >> than the frequency of the sound. >> >> Since I'm interested in power over a band of frequencies, is it >> justifiable to filter by convolving the input with ONLY the real part >> of the impulse response of my filter? > > > What kinds of filters have a complex impulse response?A confused one ;) I was starting with a frequency domain sketch of my desired response. I would then use Scilab's FFT function to get the impulse response of my desired filter. That gives a complex result. I just couldn't justify to myself why a tapped delay line with real multipliers couldn't do anything that complex multipliers could do. Rick Lyons uses complex math to simplify his proofs. I may have let that distract me. I'll have to take another look at Smith's book.> A complex signal > that is not modulated onto a carrier needs two wires (plus ground). > > Jerry
