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High pass bessel?

Discussion in 'Electronic Design' started by Michael, Oct 7, 2003.

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  1. Michael

    Michael Guest

    Is it possible to generate a high pass filter with a constant group
    delay in the pass band (bessel response)?

    This is for car audio, although people claim that phase error cannot
    be heard, I believe it can at low F, where the delay created by the
    phase shift becomes more significant.

    I have seen methods for calculating values on the net but they don't
    seem to have a bessel phase response.
    I am capable of analysing active filter circuits and deriving
    transfer function, I then write simple basic programs to plot the
    response. I have verified my program by matching values and creating
    the same plots as Microchips filter lab. I have also noticed that
    filter lab 2.0 will not generate high pass bessel.

    If this is impossible I will be forced to continue with a DSP
    approach, which is turing out to be a lot of work.
     
  2. TI has a program FilterPro. You might want to look into it.

    Cheers
     
  3. maxfoo

    maxfoo Guest

    Read page 275 from the 2nd edition of "The Art of Electronics"
    Available at Borders or Barnes & Noble.
     
  4. Michael

    Michael Guest

    Thanks Martin, thats a nice program. Much better than Microchips
    filterlab. It looks as though hi-pass filters can have a flat group
    delay only in the cutoff band, and drop to a delay of zero through the
    pass band. I was able to achive a suitable alignment that only has a
    delay of 4-5mS under the crossover point.
     
  5. The choice of bessel or something else has nothing to do
    with analog or digital. A DSP can do both.
    A somewhat better understanding of the subject than just
    using an application may be necessary though.

    Rene
     
  6. Bill Sloman

    Bill Sloman Guest

    Get hold of a copy of the "Electronic Filter Design Handbook" by
    Arthur B.Williams and Fred J.Taylor.
    My copy is the second edition, ISBN 0-07-070434-1.
    The third edition, ISBN 0-07-070430-9, has been claimed to be even
    better.

    The book seems to be out of print a the moment, and Amazon has three
    buyers waiting. You may be able to find it in a university library.

    Very useful for precisely your sort of problem - and it also covers
    linear phase filters with equi-ripple phase error, whihc you might
    find useful.
     
  7. Below 600Hz the output signals of the neurons responsible for sound
    processing are completely in sync with the audio signal, therefore phase is
    important. Between 600Hz-1.8kHz the output signal of our neurons is still
    synchronous with the audio signal, but since our neurons cannot fire that
    fast, not every top in the audio signal is a neuron output peak, so phase
    sensitivity becomes less. Above 1.8kHz there is no synchronicity between
    the signal and the output of our neurons.

    So a constant group delay below 2kHz should be ok.

    But since it's for car-audio, try to calculate the effect of the car
    itself, reflections against the windows etc. on your sound, much bigger
    than a little filter phase shift.
     
  8. Active8

    Active8 Guest

    look what happens when you use google to find TI's program the fast way.

    http://www.circuitsage.com/filter.html

    i forgot about that site. lots of links.

    brs,
    mike
     
  9. Phil Hobbs

    Phil Hobbs Guest

    The classical design procedure for filters is to start with a low-pass
    prototype, and apply a conformal mapping in the complex frequency plane.

    For a high pass, this means transforming f ->fc**2/f. Doing this and
    keeping all the reactances the same in magnitude (inductors become
    capacitors, capacitors become inductors) gives you a highpass.

    This works great for the magnitude response, but since the frequency
    stretch is nonlinear, your nice linear phase response has suddenly
    become a nice approximation to a particular nonlinear curve, instead.

    Bandpass has the same trouble.

    A bit of Matlab code will optimize one for you.

    Cheers,

    Phil Hobbs
     
  10. Zak

    Zak Guest

    Makes sense - how can a few capacitors store hundreds of cycles of 20
    KHz signal? That would be needed to delay these as much as a 90 degree
    shift at low frequency.


    Thomas
     
  11. Ken Smith

    Ken Smith Guest

    A does not prove B in this case. A rapid change in phase VS frequency can
    still be detected above 2KHz. The simplest proof is to imagine an AM
    modulated 2KHz sine wave. If the modulation frequency is low enough, you
    can hear the signal decrease to zero amplitude. If this signal is then
    run through a circuit with a very rapid change in phase, the amplitude
    will no longer decrease to zero.

    Besides, if it is for a car the environment adds a lot of noise to the
    music. This makes errors in the sound system harder to hear.
     
  12. It is not so easy.
    The DSP response is limited to Fsa/2, versus the analog response which
    goes to the infinite frequency. The frequency warping and/or aliasing
    effect is introduced. The DSP can never have the exact Bessel,
    Butterworth or whatsoever transfer function. However you can do a lot of
    other different things with the DSP.

    That is very true :)
    Vladimir Vassilevsky

    DSP and Mixed Signal Design Consultant

    http://www.abvolt.com
     
  13. And note my one:) It does do all the main HP and LP filters, LC and
    opamp versions.

    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
     
  14. Well, this is a bit misleading. Static phase shift, is indeed, to all
    practicable intents and purposes, not detectable by the ear. That is,
    put a signal through an all pass filter, i.e constant magnitude and
    varying phase with frequency, and you simply wont be able to tell the
    phase shifted signal from the unshifted signal.

    However, two signals mixed together with differing static phases can
    result in huge audible differences. Such a combined signal will result
    in cancellations and/or peaks in the frequency response.

    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
     
  15. Active8

    Active8 Guest

    oh yeah. don't forget kevin's filter designer in SS :)
     
  16. Ban

    Ban Guest

    Zak,
    the delay drops to zero in the pass-band, which is in our case the high
    frequencies.
    The transfer function for a 2nd order high-pass with gain(oo)=1 will be:

    A(P)= 1/(1+ a1/P+ b1/P^2) with P= j*Omega= j*f/fg
    for a Bessel characteristic a1= 1.3617 and b1= 0.618.

    Since our transfer function returns complex values, we can calculate
    amplitude and phase with it.
    Let's calculate a few values:

    P= j0.1 A(P)=1/(1+ 1.3617/j0.1+ 0.618/0.01j^2)
    =1/(1- j13.617- 61.8) = -1/(60.8+ j13.617)
    when transformed into polar we get: |A|= 0.01605 and phi= -7.8°
    with 100Hz the group delay would be 0.2167ms

    P= j1 A(P)=1/(1+ 1.3617/j1+ 0.618/1j^2)
    =1/(1- j1.3617- 0.618) = 1/(0.382- j1.3617)
    when transformed into polar we get: |A|= 0.7071 and phi= -74.3°
    with 1000Hz the group delay would be 0.2065ms

    P= j10 A(P)=1/(1+ 1.3617/j10+ 0.618/100j^2)
    =1/(1- j0.13617- 0.00618) = 1/(0.994- j0.13617)
    when transformed into polar we get: |A|= 1.00 and phi= -12.6°
    with 10000Hz the group delay would be 0.0035ms

    ciao Ban
     
  17. You're right.
    But the analog filters do not go to infinity, neither the ones
    with passive elements only, nor the one with opamps.

    I was thinking of using the DSP for frequencies far below
    the sampling frequency. Yes, much is possible.

    Rene
     
  18. Michael

    Michael Guest

    So was I, my dsp approach was such:
    Keep in mind this is a one off project for personal use, and I have
    limited resources.

    I have an MSP430F147 processing two 147 tap Low pass FIR filters,
    sample rate is 2kHz.
    Analog filters remove alias F's over 1k and remove step noise from the
    output.
    A digital delay (bunch of ram chips, a2d's and d2'a, and a pic to run
    it all) will then delay the original signal 36mS to bring it in phase
    with the FIR filter output.
    Because the low pass and original signal will remain in phase I will
    be able to use opamps to subtract the bass from the original to get my
    mids & highs.
    I will use digital attenuators after the filters to control overall
    volume of the 9 channels.

    However:
    Last night I measured the phase response of the vented sub in my car,
    it was filthy and I'm not so worried about the phase response of my
    xover anymore, so I'm just gonna use some analog filters.

    Thanks for the help,

    Regards, Michael.
     
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