Re: Hilbert transform using FFT approach

Jerry Avins <jya@xxxxxxxx> wrote in news:Pv6dneqMBPQ6S6zeRVn-gg@xxxxxxx:

> Al Clark wrote:
>> Jerry Avins <jya@xxxxxxxx> wrote in
>> news:DNqdnTN5Vq4ZM6zenZ2dnUVZ_tCdnZ2d@xxxxxxx:
>>
>>
>>>w106pjs wrote:
>>>
>>>>>w106pjs wrote:
>>>>>
>>>>> ...
>>>>>
>>>>>
>>>>>
>>>>>>The purpose [of the quadrature signals] is to generate the
>>>>>>envelope of
>>>>
>>>>the real
>>>>
>>>>
>>>>>>sequence of data using the analytic signal approach using the FFT
>>>>
>>>>approach
>>>>
>>>>
>>>>>Then you don't want the phase distortion that comes with
>>>>>computationally
>>>>
>>>>
>>>>>cheaper ways. If the frequencies that in the envelope lie in a
>>>>>relatively narrow band around the carrier, and the sample rate is
>>>>>high enough to reproduce the carrier, then it sounds quite doable.
>>>>>Narrow-band HTs aren't too hard. Do you have Matlab or anything
>>>>>like it?
>>>>>
>>>>>Where does the FFT fit in? Given quadrature signals I[n] and Q[n],
>>>>>the envelope is E[n] = sqrt(I[n]^2 + Q[n]^2]. There are decent
>>>>>approximations for the square root of the sum of squares.
>>>>>
>>>>>Jerry
>>>>>--
>>>>>Engineering is the art of making what you want from things you can
>>>>>get.
>>>>
>>>>
>>>>Jerry,
>>>>
>>>>what I meant is Hilbert function in MATLAB uses fft approach in
>>>>generating the analytic signal.
>>>>Is that similar approach implementable in real time. ?
>>>>FYI
>>>>Fsig = 240khz, Fs = 10 Mhz..
>>>
>>>A Hilbert transformer can be just an antisymmetric FIR with alternate
>>>taps zero and the other coefficients inversely proportional to the
>>>tap's distance from the center. If the number of taps is odd, there's
>>>a bonus in that the signal at the center tap (which must be zero for
>>>the FT) is the delayed version of the input without the quadrature
>>>shift. Neither an extra delay line nor half-period delay are needed.
>>>But thinking more on it, the possibly cheaper filter pair with
>>>relatively quadrature outputs ought to work also with negligible
>>>distortion unless the modulating waveform is wide compared to the
>>>carrier.
>>>
>>>Jerry
>>
>>
>> The alternate taps are not always 0. This is true (or perhaps tends
>> to be true) for window based designs of Hilbert transformers. If you
>> use the PM (remez exchange) method, you will have values at all taps
>> except the middle coefficient for an odd length FIR filter. The
>> coefficients will always be antisymmetric.
>>
>> The reason to use remez exchange vs windowing methods is that
>> although the phase will always be exactly 90 degrees apart if the FIR
>> filter is antisymmetric, the amplitude response will have errors in
>> the passband (the filter will be bandpass). You can make the the
>> passband very flat with the remez exchange method. This makes your 0
>> and 90 degree outputs a nearly perfect pair (as long as you are in
>> the passbamd of the FIR) It many cases, you have plenty of MIPS for
>> the additional non zero calculations. The length of the FIR filter
>> needs to be long enough to accommodate the lowest frequency of
>> interest. If you want a 90 phase shift of DC, it would take a FIR
>> filter with infinite taps (it would have a very long group delay as
>> well).
>
> In my limited experience, if a longer filter is no problem, windowed
> filters can execute faster. Although they have longer delay lines, one
> can step through them with a stride of two. I found that a Nuttall
> window worked very well.
>
> Jerry

Clearly, an advantage of the windowed filters is that you can use a
filter of twice the length for the same computation cost (and twice the
group delay).

This is a good illustration of "there's no free lunch" principle. It's
always about balancing one choice against another.

--
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com
.

Relevant Pages

  • Re: Hilbert transform using FFT approach
    ... >>> The alternate taps are not always 0. ... >>> to be true) for window based designs of Hilbert transformers. ... >>> except the middle coefficient for an odd length FIR filter. ... >>> although the phase will always be exactly 90 degrees apart if the FIR ...
    (comp.dsp)
  • Re: Envelope Detection
    ... You use an FIR to do the transform. ... Odd numbers of taps have the advantage that the properly delayed ... In order not to waste the end coefficients, ... window for 4k+1 if it tapers to zero at the ends. ...
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  • Re: LP Filter - Minimize Ringing
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  • Re: Equalization using DFT
    ... in a windowed sinc type filter correct? ... designing the filter using the window method with a hamming window? ... A proper way to design the frequency mask for use with this method if to select the impulse response corresponding to the filter you want, and then FFT that to get the mask. ... A hamming or other tapered window can be useful in making a mask for an FFT FIT, just as it is when calculating coefficients for a transversal FIR. ...
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  • Re: Relation between length of a filter and number of taps
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