Re: Some questions on digital filter design
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Reg, my apologies, but I'm confused as to what you are trying to say.
It looks to me as though you are discussing a standard Finite-Impulse-Response (FIR) filter, which can be thought of as a physical realization of a convolution integral, in which the input signal is convolved with the impulse response of the filter being realized.
I don't know what you mean when you say "the filter output begins *before* the input arrives."
The filter output is not starting *before* the signal arrives -- it starts *the moment* the signal arrives.? If you were to connect the filter's input and output signals to two channels of a scope and then generate, as an input, a gated signal, you'd see on the output channel a filtered version of that gated signal that looks like it has been delayed, in time, by half the number of FIR taps (actually, the delay is (N-1/)2, where N is the number of taps).
My apologies if I am misinterpreting the point you are trying to make.
Best regards,
- Jeff, k6jca
On Saturday, July 6, 2024 at 06:54:36 AM PDT, Reginald Beardsley via groups.io <pulaskite@...> wrote:
I?am?working?on?numerical?modeling?of?CCW?and?am?at?the?point?that?I?need?to?write?the?code?to?implement?twin?pass?band?tuning.??As?this?is?NOT?seismic?processing?I?pulled?a?small?stack?of?my?EE?DSP?classics?and?started?reading?them.
I?have?always?found?the?descriptions?of?digital?filter?design?in?the?EE?literature?baffling?complex.??As?seismic?is?done?in?recorded?time?it?has?a?great?deal?of?latitude?in?implementation?that?a?real?time?DSP?implementation??lacks.??So?I?presumed?that?the?reason?lay?in?the?real?time?constraint.
Yesterday?I?realized?that?the?design??of?a?static?filter?is?completely?trivial.??Specify?the?frequency?domain?characteristics?and?back?transform?to?the?time?domain.??The?impulse?response?is?the?taps?for?any?arbitrary?filter.??I?also?noticed?that?the?filters?in?the?examples?were?zero?phase?filters.
In?seismic?we?always?use?zero?phase?(aka?"linear?phase"?in?EE?jargon)??filters?as?interpreting?a?symmetric?waveform?is?much?easier.
The?first?step?in?seismic?processing?is?called?"designature".??This?consists?of?using?a?recording?of?the??system?impulse?response?to?create?an?all?pass?filter?which?removes?the?phase?imposed?by?causality.??Typically?the?recording?system?impulse?response?is?measured?and??then?the?phase?of?the?source?is?recorded?for?marine?work?using?arrays?of?air?guns.
Analog?filters?are?minimum?phase?as?are?all?physical?processes.??But?the?digital?design?examples?I?saw?were?zero?phase?with?a?symmetric?impulse?response.??This?leads?to?a?non-physical?result.??The?filter?output?begins?*before*?the?input?arrives.??I?find?that?rather?hard?to?justify?in?a?communication?system.??A?quick?check?of?the?indices?revealed?that?except?for?a?very?brief?mention?of?minimum?phase?and?causality?the?issue?is?completely?ignored.??Oppenheim?and?Schafer?devote?a?few?page?and?Rabiner??and?Gold?a?paragraph?before?dismissing?the?matter.? Another text made no mention of it at all.
Would?a?DSO?which?responded?to?an?impulse?showing?the?trace?varying?*before*?the?peak?of?the?impulse?be?acceptable???I?can't?imagine?why?anyone?would?accept?that.
So?why?should?it?be?acceptable?in?a?communication?system???Can?anyone?elucidate?the?matter?
Have?Fun!
Reg
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