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questions raised by reading and thinking with possibly missing background

Started by Richard Owlett December 10, 2005
I'm interested in speech recognition.
One of current problems seems to be requiring a "good" acoustic 
environment. I have "gut feel" that appropriate filtering of input would 
be useful.

That got me thinking of restrictions on filtering methods.
It also got me interested in DSP.

I start with a basic presupposition that however humans recognize speech 
is, in some sense, the "best" way. That leads me to believe that any 
filtering should be constant group delay -- ie linear phase.

I have an idea of what might be a useful frequency response - 4 or 5 
'humps' corresponding to formant frequencies.

If implemented as a FIR filter can it be 'linear phase'.

Looking at a pdf discussing various windows, I think individual 
frequency responses similar to shape of a "Blackman Window" would be 
optimal. The individual pass band peaks would probably be at least a 1/2 
octave apart.

what would be relative advantages of implementing:
1. by adding outputs of individual filters
2. a single filter with appropriate frequency response

Separate topic -- how many issues have I missed?

BTW -- Remember the number one rule of education: A paragraph in a book 
doesn't give you a license to stop thinking.
(seen on WEB somewhere)
Richard Owlett wrote:

   ...

> I start with a basic presupposition that however humans recognize speech > is, in some sense, the "best" way. That leads me to believe that any > filtering should be constant group delay -- ie linear phase.
I don't see the connection between "human" and "constant group delay". Is there an unexamined (or at least unexpressed) assumption involved?
> I have an idea of what might be a useful frequency response - 4 or 5 > 'humps' corresponding to formant frequencies.
Formant frequencies vary among individuals, and we are very sensitive to such variations. (I can distinguish my identical twin sisters by voice or sneeze.)
> If implemented as a FIR filter can it be 'linear phase'. > > Looking at a pdf discussing various windows, I think individual > frequency responses similar to shape of a "Blackman Window" would be > optimal. The individual pass band peaks would probably be at least a 1/2 > octave apart.
How would you measure the frequency response of a window? (I don't mean to claim that you cant, provided other factors are specified.) Windows are typically applied to time-domain data.
> what would be relative advantages of implementing: > 1. by adding outputs of individual filters
Easier to design?
> 2. a single filter with appropriate frequency response
easier to program?
> Separate topic -- how many issues have I missed?
I don't know. How many false assumptions have you made? At this stage, spell out your assumptions, even if it seems tedious.
> BTW -- Remember the number one rule of education: A paragraph in a book > doesn't give you a license to stop thinking. > (seen on WEB somewhere)
That's a good rule, but "the one rule"? Nah! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Jerry Avins wrote:
> Richard Owlett wrote: > > ... > >> I start with a basic presupposition that however humans recognize >> speech is, in some sense, the "best" way. That leads me to believe >> that any filtering should be constant group delay -- ie linear phase. > > I don't see the connection between "human" and "constant group delay". > Is there an unexamined (or at least unexpressed) assumption involved?
Yes I was explicitly assuming the connection. Maybe "presuming" would be a better word. But as it led to my question, we'll just take it as a given whether or not it is an accurate description of reality.
> >> I have an idea of what might be a useful frequency response - 4 or 5 >> 'humps' corresponding to formant frequencies. > > Formant frequencies vary among individuals, and we are very sensitive to > such variations. (I can distinguish my identical twin sisters by voice > or sneeze.)
Yes, and I was going to identify formant frequencies during training mode. Doing much violence to standard nomenclature, I was thinking in terms of "voice pass" and "interference stop" filters. The "why" and "reasonableness" is *OT* for my question. Please take as a given that I wish a passband filter with a particular arbitrary lumpy shape which is also linear phase.
> >> If implemented as a FIR filter can it be 'linear phase'. >> >> Looking at a pdf discussing various windows, I think individual >> frequency responses similar to shape of a "Blackman Window" would be >> optimal. The individual pass band peaks would probably be at least a >> 1/2 octave apart. > > How would you measure the frequency response of a window? (I don't mean > to claim that you cant, provided other factors are specified.) Windows > are typically applied to time-domain data.
Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ". I was looking at various windows and their transforms. A DFT/IFT has no way of knowing that the numbers it feeds upon are in time or frequency domain.
> >> what would be relative advantages of implementing: >> 1. by adding outputs of individual filters > > Easier to design? > >> 2. a single filter with appropriate frequency response > > easier to program?
I'll try to rephrase in "domain neutral" terms. -- Then again that will cause more problems than it's worth ;{ [--- perhaps very relevant side issue If linear superposition applies in time/frequency domain, does it survive FT to frequency/time domain followed by IFT back to time/frequency domain? ---] I'll restate my problem. For arbitrary and unchangeable reasons I wish a filter defined in frequency domain to have certain characteristics. 1. it *shall* be linear phase 2. its passband is of arbitrary shape a. it can be treated as a whole b. it can be seen as linear superposition of a few simple terms So I repeat my basic question What would be relative advantages of implementing: 1. by adding outputs of individual filters 2. a single filter with appropriate frequency response
> >> Separate topic -- how many issues have I missed? > > > I don't know. How many false assumptions have you made? At this stage, > spell out your assumptions, even if it seems tedious. > >> BTW -- Remember the number one rule of education: A paragraph in a >> book doesn't give you a license to stop thinking. >> (seen on WEB somewhere) > > > That's a good rule, but "the one rule"? Nah!
It only said "number one rule", it did not say "the *only* rule" ;)
Richard Owlett <rowlett@atlascomm.net> writes:

> I'll restate my problem. > For arbitrary and unchangeable reasons I wish a filter defined in > frequency domain to have certain characteristics. > > 1. it *shall* be linear phase > 2. its passband is of arbitrary shape > a. it can be treated as a whole > b. it can be seen as linear superposition of a few simple terms > > So I repeat my basic question > What would be relative advantages of implementing: > 1. by adding outputs of individual filters
This option might be nice if you're thinking along the lines of a graphic equalizer: being able to arbitrarily change the gain (volume) of a particular band of frequencies might be useful.
> 2. a single filter with appropriate frequency response
This might be good if you know that the response doesn't have to change much. Changing this sort of a filter on-the-fly, though, might be problematic. Ciao, Peter K.
Richard Owlett wrote:
> Jerry Avins wrote: > >> Richard Owlett wrote: >> >> ... >> >>> I start with a basic presupposition that however humans recognize >>> speech is, in some sense, the "best" way. That leads me to believe >>> that any filtering should be constant group delay -- ie linear phase. >> >> >> I don't see the connection between "human" and "constant group delay". >> Is there an unexamined (or at least unexpressed) assumption involved? > > > Yes I was explicitly assuming the connection. Maybe "presuming" would be > a better word. But as it led to my question, we'll just take it as a > given whether or not it is an accurate description of reality. > >> >>> I have an idea of what might be a useful frequency response - 4 or 5 >>> 'humps' corresponding to formant frequencies. >> >> >> Formant frequencies vary among individuals, and we are very sensitive >> to such variations. (I can distinguish my identical twin sisters by >> voice or sneeze.) > > > Yes, and I was going to identify formant frequencies during training > mode. Doing much violence to standard nomenclature, I was thinking in > terms of "voice pass" and "interference stop" filters. The "why" and > "reasonableness" is *OT* for my question. > > Please take as a given that I wish a passband filter with a particular > arbitrary lumpy shape which is also linear phase. > >> >>> If implemented as a FIR filter can it be 'linear phase'. >>> >>> Looking at a pdf discussing various windows, I think individual >>> frequency responses similar to shape of a "Blackman Window" would be >>> optimal. The individual pass band peaks would probably be at least a >>> 1/2 octave apart. >> >> >> How would you measure the frequency response of a window? (I don't >> mean to claim that you cant, provided other factors are specified.) >> Windows are typically applied to time-domain data. > > > Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ". > I was looking at various windows and their transforms. > A DFT/IFT has no way of knowing that the numbers it feeds upon are in > time or frequency domain.
The the differences between the shapes of filters is subtle. If those filters without steps at the ends, I find it difficult to distinguish a Blackman from Nuttall, Blackman-Harris, von Hann, and others. What distinguishing feature of Blackman attracts you?
>>> what would be relative advantages of implementing: >>> 1. by adding outputs of individual filters >> >> >> Easier to design? >> >>> 2. a single filter with appropriate frequency response >> >> >> easier to program? > > > I'll try to rephrase in "domain neutral" terms. > -- Then again that will cause more problems than it's worth ;{ > > [--- perhaps very relevant side issue > If linear superposition applies in time/frequency domain, does > it survive FT to frequency/time domain followed by IFT back to > time/frequency domain? > ---]
Yes
> I'll restate my problem. > For arbitrary and unchangeable reasons I wish a filter defined in > frequency domain to have certain characteristics. > > 1. it *shall* be linear phase > 2. its passband is of arbitrary shape > a. it can be treated as a whole > b. it can be seen as linear superposition of a few simple terms > > So I repeat my basic question > What would be relative advantages of implementing: > 1. by adding outputs of individual filters
Easier to design?
> 2. a single filter with appropriate frequency response
Easier to program? ... Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Peter K. wrote:
> Richard Owlett <rowlett@atlascomm.net> writes: > > >>I'll restate my problem. >>For arbitrary and unchangeable reasons I wish a filter defined in >>frequency domain to have certain characteristics. >> >>1. it *shall* be linear phase >>2. its passband is of arbitrary shape >> a. it can be treated as a whole >> b. it can be seen as linear superposition of a few simple terms >> >>So I repeat my basic question >>What would be relative advantages of implementing: >>1. by adding outputs of individual filters > > > This option might be nice if you're thinking along the lines of a > graphic equalizer: being able to arbitrarily change the gain (volume) > of a particular band of frequencies might be useful. > > >>2. a single filter with appropriate frequency response > > > This might be good if you know that the response doesn't have to > change much. Changing this sort of a filter on-the-fly, though, might > be problematic. > > Ciao, > > Peter K. > >
It would be set once per "user".
Jerry Avins wrote:

> Richard Owlett wrote: > >> Jerry Avins wrote: >> >>> Richard Owlett wrote: >>> ... >>>> I start with a basic presupposition that however humans recognize >>>> speech is, in some sense, the "best" way. That leads me to believe >>>> that any filtering should be constant group delay -- ie linear phase. >>> >>> I don't see the connection between "human" and "constant group >>> delay". Is there an unexamined (or at least unexpressed) assumption >>> involved? >> >> Yes I was explicitly assuming the connection. Maybe "presuming" would >> be a better word. But as it led to my question, we'll just take it as >> a given whether or not it is an accurate description of reality. >> >>> >>>> I have an idea of what might be a useful frequency response - 4 or 5 >>>> 'humps' corresponding to formant frequencies. >>> >>> Formant frequencies vary among individuals, and we are very sensitive >>> to such variations. (I can distinguish my identical twin sisters by >>> voice or sneeze.) >> >> Yes, and I was going to identify formant frequencies during training >> mode. Doing much violence to standard nomenclature, I was thinking in >> terms of "voice pass" and "interference stop" filters. The "why" and >> "reasonableness" is *OT* for my question. >> >> Please take as a given that I wish a passband filter with a particular >> arbitrary lumpy shape which is also linear phase. >> >>> >>>> If implemented as a FIR filter can it be 'linear phase'. >>>> >>>> Looking at a pdf discussing various windows, I think individual >>>> frequency responses similar to shape of a "Blackman Window" would be >>>> optimal. The individual pass band peaks would probably be at least a >>>> 1/2 octave apart. >>> >>> How would you measure the frequency response of a window? (I don't >>> mean to claim that you cant, provided other factors are specified.) >>> Windows are typically applied to time-domain data. >> >> Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ". >> I was looking at various windows and their transforms. >> A DFT/IFT has no way of knowing that the numbers it feeds upon are in >> time or frequency domain. > > > The the differences between the shapes of filters is subtle. If those > filters without steps at the ends, I find it difficult to distinguish a > Blackman from Nuttall, Blackman-Harris, von Hann, and others. What > distinguishing feature of Blackman attracts you?
I have a pdf of unknown title ( got saved as Windows.pdf ) written by Craig Stuart Sapp <craig@ccrma.stanford.edu> 25 Feb 1997. I has a collection of various windows and their transforms. The particular Blackman window illustrated had a "nice" central lobe and all the residual lobes were of "uniform" shape and at least 60 dB down. *DARN YOU MR. AVINS* You just made me read rather than just look at pretty pictures ;{ The plot of the particular Blackman-Harris window had max side lobes another 20 dB down, but scale of drawing emphasized the side lobes near the central one. Transform of illustrated Hann window -- too much slop Transform of illustrated Hann-Poisson window has a "pleasing shape" with less "rejection" off central peak. I've been "hit over head with 2x4" on another issue. What a implications of all these being symmetric about some point. Obviously if I'm going to have "passband 1 of width a centered at freq b" and "passband 2 of width y centered at freq z" what strange effects will asymmetry have?
> >>>> what would be relative advantages of implementing: >>>> 1. by adding outputs of individual filters >>> >>> Easier to design? >>> >>>> 2. a single filter with appropriate frequency response >>> >>> easier to program? >> >> I'll try to rephrase in "domain neutral" terms. >> -- Then again that will cause more problems than it's worth ;{ >> >> [--- perhaps very relevant side issue >> If linear superposition applies in time/frequency domain, does >> it survive FT to frequency/time domain followed by IFT back to >> time/frequency domain? >> ---] > > > Yes > >> I'll restate my problem. >> For arbitrary and unchangeable reasons I wish a filter defined in >> frequency domain to have certain characteristics. >> >> 1. it *shall* be linear phase >> 2. its passband is of arbitrary shape >> a. it can be treated as a whole >> b. it can be seen as linear superposition of a few simple terms >> >> So I repeat my basic question >> What would be relative advantages of implementing: >> 1. by adding outputs of individual filters > > > Easier to design? > >> 2. a single filter with appropriate frequency response > > > Easier to program? > > ... > > Jerry
Richard Owlett wrote:

> ... > That got me thinking ;<
What are the *NECESSARY* conditions for a FIR filter of an arbitrary shape in the frequency domain to be "linear phase". One of the references I was reading stated that "a FIR filter would be 'linear phase' if its coefficients were symmetric about the middle coefficient." Is that a "sufficient" condition or a "necessary" condition? What implication does it have for the passband response?
Richard Owlett <rowlett@atlascomm.net> writes:

> Richard Owlett wrote: > >> ... >> That got me thinking ;< > > What are the *NECESSARY* conditions for a FIR filter of an arbitrary > shape in the frequency domain to be "linear phase". > > One of the references I was reading stated that "a FIR filter would be > 'linear phase' if its coefficients were symmetric about the middle > coefficient." > > Is that a "sufficient" condition or a "necessary" condition? > What implication does it have for the passband response?
Hi Richard, It is a sufficient condition. A trivial example of an FIR filter that does not meet this condition but is still linear phase is the FIR given by h[0] = 0, h[1] = 0, and h[2] = 1. I've heard that a linear-phase filter has magnitude and phase responses that are Hilbert transforms of each other, but I've never been interested enough to investigate. -- % Randy Yates % "Rollin' and riding and slippin' and %% Fuquay-Varina, NC % sliding, it's magic." %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Living' Thing', *A New World Record*, ELO http://home.earthlink.net/~yatescr
Randy Yates <yates@ieee.org> writes:
> [...] > I've heard that a linear-phase filter has magnitude and phase > responses that are Hilbert transforms of each other, but I've > never been interested enough to investigate.
Sorry - correction!: Those are *minimum-phase* filters. -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://home.earthlink.net/~yatescr