How to design this complex filter?

Hi all.
   I'm in trouble on designing this linear time-invariant digital
filter. It has five peaks and two notches in its magnitude frequency
response. Each peak/notch is specified by its frequency, 3dB-bandwidth
and magnitude. These parameters and of course, the sampling frequency,
can be chosen arbitrarily. Please give me any solution. Thanks in
advance.
   Best regards,
   Canmc

canmc wrote:
> Hi all.
>    I'm in trouble on designing this linear time-invariant digital
> filter. It has five peaks and two notches in its magnitude frequency
> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> and magnitude. These parameters and of course, the sampling frequency,
> can be chosen arbitrarily. Please give me any solution. Thanks in
> advance.
>    Best regards,
>    Canmc

What do you want to use it for? IIR, or FIR? More than two notches are
needed to separate five peaks, so something is missing in the spec.

Jerry
-- 
... they proceeded on the sound principle that the magnitude of a lie
always contains a certain factor of credibility, ... and that therefor
... they more easily fall victim to a big lie than to a little one ...
                                                                   A. H.
�����������������������������������������������������������������������

Jerry Avins wrote:
> canmc wrote:
> 
>> Hi all.
>>    I'm in trouble on designing this linear time-invariant digital
>> filter. It has five peaks and two notches in its magnitude frequency
>> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
>> and magnitude. These parameters and of course, the sampling frequency,
>> can be chosen arbitrarily. Please give me any solution. Thanks in
>> advance.
>>    Best regards,
>>    Canmc
> 
> 
> What do you want to use it for? IIR, or FIR? More than two notches are
> needed to separate five peaks, so something is missing in the spec.
> 
> Jerry

Since this was posted to comp.speech.research , I suspect the five peaks 
correspond to five formants in a speech signal and the two notches to a 
specific interference problem.

On Tue, 05 Oct 2004 23:26:21 -0400, Jerry Avins <jya@ieee.org> wrote:

>canmc wrote:
>> Hi all.
>>    I'm in trouble on designing this linear time-invariant digital
>> filter. It has five peaks and two notches in its magnitude frequency
>> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
>> and magnitude. These parameters and of course, the sampling frequency,
>> can be chosen arbitrarily. Please give me any solution. Thanks in
>> advance.
>>    Best regards,
>>    Canmc
>
>What do you want to use it for? IIR, or FIR? More than two notches are
>needed to separate five peaks, so something is missing in the spec.
>
>Jerry

Sniff, sniff, ... do I smell a homework problem here?
You want to design a filter whose parameters are arbitrary 
*and* the sample rate of your input data is not specified.  
Humm, something's "fishy" here.

To add to Jerry's questions:

In your "Subject:", you wrote "complex filter".
By "complex" do you mean "complicated", or do you 
mean "complex-valued (I & Q) filter coefficients"?

Do those "five peaks and two notches" cover the filter's 
positive and negative frequency range, or just the 
positive frequency range?

[-Rick-]

Richard Owlett wrote:

> Jerry Avins wrote:
> 
>> canmc wrote:
>>
>>> Hi all.
>>>    I'm in trouble on designing this linear time-invariant digital
>>> filter. It has five peaks and two notches in its magnitude frequency
>>> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
>>> and magnitude. These parameters and of course, the sampling frequency,
>>> can be chosen arbitrarily. Please give me any solution. Thanks in
>>> advance.
>>>    Best regards,
>>>    Canmc
>>
>>
>>
>> What do you want to use it for? IIR, or FIR? More than two notches are
>> needed to separate five peaks, so something is missing in the spec.
>>
>> Jerry
> 
> 
> Since this was posted to comp.speech.research , I suspect the five peaks 
> correspond to five formants in a speech signal and the two notches to a 
> specific interference problem.
> 


I found a plot of a typical formant spectra at 
http://www.brunel.ac.uk/depts/ee/Research_Programme/COM/Home_Esfandiar/Formants.htm

http://www.harmony-central.com/Computer/Programming/Audio-EQ-Cookbook.txt shows
how to compute peaking/notch filters (as well as some other common ones).
String together 7 of those biquads in series and you should be in business.

"canmc" <canmcbk@yahoo.com> wrote in message
news:a01b5002.0410051902.4cccb48e@posting.google.com...
> Hi all.
>    I'm in trouble on designing this linear time-invariant digital
> filter. It has five peaks and two notches in its magnitude frequency
> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> and magnitude. These parameters and of course, the sampling frequency,
> can be chosen arbitrarily. Please give me any solution. Thanks in
> advance.
>    Best regards,
>    Canmc

canmcbk@yahoo.com (canmc) wrote in message news:<a01b5002.0410051902.4cccb48e@posting.google.com>...
> Hi all.
>    I'm in trouble on designing this linear time-invariant digital
> filter. It has five peaks and two notches in its magnitude frequency
> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> and magnitude. These parameters and of course, the sampling frequency,
> can be chosen arbitrarily. Please give me any solution. Thanks in
> advance.
>    Best regards,
>    Canmc

Hi, I'm new to this group, I guess you could call me a 'long time
listener-first time caller'. The filter you need only looks
complicated because you are trying to think of it as one big filter.
As John has already pointed out, you need a bunch of filters. A good
place to start for the peaking filters is what's known as a 'reson'
filter to dsp audio effects gurus (which I am not).
It can be parameterised in terms of it's centre frequency and 3dB
bandwidth and tweaked for gain. It's basically a discrete time
equivalent of an LCR tank resonant circuit. A good book on this
subject is Digital Signal Processing-A Primer, by Ken Steiglitz. I'm
not at home so I don't have the publisher info but I can remember the
formulae to convert the parameters to filter co-efficients, let me
know if you want me to post them. Another point of caution,
if you are using peaking filters like this you need to apply them in
parallel
and not in series as Jon pointed out. I.e. sum the outputs of the
seperate sections. Hope this helps.

Jerry Avins <jya@ieee.org> wrote in message news:<cjvol0$o1j$1@bob.news.rcn.net>...
> canmc wrote:
> > Hi all.
> >    I'm in trouble on designing this linear time-invariant digital
> > filter. It has five peaks and two notches in its magnitude frequency
> > response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> > and magnitude. These parameters and of course, the sampling frequency,
> > can be chosen arbitrarily. Please give me any solution. Thanks in
> > advance.
> >    Best regards,
> >    Canmc
> 
> What do you want to use it for? IIR, or FIR? More than two notches are
> needed to separate five peaks, so something is missing in the spec.
> 
> Jerry

Hi Jerry,

Thanks for your interest. The filter is intended to be used for
synthesizing any single voiced sound from glottal waveform. But
another more important use of its is that its inverse version,e.g the
inverse filter, can be used to obtain the glottal source from any
single voiced speech waveform. The filter can be IIR or FIR.

> More than two notches are needed to separate five peaks, so something is 
> missing in the spec.

I don't understand this. Please give me further explanation.

Best regards,
Canmc

davec@quantized.com (David Coffey) wrote 
> canmcbk@yahoo.com (canmc) wrote in message 
> >    I'm in trouble on designing this linear time-invariant digital
> > filter. It has five peaks and two notches in its magnitude frequency
> > response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> > and magnitude. These parameters and of course, the sampling frequency,
> > can be chosen arbitrarily. 
> >    Canmc
> 
> The filter you need only looks
> complicated because you are trying to think of it as one big filter.
> As John has already pointed out, you need a bunch of filters.Another point of caution,
> if you are using peaking filters like this you need to apply them in
> parallel
> and not in series as Jon pointed out. I.e. sum the outputs of the
> seperate sections. Hope this helps.

Hi.
It is simple to implement a digital resonator/anti-resonator given the
parameters as I said previously. The problem is that when these
peak/notch filters are combined in series/parallel, the parameters of
each peak/notch in the magnitude response of the resulting filter will
be changed. It's hard for me to find out how to combine the component
filters and the parameters of each to meet a given magnitude response.
Combining some peak filters in parallel as you proposed will result in
some notches undesired in the resulting magnitude response. Thanks
anyway.

Regards,
Canmc

r.lyons@_BOGUS_ieee.org (Rick Lyons) wrote in message news:<4163c0f8.257202843@news.sf.sbcglobal.net>...

> >canmc wrote:
> >> Hi all.
> >>    I'm in trouble on designing this linear time-invariant digital
> >> filter. It has five peaks and two notches in its magnitude frequency
> >> response. Each peak/notch is specified by its frequency, 3dB-bandwidth
> >> and magnitude. These parameters and of course, the sampling frequency,
> >> can be chosen arbitrarily. Please give me any solution. Thanks in
> >> advance.
> >>    Best regards,
> >>    Canmc
> >
> 
> In your "Subject:", you wrote "complex filter".
> By "complex" do you mean "complicated", or do you 
> mean "complex-valued (I & Q) filter coefficients"?
> 
> Do those "five peaks and two notches" cover the filter's 
> positive and negative frequency range, or just the 
> positive frequency range?
> 
> [-Rick-]

Hi,
It takes me a long time to work on this filter. So it's complex for
me. Of course, the filter has only real coefficients and I only
concern positive frequency range.

Regards,
Canmc