Complementary filters

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5 total messages Started by Vance Maverick Tue, 04 Dec 1990 18:38

#1162

Author: Vance Maverick
Date: Tue, 04 Dec 1990 18:38

13 lines
1186 bytes

In the computer-music literature, I've seen the term "complementary"
used to describe a pair of filters.  For example, in the waveguide
clarinet model proposed by Julius Smith, the signal traveling down the
bore is partly transmitted and partly reflected; the reflected version
is lowpass, the transmitted version is highpass.  These filters are
described as complementary, which I take to mean that, at any given
frequency, the sum of the energy coming out of the two filters is equal
to the energy going down the bore.

Is there a recipe for generating the "complement" of a given filter?  Or
for generating a pair of filters which are complementary in this sense? 
I've seen the basic transformations between lowpass and highpass
filters, and I don't think they qualify.

Re: Complementary filters

#1357

Author: Joe Buck
Date: Wed, 05 Dec 1990 19:24

21 lines
1280 bytes

In article <9441@pasteur.Berkeley.EDU>, maverick@fir.Berkeley.EDU (Vance Maverick) writes:
> Is there a recipe for generating the "complement" of a given filter?  Or
> for generating a pair of filters which are complementary in this sense? 
> I've seen the basic transformations between lowpass and highpass
> filters, and I don't think they qualify.

It's easy.  You want the two filters to sum to one; equivalently, you
want the sums of the two impulse responses to sum to 1 for n=0 and
0 for everywhere else.  Let's say you have an FIR filter and you want
its complement.  Let h(n) be the value of the nth tap of the filter.
Then

c(0) = 1 - h(0)
c(n) = -h(n), n > 0

Voila.  Note that the outputs of the two filters sum to give the
original signal back.

--
Joe Buck
jbuck@galileo.berkeley.edu	 {uunet,ucbvax}!galileo.berkeley.edu!jbuck

Re: Complementary filters

#1348

Author: Bruce Karsh
Date: Fri, 07 Dec 1990 05:03

12 lines
1028 bytes

In article <9441@pasteur.Berkeley.EDU> maverick@fir.Berkeley.EDU (Vance Maverick) writes:

>Is there a recipe for generating the "complement" of a given filter?  Or
>for generating a pair of filters which are complementary in this sense? 
>I've seen the basic transformations between lowpass and highpass
>filters, and I don't think they qualify.

Generate one of the too signals, e.g. the low passed signal.  Subtract it
from the original signal to get the high passed signal.

			Bruce Karsh
			karsh@sgi.com

Re: Complementary filters

#1351

Author: Wilf Leblanc
Date: Fri, 07 Dec 1990 21:04

33 lines
1605 bytes

karsh@trifolium.esd.sgi.com (Bruce Karsh) writes:

>In article <9441@pasteur.Berkeley.EDU> maverick@fir.Berkeley.EDU (Vance Maverick) writes:

>>Is there a recipe for generating the "complement" of a given filter?  Or
>>for generating a pair of filters which are complementary in this sense? 
>>I've seen the basic transformations between lowpass and highpass
>>filters, and I don't think they qualify.

>Generate one of the too signals, e.g. the low passed signal.  Subtract it
>from the original signal to get the high passed signal.

>			Bruce Karsh
>			karsh@sgi.com

This is a nice idea, but it won't work in general.

If H(z) is the low pass prototype, then, 1 - H(z)
is a high pass ?  No, sorry this does not work.

i.e., say H(e^jw) = j  (at a certain low frequency).
Then 1 - H(e^jw) = 1 - j (which is nothing like a high pass).

i.e. simple subtraction doesn't consider the phase response of
H(z).


Something must have been written on this, what about Quadrature Mirror
Filterbanks ??
--
Wilf LeBlanc                                 Carleton University
Internet: wilf@sce.carleton.ca               Systems & Computer Eng.
    UUCP: ...!uunet!mitel!cunews!sce!wilf    Ottawa, Ont, Canada, K1S 5B6

Compression Techniques for Speech

#1371

Author: Daniel Collins
Date: Wed, 12 Dec 1990 18:35

9 lines
929 bytes

I am working on a project where I have to compress a speech signal  
by 20-to-1 ratio in real-time.  If 20-to-1 not practical, what are 
limiting factors, and what is achievable I will be using an 8 bit ADC 
with a 8KHz conversion rate.  Can anyone offer any pointers to DSP 
chips, other special purpose chips, literature, code fragments, etc. 

Dan Collins
dcollins@pittslug.sug.org

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