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From: davew@hp-ptp.HP.COM (Dave_Waller)
Newsgroups: sci.electronics
Subject: Re: Orthogonality in general
Message-ID: <1920001@hp-ptp.HP.COM>
Date: 9 Oct 90 21:08:28 GMT
References: <675@paladin.Owego.NY.US>
Organization: HP Pacific Technology Park - Sunnyvale, Ca.
Lines: 36

nick@paladin.Owego.NY.US (Carmine Nicoletta) writes:
> In signal detection of M-ary signals, there is often the need to obtain 
> orthonormal basis vector sets.  There are many suitable choices, the most
> ovious are sin(x) and cos(x).  But there are also Legendre functions, Hermite
> functions, and Bessel functions.
> For a finite set of signals, s1(t), s2(t),.... sm(t) defined on some interval,
> an orthonormal basis for the signal space can be obtained by using the
> Gram-Schmidt procedure.  This is a very straight forward procedure discussed
> in many Linear Algebra texts.
> My problem is this: how does this procedure relate to frequency response of
> filters.  For example, how does one come up with an N set of filters whose
> frequency responses are orthogonal to each other.

The answer to this is obvious. Frequency response in this situation is
described by the Putz-Schmuckmann function, integrated over the
frequency domain for time-invariancy. With this result, the time domain
representation of a filter can be convoluted using semiharmonic
imaginary logs, resulting in a homogenous well-behaved function that is
linear over a range suitable to your problem.

Or, you can hook up a resistor and a cap and wing it.







Oh yeah, :-) :-) :-) :-) :-)

Thanks for reminding me, Carmine, how much I've forgotten since school.
The above blathering is for entertainment purposes only.

Dave Waller  \  The opinions expressed are solely my own, and in no way
Hewlett-Packard Co.  \  represent those of my employer (but we all know
dave@hpdstma.ptp.hp.com | hplabs!hpdstma!dave  \  they should!)