nick@paladin.Owego.NY.US (Carmine Nicoletta) (10/09/90)
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. Please respond via E-mail.
davew@hp-ptp.HP.COM (Dave_Waller) (10/10/90)
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!)
larry@kitty.UUCP (Larry Lippman) (10/11/90)
In article <1920001@hp-ptp.HP.COM>, davew@hp-ptp.HP.COM (Dave_Waller) writes: > 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. I always thought that the Putz-Schmuckmann function was used to describe the instantaneous signal-grid transconductance of fallopian tubes. :-) Larry Lippman @ Recognition Research Corp. "Have you hugged your cat today?" VOICE: 716/688-1231 {boulder, rutgers, watmath}!ub!kitty!larry FAX: 716/741-9635 {utzoo, uunet}!/ \aerion!larry
davew@hp-ptp.HP.COM (Dave_Waller) (10/12/90)
larry@kitty.UUCP (Larry Lippman) writes: > In article <1920001@hp-ptp.HP.COM>, davew@hp-ptp.HP.COM (Dave_Waller) writes: > > 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. > > I always thought that the Putz-Schmuckmann function was used to > describe the instantaneous signal-grid transconductance of fallopian tubes. > It is; however when the Putz-Schmuckmann function is integrated over the TIME domain (assuming frequency invariancy), hyperbolic incongruities cancel out (rather nicely, I might add), leaving behind a value proportional to the instantaneous signal-grid transconductance of fallopian tubes. The proportionality constant depends upon the age of the woman in question. > :-) > > Larry Lippman @ Recognition Research Corp. "Have you hugged your cat today?" > VOICE: 716/688-1231 {boulder, rutgers, watmath}!ub!kitty!larry > FAX: 716/741-9635 {utzoo, uunet}!/ \aerion!larry > ---------- :-) again. 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!)
markz@ssc.UUCP (Mark Zenier) (10/12/90)
In article <1920001@hp-ptp.HP.COM>, davew@hp-ptp.HP.COM (Dave_Waller) writes: > nick@paladin.Owego.NY.US (Carmine Nicoletta) writes: > > 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. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (Thanks for subverting that damn followup ) Since when is time multidimensional? Or are you trying to get a phase detector? Mark Zenier markz@ssc.uucp