Re: Detecting a waveform at arbitrary positions and scales


"Randy Yates" <yates@xxxxxxxx> wrote in message
news:m33aeaduge.fsf@xxxxxxxxxxxxxxxxxx
Vladimir Vassilevsky <antispam_bogus@xxxxxxxxxxx> writes:

Randy Yates wrote:

Given a reference signal r(t) defined over the interval T1 < t < T2,
what practical algorithm can be used to detect A*r(B*t + C) in a given
input signal x(t), where A, B, and C are unknown?

This is the inverse problem.
What is known about r(t) ? Is it linear or at least analytical
function?

Hi Vladimir,

The "inverse problem." Hmmm - ok.

For the sake of illustration, make any assumptions you'd like regarding
r(t).

If r(t) is analytical then you can take partial derivatives by A, B, C and
solve for the best match. Furthermore, if r(t) is linear then the solution
is likely to be unique and easy to find.

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com


.

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