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? -- % Randy Yates % "With time with what you've learned, %% Fuquay-Varina, NC % they'll kiss the ground you walk %%% 919-577-9882 % upon." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://www.digitalsignallabs.com
Detecting a waveform at arbitrary positions and scales
Started by ●February 19, 2009
Reply by ●February 19, 20092009-02-19
On Feb 19, 8:02�pm, Randy Yates <ya...@ieee.org> 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?Are we supposed to assume that the signal is of the form: f(t) , -infty < t <= (T1 - C) / B A r(Bt + C) , (T1 - C) / B < t < (T2 - C) / B g(t) , (T2 - C) / B < t < infty ? If not, what do you mean by "in a given input signal"? illywhacker;
Reply by ●February 19, 20092009-02-19
Randy Yates <yates@ieee.org> writes:> 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?Let's give some constraints too: -1 <= A <= +1 0 < B < 1 -1 <= C <= +1 (T2 - T1)*B < 2 -- % Randy Yates % "Bird, on the wing, %% Fuquay-Varina, NC % goes floating by %%% 919-577-9882 % but there's a teardrop in his eye..." %%%% <yates@ieee.org> % 'One Summer Dream', *Face The Music*, ELO http://www.digitalsignallabs.com
Reply by ●February 19, 20092009-02-19
illywhacker <illywacker@gmail.com> writes:> On Feb 19, 8:02�pm, Randy Yates <ya...@ieee.org> 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? > > Are we supposed to assume that the signal is of the form: > > f(t) , -infty < t <= (T1 - C) / B > > A r(Bt + C) , (T1 - C) / B < t < (T2 - C) / B > > g(t) , (T2 - C) / B < t < infty > > ?Yes. In other words, A*r(B*t + C) is a "chunk" of the input signal at some unknown time. See also the constraints I give just now in a parallel post. -- % Randy Yates % "Rollin' and riding and slippin' and %% Fuquay-Varina, NC % sliding, it's magic." %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Living' Thing', *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●February 19, 20092009-02-19
On Feb 19, 8:26�pm, Randy Yates <ya...@ieee.org> wrote:> illywhacker <illywac...@gmail.com> writes: > > On Feb 19, 8:02�pm, Randy Yates <ya...@ieee.org> 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? > > > Are we supposed to assume that the signal is of the form: > > > f(t) , �-infty < t <= (T1 - C) / B > > > A r(Bt + C) , (T1 - C) / B < t < (T2 - C) / B > > > g(t) , (T2 - C) / B < t < infty > > > ? > > Yes. In other words, A*r(B*t + C) is a "chunk" of the input signal at > some unknown time. > > See also the constraints I give just now in a parallel post.This is essentially an optimization problem. In 2d it is known as registration. The problem has been addressed in many ways, including the Anderson method you mentioned in another group. It helps if something is known about the rest of the signal. For example, if it is zero, the problem is easy. Typical methods may involve: exhaustive search, perhaps organized in an intelligent coarse to fine fashion; local descent procedures, which can get stuck in local minima; stochastic descent procedures, which typically take a while; and so on. illywhacker;
Reply by ●February 19, 20092009-02-19
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? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●February 19, 20092009-02-19
Vladimir Vassilevsky <antispam_bogus@hotmail.com> 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). -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●February 19, 20092009-02-19
On Thu, 19 Feb 2009 14:02:50 -0500, Randy Yates <yates@ieee.org> 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?Do you really mean that B scales time t? So that B = 0.5 make r(t) last half as long as when B = 1? If so, that sounds like a potential wavelet application depending on the properties of r(t). Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by ●February 19, 20092009-02-19
Eric Jacobsen <eric.jacobsen@ieee.org> writes:> On Thu, 19 Feb 2009 14:02:50 -0500, Randy Yates <yates@ieee.org> > 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? > > Do you really mean that B scales time t? So that B = 0.5 make r(t) > last half as long as when B = 1?Yes, that's right Eric.> If so, that sounds like a potential wavelet application depending on > the properties of r(t).Could be. -- % Randy Yates % "How's life on earth? %% Fuquay-Varina, NC % ... What is it worth?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●February 19, 20092009-02-19
"Randy Yates" <yates@ieee.org> wrote in message news:m33aeaduge.fsf@local.localhost...> Vladimir Vassilevsky <antispam_bogus@hotmail.com> 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
