What is the basic approach for the following DSP tasks: 1. Estimation of the inverse transfer function, which transform output signal to the input signal of the black-box system via known measurements of the input and output signals for both amplitude and phase characteristics simultaneously. 2. Transformation of the previously estimated inverse transfer function from spectral domain to the time domain. Michal
reconstruction of the input signal in time domain
Started by ●August 2, 2006
Reply by ●August 2, 20062006-08-02
Pi skrev:> What is the basic approach for the following DSP tasks: > > 1. Estimation of the inverse transfer function, which transform output > signal to the input signal of the black-box system via known measurements of > the input and output signals for both amplitude and phase characteristics > simultaneously. > > 2. Transformation of the previously estimated inverse transfer function from > spectral domain to the time domain.Is this homework or are you just interested? Answering these two questions are basically the purpose of DSP as both profession and research subject. Generally speaking, once one can confidently determine the transfer function through a black-box system, one can often tell what that black box contains. This is the philosophical basis for radar, sonar, and seismics as well as various medical techniques (CT, NMR, X-rays, ultrasound,...). As might be obvious, there is no single method or technique to get this to work. One only has available an ensemble of techniques that may work more or less well in any given scenario. Rune
Reply by ●August 2, 20062006-08-02
"Rune Allnor" <allnor@tele.ntnu.no> writes:> Pi skrev: >> What is the basic approach for the following DSP tasks: >> >> 1. Estimation of the inverse transfer function, which transform output >> signal to the input signal of the black-box system via known measurements of >> the input and output signals for both amplitude and phase characteristics >> simultaneously. >> >> 2. Transformation of the previously estimated inverse transfer function from >> spectral domain to the time domain. > > Is this homework or are you just interested? > > Answering these two questions are basically the purpose of DSP > as both profession and research subject. Generally speaking, > once one can confidently determine the transfer function through > a black-box system, one can often tell what that black box > contains. This is the philosophical basis for radar, sonar, and > seismics as well as various medical techniques (CT, NMR, > X-rays, ultrasound,...). > > As might be obvious, there is no single method or technique to > get this to work. One only has available an ensemble of techniques > that may work more or less well in any given scenario. > > RuneHi Rune, I don't really understand, I thought if X(w) and Y(w) are fourier transforms for input and output and H(w) the transfer function of the system. H(w) = Y(w) / X(w) So couldn't you now just take 1/H(w) as inverse transfer function? Of course all of that works just for LTI systems, and you can not reconstruct data where H(w)=0. But what other methods are used? gr. Anton
Reply by ●August 2, 20062006-08-02
Anton skrev:> "Rune Allnor" <allnor@tele.ntnu.no> writes: > > > Pi skrev: > >> What is the basic approach for the following DSP tasks: > >> > >> 1. Estimation of the inverse transfer function, which transform output > >> signal to the input signal of the black-box system via known measurements of > >> the input and output signals for both amplitude and phase characteristics > >> simultaneously. > >> > >> 2. Transformation of the previously estimated inverse transfer function from > >> spectral domain to the time domain. > > > > Is this homework or are you just interested? > > > > Answering these two questions are basically the purpose of DSP > > as both profession and research subject. Generally speaking, > > once one can confidently determine the transfer function through > > a black-box system, one can often tell what that black box > > contains. This is the philosophical basis for radar, sonar, and > > seismics as well as various medical techniques (CT, NMR, > > X-rays, ultrasound,...). > > > > As might be obvious, there is no single method or technique to > > get this to work. One only has available an ensemble of techniques > > that may work more or less well in any given scenario. > > > > Rune > > Hi Rune, > > I don't really understand, I thought > if X(w) and Y(w) are fourier transforms for input and output and > H(w) the transfer function of the system. > > H(w) = Y(w) / X(w) > > So couldn't you now just take 1/H(w) as inverse transfer function?No. And you already understand why:> Of course all of that works just for LTI systems, and > you can not reconstruct data where H(w)=0.This is the one, single, tiny detail that throws a spanner in the works: Your approach only works if H(w) has all its nulls well inside the unit circle. Not poles. Nulls.> But what other methods are used?Google for "deconvolution" and find out. Rune
Reply by ●August 2, 20062006-08-02
This question is not motivated by homework at all. I am looking for reliable and effective way how to reconstruct input signal with respect of its amplitude and phase!!! characteristics in time domain. Michal "Rune Allnor" <allnor@tele.ntnu.no> p�se v diskusn�m pr�spevku news:1154521513.725234.129720@p79g2000cwp.googlegroups.com...> > Pi skrev: >> What is the basic approach for the following DSP tasks: >> >> 1. Estimation of the inverse transfer function, which transform output >> signal to the input signal of the black-box system via known measurements >> of >> the input and output signals for both amplitude and phase characteristics >> simultaneously. >> >> 2. Transformation of the previously estimated inverse transfer function >> from >> spectral domain to the time domain. > > Is this homework or are you just interested? > > Answering these two questions are basically the purpose of DSP > as both profession and research subject. Generally speaking, > once one can confidently determine the transfer function through > a black-box system, one can often tell what that black box > contains. This is the philosophical basis for radar, sonar, and > seismics as well as various medical techniques (CT, NMR, > X-rays, ultrasound,...). > > As might be obvious, there is no single method or technique to > get this to work. One only has available an ensemble of techniques > that may work more or less well in any given scenario. > > Rune >
Reply by ●August 2, 20062006-08-02
Michal Kvasnicka skrev:> This question is not motivated by homework at all. I am looking for reliable > and effective way how to reconstruct input signal with respect of its > amplitude and phase!!! characteristics in time domain.You may have to search for some time, then. The spectrum amplitude response can to some extent be estimated by analyzing cross correlations between input and output signals. Obviously, this trick breaks down near nulls in the inputs signal. The phase is notoriously difficult due to the ambiguity exp(ix) = exp(i(x+2pi)). Check out the book Bendat & Piersol: "Random Data", Wiley, 2000 for some techniques that may or may not work. Rune
Reply by ●August 2, 20062006-08-02
Anton wrote:> I don't really understand, I thought > if X(w) and Y(w) are fourier transforms for input and output and > H(w) the transfer function of the system. > > H(w) = Y(w) / X(w) > > So couldn't you now just take 1/H(w) as inverse transfer function? > Of course all of that works just for LTI systems, and > you can not reconstruct data where H(w)=0.Nor can you reasonably reconstruct quantized and possibly noisy data when H(w) is small. "Small" can be distressingly large.> But what other methods are used?In the online book at http://www.dspguide.com/, pages 179 and 180 (Chapter 9) lay out the basic idea (which you evidently understand) and pages 300 to 305 (Chapter 17) have more discussion and some examples. almost always, compromises need to be made, and they depend on the original data and the final use. Pages 407 to 410 (Chapter 24) describe deconvolution of if the illumination in an image to flatten brightness and contrast. Just about every application is a special case. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 3, 20062006-08-03
Rune Allnor wrote:> Anton skrev:...> > I don't really understand, I thought > > if X(w) and Y(w) are fourier transforms for input and output and > > H(w) the transfer function of the system. > > > > H(w) = Y(w) / X(w) > > > > So couldn't you now just take 1/H(w) as inverse transfer function? > > No. And you already understand why: > > > Of course all of that works just for LTI systems, and > > you can not reconstruct data where H(w)=0. > > This is the one, single, tiny detail that throws a spanner in > the works: Your approach only works if H(w) has all its nulls > well inside the unit circle. Not poles. Nulls.what we call "zeros" on this side of the pond. (i had to read this twice to figger out what you meant, Rune.) r b-j
Reply by ●August 3, 20062006-08-03
robert bristow-johnson skrev:> Rune Allnor wrote: > > Anton skrev: > ... > > > I don't really understand, I thought > > > if X(w) and Y(w) are fourier transforms for input and output and > > > H(w) the transfer function of the system. > > > > > > H(w) = Y(w) / X(w) > > > > > > So couldn't you now just take 1/H(w) as inverse transfer function? > > > > No. And you already understand why: > > > > > Of course all of that works just for LTI systems, and > > > you can not reconstruct data where H(w)=0. > > > > This is the one, single, tiny detail that throws a spanner in > > the works: Your approach only works if H(w) has all its nulls > > well inside the unit circle. Not poles. Nulls. > > what we call "zeros" on this side of the pond. > > (i had to read this twice to figger out what you meant, Rune.)Sorry. "Null" means zero in Norwegian. I guess I mixed in some C NULL pointer terminology here... Rune
Reply by ●August 3, 20062006-08-03
Rune Allnor wrote:> > Sorry. "Null" means zero in Norwegian. I guess I mixed in some > C NULL pointer terminology here...it usually means "zero" here, too. sometimes it means "nothing" ("null and void" w.r.t. a contract) or similar. sometimes it means a dip or low point (35 years ago, when i was WB0CCA, when tuning the coupling capicitor in an antenna coupling circuit, we adjusted to get a "null" in the SWR meter - it wasn't always zero but it would be nice if the SWR *was* zero). but i hadn't seen, in any English language textbook about LTI system theory, Laplace or Z transforms, etc. those things that were the opposite of "poles" called "nulls". one day, i embarassed myself in the front of a class calling them "holes". can't imagine what Freudian recesses that came from! r b-j