Subject: Re: Noise in linearized exponential decay Žtting > you mean ??? > y(i)= a*exp(b*x(i)) + noise => > log(y(i)) = log(a*exp(b*x(i)) +noise) = > = log(a) + b*x(i) + log(1+noise/y(i)) > (assuming small residuals such that y(i) approx a*exp(b*x(i)) > and by weighting the data by y(i) to make the variances in the new model of > equal size? Yes Peter, that¹s exactly it - your equation makes it so clear what¹s === Subject: about dicrete fourier transform I confuse about DFT. There is a coefŽcient 1/N before the formulation. Some books put it before forward Ft some put it before revese FT. If I get a spectrum (measured), I want to recover real signal (amplitude is important). Where should I put 1/N? For forwart FT, most deŽne it has e^(-jwt) but inverse FT is e^(jwt). Is that matter I exchange them? Beacuse the domain can be deŽned in any ways. HH === Subject: Re: about dicrete fourier transform charset=iso-8859-1 > I confuse about DFT. There is a coefŽcient 1/N before the > formulation. Some books put it before forward Ft some put it before > revese FT. If I get a spectrum (measured), I want to recover real > signal (amplitude is important). Where should I put 1/N? I¹m very much not a mathematician, but an engineer who works with frequency analysis of real signals, and have wondered why this is not clearly spelt out more often. I believe you should apply 1/N to the forward (time->freqy) FT to get real signal amplitudes in the frequency domain. You can, of course, test this out on simple signals. HTH, Martin === Subject: Re: about dicrete fourier transform > I confuse about DFT. There is a coefŽcient 1/N before the > formulation. Some books put it before forward Ft some put it before > revese FT. If I get a spectrum (measured), I want to recover real > signal (amplitude is important). Where should I put 1/N? > For forward FT, This is commonly called the *direct* [discrete] Fourier transform. > most deŽne it has e^(-jwt) but inverse FT is e^(jwt). > Is that matter I exchange them? > Beacuse the domain can be deŽned in any ways. Suppose that ddFt is the direct discrete Fourier transform and that idFt is the inverse discrete Fourier transform, then N*v = idFt(ddFt(v)) In other words, the idFt is *not* exactly the inverse of the ddFt. Neither transform preserves the length of vector v: |ddFt(v)| = sqrt(N)*|v| and |idFt(v)| = sqrt(N)*|v| We deŽne these transforms this way to obviate the division through the elements of v by sqrt(N). === Subject: Re: about dicrete fourier transform > I confuse about DFT. There is a coefŽcient 1/N before the > formulation. Some books put it before forward Ft some put it before > revese FT. If I get a spectrum (measured), I want to recover real > signal (amplitude is important). Where should I put 1/N? > For forwart FT, most deŽne it has e^(-jwt) but inverse FT is e^(jwt). > Is that matter I exchange them? Beacuse the domain can be deŽned in > any ways. You can deŽne it with any multiplicative constant you like, as long as IDFT(DFT(f))= f for all f. The choice of normalization makes a lot of difference in some of those nice useful theorems, e.g. that the transform of the convolution of two functions is the product of their transforms. As long as you don¹t mind dealing with odd multiplicative constants in those sorts of applications, redeŽne away. Just don¹t expect me to read your papers. Phil Hobbs === Subject: pointer witch Template Numerical Toolkit by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i8L1Q8r23590; I have a program that i need to use a pointer when i use the TNT library, here are the example: #include #include tnt.h using namespace TNT; //using namespace std; int main (void) { Array1D * jaja; jaja= new Array1D (4); //working without problems jaja[0] = 30; cout << jaja[0]; //don¹t working jaja[1] = 31; cout << jaja[1]; return 0; } i tried with vc++ and gnu gcc, i have no ideia how i can make this. i need to use new , beucase i don¹t know how much element i will need to make.if someone can help me ? thank you Marcelo === Subject: Re: Bessel Function - J0(x) > : Not your fault. Microsoft provides less support for DOS and DOS based > : graphics as their Windows OS evolves. By mess up the graphics I mean > that > : when I exit your applications and return to Windows the screen is > : completely garbled and I have to reboot to correct the problem as neither > : the mouse nor keyboard functions are useable. (Newer versions of Windows > : similarly do not support sound cards like the older versions did, so I > : think there¹s a trend here.) > The problem lies in Windows, No it doesn¹t, it lies in your inability to write software for Windows.Net. Others have done it so why are you relying on sci.math.num-analysis to do your QA for the beaten to death J0(x)? -- You¹re Welcome, Gerry T. ______ Ah, Klinger, my constant reminder that Darwin was right!. -- Maj Charles Winchester III, the 4077th M*A*S*H === Subject: Re: Bessel Function - J0(x) charset=iso-8859-1 : : > The problem lies in Windows, : : No it doesn¹t, it lies in your inability to write software for Windows.Net. : Others have done it so why are you relying on sci.math.num-analysis to do : your QA for the beaten to death J0(x)? All time-sharing operating systems, like Windows, are problematic when it comes to time measurements. What other (non) beaten to death transcendental functions would be desirable as a benchmark? D. Baruth === Subject: Solution tool for special math puzzles/riddles A message was posted by Karl Neischen to this conference some time ago with a theme Need solution tool for special math puzzles/riddles. The famous problem WHO OWNS THE FISH? attracted some attention and more than one solution was proposed. I found in the Net information about simple and interesting tool Crocopat, which implements RML language for management of relations. It is much simpler then Prolog, works very fast and is capable to handle a big amount of data. The URL is: http://www-sst.informatik.tu-cottbus.de/~db/CrocoPat/ Below is the CrocoPat solutuion of the WHO OWNS THE FISH? problem. ---- PRINT FISH.RML, ENDL; PRINT WHO OWNS THE FISH?, ENDL; house(1); house(2); house(3); house(4); house(5); PRINT [house] house(x); color(red); color(white); color(yellow); color(blue); color(green); PRINT [color] color(x); nationality(brit); nationality(swede); nationality(norwegian); nationality(german); nationality(dane); PRINT [nationality] nationality(x); beverage(water); beverage(beer); beverage(milk); beverage(tea); beverage(coffee); PRINT [beverage] beverage(x); cigar(blend);