From: Nicholas Kinar on 9 Mar 2010 15:53 Hello-- I am reading a very interesting paper on acoustics which describes a numerical procedure used to construct a discrete vector of values from a signal. This vector is then used along with some mathematics to calculate the attenuation of a sound pulse through a medium. Essentially, the procedure has the following steps: (1) Compute the frequency spectrum U[tau, omega] using the Gabor transform of a discrete signal s[t]. The time is tau, and the angular frequency is omega. Thus U[tau, omega] is a 2D matrix with each element having real and complex parts. (2) From U[tau, omega], compute the amplitude A[tau, omega] from the real and imaginary parts. Thus A[tau, omega] = sqrt( (U_r^2) + (U_i^2) ), where U_r is the real part of U[tau, omega], and U_i is the imaginary part of U[tau, omega]. (3) Next, define chi = (tau * omega), and then construct a 1D vector A[chi] = A[tau * omega] from A[tau, omega] by integrating along constant chi. So what I need to do is take the 2D matrix A[tau, omega], and convert it to A[tau * omega] by performing numerical integration along constant chi. What is the most efficient way to perform numerical integration along constant chi so that I can obtain A[tau * omega]? I've been running around in circles for a while trying to do this, and I can't see a very clear-cut or efficient solution. Thanks, Nicholas From: Nicholas Kinar on 11 Mar 2010 18:23 > What is the most efficient way to perform numerical integration along > constant chi so that I can obtain A[tau * omega]? I've been running > around in circles for a while trying to do this, and I can't see a very > clear-cut or efficient solution. > I've found a paper that deals with the numerical integration of line integrals , but I'm still puzzled about performing the integration along constant chi.  K. Atkinson and E. Venturino, �Numerical evaluation of line integrals,� SIAM Journal on Numerical Analysis, 1993, pp. 882�888. Hmm.... Nicholas From: Nicholas Kinar on 12 Mar 2010 10:31 >>> What is the most efficient way to perform numerical integration along >> constant chi so that I can obtain A[tau * omega]? I've been running >> around in circles for a while trying to do this, and I can't see a very >> clear-cut or efficient solution. >> Perhaps the integration is nothing more than an "average" along constant chi. I'm going to run with this idea for a while and see where it leads me, since this appears to be the most logical. Nicholas  |  Pages: 1 Prev: ICNAAM 2010 Mini-Symposium on Computational Bioimaging and VisualizationNext: Test