Title: "PDF estimation by use of characteristic functions and the FFT"
Abstract:
The characteristic function (CF) is the Fourier transform of the probability density function (PDF) of a random variable. When working with random variables, it is frequently helpful to work in the CF domain, to take advantage of that domains various properties. For example, by looking at the “spectrum” of the CF, it is possible to determine the “bandwidth” of the PDF. This allows one to determine the PDF’s “sampling-rate.” The addition of independent “lowpass” noise is equivalent to “low-pass filtering” the CF, allowing one to define the Nyquist sampling values which are interpreted as “quantized levels ” of the PDF. Here we shall show that: a) that estimates of PDF’s are simpler and more accurate in the CF domain, b) by working in the CF domain we may separate binning errors typically made when forming histograms from sampling uncertainty due to the finite number of samples, c) that a bit rate/sample may be derived, d) that this theory allows for a rational design of vector quantizers in the CF frequency domain.
Bio: Yashuo Wu is a grad research student with Professor Jont Allen, Electrical & Computer Engineering.
