bracewell -- Perform sample Fourier transforms from Bracewell's book "The Fourier Transform and Its Applications."
bracewell function npts shift
NOTE: Before running this task the plot package must be loaded.
This is an educational script intended to help Fourier analysis neophytes develop a feel for how things in the spatial (or time) domain map onto the transform domain. The user may select the functional form from among a set of old favorites (for Bracewell readers) and the number of points in the data set. The center of the function may also be shifted away from the origin of the coordinate system, which is pixel 1 for the routines used in this procedure.
The bold and inquisitive user may also adjust the "characteristic width" of the function, which may have different meanings for different functions. For things like the boxcar or Gaussian functions, the notion of width is pretty intuitive; for things like the impulse pairs function, it represents the separation of the pulses. "Characteristic width" is meaningless for things like a delta function or a step function.
- function [string]
- [Allowed values: bessel | constant | delta | gaussian |
heaviside | pe | po | box | rectangle | signum | shah |
comb | sinc | sine | cosine | triangle | y | line]
Function to transform. (For an explanation of how each transform is applied, please refer to "The Fourier Transform and Its Application," by Bracewell).
- npts = [integer, min=1]
- Number of points in the data set.
- shift = [integer]
- Number of pixels to shift the center of the function.
- (const = 1.0) [real]
- Value of constant function.
- (fcw = 10.0) [real, min=1.]
- Characteristic width of function.
1. Perform a box function with 100 data points and no shift.
fo> bracewell box 100 0
Type "help fourier option=sys" for a higher-level description of the fourier package.