mkhdiff.cwp.lib

su 的源代码库

MKHDIFF - Compute filter approximating the bandlimited HalF-DIFFerentiator.

mkhdiff - Compute filter approximating the bandlimited half-differentiator.

Function Prototype:
void mkhdiff (float h, int l, float d[]);

Input:
h		sampling interval
l		half-length of half-differentiator (length = 1+2*l is odd)

Output:
d		array[1+2*l] of coefficients for half-differentiator

Notes:
The half-differentiator is defined by

				  pi
    d[l+j] = sqrt(1/h)/(2pi) * integral dw sqrt(-iw)*exp(-iwj)
				 -pi

				  pi
           = sqrt(2/h)/(2pi) * integral dw sqrt(w)*(cos(wj)-sin(wj))
				  0 

    for j = -l, -l+1, ... , l.

An alternative definition is that f'(j) = d(j)*d(j)*f(j), where
f'(j) denotes the derivative of a sampled function f(j) and *
denotes a convolution sum.

The half-derivative g(j) of f(j) may be computed by the following sum:

	g(j) = d[0]*f(j+l) + d[1]*f(j+l-1) + ... + d[2*l]*f(j-l)

The integral over frequency is evaluated numerically using Simpson's
method.  Although the Filon method of numerical integration is more
appropriate for this integral, the truncation of d[l+j] for |j| > l
is probably the greatest source of error.  In any case, d[l+j] is 
cosine-tapered to reduce these truncation errors.

Author:  Dave Hale, Colorado School of Mines, 06/02/89