ellf.doc

巴特沃斯、切比雪夫I和椭圆滤波器设计的源程序！非常难得！ 简洁的C语言编写

                       ellf.c
This program calculates design coefficients for
digital filters of the Butterworth, Chebyshev, or
elliptic varieties.



Usage:

Inputs are entered by keyboard, or are redirected to come from
a command file, as follows:

Kind of filter (1: Butterworth, 2: Chebyshev, 3: Elliptic,
                0: exit to monitor)

Shape of filter (1: low pass, 2: band pass, 3: high pass,
                4: band reject, 0: exit to monitor)

Order of filter (an integer)

Passband ripple (peak to peak decibels)

Sampling frequency (Hz)

Passband edge frequency (Hz)

Second passband edge frequency (for band pass or reject filters)

Stop band edge frequency (Hz)
     or stop band attenuation (entered as -decibels)

The "exit to monitor" type 0 may be used to terminate the
program when input is redirected to come from a command file.

If your specification is illegal, e.g. the stop band edge
is in the middle of the passband, the program will make you
start over.  However, it remembers and displays the last
value of each parameter entered.  To use the same value, just
hit carriage return instead of typing it in again.

The program displays relevant pass band and stop band edge
frequencies and stop band attenuation. The z-plane coefficients
are printed in these forms:
  Numerator and denominator z polynomial coefficients
  Pole and zero locations
  Polynomial coefficients of quadratic factors

After giving all the coefficients, the program prints a
table of the frequency response of the filter.  You can
get a picture by reading the table into gnuplot.



Filter design:

The output coefficients of primary interest are shown as follows:

(z-plane pole location:)
pole     3.0050282041410E-001    9.3475816516366E-001
(quadratic factors:)
q. f.
z**2    9.6407477241696E-001
z**1   -6.0100564082819E-001
(center frequency, gain at f0, and gain at 0 Hz:)
f0  2.00496167E+003  gain  2.9238E+001  DC gain  7.3364E-001

zero     1.7886295237392E-001    9.8387399816648E-001
q. f.
z**2    1.0000000000000E+000
z**1   -3.5772590474783E-001
f0  2.21379064E+003  gain  0.0000E+000  DC gain  1.6423E+000

To make a biquad filter from this, the equation for the
output y(i) at the i-th sample as a function of the input
x(i) at the i-th sample is

y(i) + -6.0100564082819E-001 y(i-1) +  9.6407477241696E-001 y(i-2)
= x(i) + -3.5772590474783E-001 x(i-1) +  1.0000000000000E+000 x(i-2).

Thus the two coefficients for the pole would normally be
negated in a typical implementation of the filter.



Compilation:

This program has been compiled successfully on many different
computers.  See the accompanying output listing file ellf.ans,
for a set of correct answers.  Use the batch file test.bat to
check your executable program. If the low pass and high pass
options work but the others don't, then examine your atan2()
function carefully for reversed arguments or perhaps an offest of
pi.  On most systems, define ANSIC to be 1.  This sets the
expected atan2() arguments but does not otherwise imply anything
about the ANSI-ness of the program.



Files:

mconf.h        system configuration include file
               Be sure to define type of computer here!
cmplx.c        complex arithmetic subroutine package
ellf.ans       right answer file for some elliptic filters
ellf.que       elliptic filter questions
ellf.c         main program
ellf.doc       this file
ellf.mak       Microsoft MSDOS makefile
ellfu.mak      Unix makefile
ellik.c        incomplete elliptic integral of the first kind
ellpe.c        complete elliptic integral of the second kind
ellpj.c        Jacobian Elliptic Functions
ellpk.c        complete elliptic integral of the first kind
makefile       Unix makefile
mtherr.c       common math function error handler
polevl.c       evaluates polynomials
test.bat       batch file to run a test
descrip.mms    VAX makefile
ellf.opt       VAX makefile
testvax.bat    VAX test


References:

A. H. Gray, Jr., and J. D. Markel, "A Computer Program for
Designing Digital Elliptic Filters", IEEE Transactions on
Acoustics, Speech, and Signal Processing 6, 529-538
(December, 1976)

B. Gold and C. M. Rader, Digital Processing of Signals,
McGraw-Hill, Inc. 1969, pp 61-90

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical
Functions, National Bureau of Standards AMS 55, 1964,
Chapters 16 and 17


- Steve Moshier, December 1986
Last rev: November, 1992