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Poles of a Normalized Chebyshev TYPE 1 Analog Lowpass Filter
Syntax y = fnc1pole(Norder, Ap)
Include: include spt\fnc1pole.oms
See Also fnbpole

ARGUMENTS:
   INPUTS:
      Norder = SCALAR. Requested order of transfer function. Coerced to
               INTEGER before local processing. Norder >= 2.
      Ap     = SCALAR. Passband ripple in dB, Ap > 0.0 dB. Coerced to
               double for local processing.
   RETURN: VECTOR, COLUMN, COMPLEX. Poles of Chebyshev lowpass filter.

Description

Returns the poles of a normalized lowpass Chebyshev TYPE 1 analog filter function as a COMPLEX column vector.

A Chebyshev TYPE 1 filter has equi-ripple behavior in the passband and monotonically increasing attenuation in the stopband. The requested filter order 'Norder' must be >= 2. The passband peak-to-peak ripple is set via parameter 'Ap' in dB, where Ap > 0.0dB (strictly positive). Due to the nature of Chebyshev functions, even order filters cannot have a gain of unity at 0 Hz as can odd order filters. Even order filters start at Ap dB down at 0 Hz and begin passband ripple characteristics from there. All filters are passive, i.e., they can a gain of 1.0 at most at any given frequency.

Example

Find the poles of a 7th order Chebychev 1, 0.5 dB normalized filter.

include spt\spthead.oms

format complex "f12.8"
Norder = 7;     # Filter Order
Ap     = 0.5d0; # Passband Ripple [dB]
fnc1pole(Norder,Ap)

Results in:

{
( -0.05533807,  0.97701031)
( -0.15505382,  0.78350144)
( -0.22405927,  0.43481050)
( -0.24868702,  0.00000000)
( -0.22405927, -0.43481050)
( -0.15505382, -0.78350144)
( -0.05533807, -0.97701031)
}

Reference

Blinchikoff