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Converting From A Normalized To Continuous Bandpass Filter [O-Matrix function]
Syntax fn2cbp(wc, b_in, a_in, b, a)
Include: O-Matrix function. No include required.
See Also fn2clp , fn2cbp , fn2cbs

Arguments:
     wc: A two element Real or Double row vector specifying the lower and upper radian
         cutoff frequencies [rad/sec] for the new bandpass filter, such that:
            wc(1) is the lower frequency limit for bandpass filter, and
            wc(2) is the upper frequency limit for bandpass filter.
   b_in: Column Vector, Input , specifying the numerator   polynomial for the normalized filter.
   a_in: Column Vector, Input , specifying the denominator polynomial for the normalized filter.
      b: Column Vector, Output, returning  the numerator   polynomial for the bandpass filter.
      a: Column Vector, Output, returning  the denominator polynomial for the bandpass filter.

Description

This function takes the numerator and denominator polynomials of a lowpass normalized continuous transfer function (Hin = b_in/a_in), converts and frequency translates them to the desired lower and upper radian cutoff frequencies [rad/sec] given in the two element vector "wc" (Hout = b/a) of a new bandpass filter. Sources of normalized filter transfer functions can be obtained from functions such as fn2chp , fn2cbp , fn2cbs , or, any similar user defined function. The first element of "wc" is the lower cutoff frequency and the second element is the upper.

The input and output polynomials are ascending polynomials in s = jw expressed as a column vector of length n as:

          b => b(1) + n(2) * s + .. + b(n) * s^(n-1); similarly for a.

The output polynomials b and a must be declared before the function is called, though their types do not matter. They can be declared as type "b = novalue", "a = novalue", for instance.

Example

# Design CHEBYSHEV Type 2 lowpass prototype filter, fc = 1 [radian/sec]
Norder = 5;
Ap     = 3d0;
As     = 45d0;
b_in   = novalue;
a_in   = novalue;
fncheb2(Norder, Ap, As, b_in, a_in);

# Convert filter to a new bandpass cutoff frequency
b     = novalue;              # Declare output numerator   polynomial
a     = novalue;              # Declare output denominator polynomial
flow  = 800d0;                # New lower cutoff frequency
fhigh = 2000d0;               # New upper cutoff frequency
wc    = 2d0*PI*[flow,fhigh];  # Equivalent radian frequency
fn2cbp(wc, b_in, a_in, b, a); # Convert the filter

# Evaluate this filter around its cutoff.
fmin    =  1d2; # Plotting Limits
fmax    =  1d4;
ymax    =  10d0;
ymin    = -60d0;

N       = 501; # Plotting information         
n       = seq(N)'-1d0;
f       = logspace(log10(fmin),log10(fmax),N)';
H       = gains(b,a,f);
HdB     = db20(H);

A plot of the resulting filter appears as: