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Converting From A Normalized To Digital Bandpass Filter
Syntax fn2dbp(cutoffdtnumindeninnumoutdenout)
See Also fnbut , fncheb , fn2cbp

Description
Converts a normalized filter to a digital bandpass filter. The real or double-precision row vector cutoff has two elements and specifies the cutoff frequencies for the bandpass filter. The scalar dt specifies the time between samples and has the same type as cutoff. The column vector numin has the same type as cutoff and specifies the numerator polynomial for the normalized filter. The column vector denin has the same type as cutoff and specifies the denominator polynomial for the normalized filter.

The input values of numout and denout have no effect. The output value numout is set to the column vector representing the numerator polynomial for the digital bandpass filter. The output value denout is set to the column vector representing the denominator polynomial for the digital bandpass filter. The output values of numout and denout have the same type as cutoff.

The response of the normalized filter is
               2
     |numin[s]|
     |--------|
     |denin[s]|

and it is near 1 for s in the interval
           __
     [0, \/-1]

and near 0 for the rest of the positive imaginary axis. The response of the digital bandpass filter is

     |                __           |2
     | numout[ exp( \/-1 dt w ) ]  |
     -------------------------------
     |                __           |2
     | denout[ exp( \/-1 dt w ) ]  |

and it is near 1 for w in the interval [cutoff(1), cutoff(2)] and near 0 for other w in the interval [0, pi / dt].

Example
     numin   = 1.
     denin   = {1., sqrt(2.), 1.}
     cutoff  = [2., 4.]
     dt      = .2
     numout  = novalue
     denout  = novalue
     fn2dbp(cutoff, dt, numin, denin, numout, denout)
     
     ymin = 1e-5
     ymax = 1e+1
     fdplot(dt, ymin, ymax, cutoff, numout, denout)
     
returns the following plot: