Index-> contents reference index search Up-> SPT_HELP AnalogFilterFunctions fnbut Prev Next SPT_HELP-> SPTFunctionsByCategory Mathematical Functions Data Manipulation Functions SignalGeneratorMain AnalogFilterFunctions FIR Filter Design Window Functions IIR Filter Design FourierFunctions Plotting Functions Histogram Functions AnalogFilterFunctions-> fnbut fncheb1 fncheb2 fnbes fn2clp fn2chp fn2cbp fn2cbs fnbpole fnc1pole polbes gains makealog fnbut Headings-> Description Example Reference

Normalized Butterworth Lowpass Filter
 Syntax `fnbut(`Norder, b, a`)` Include: `O-Matrix file. No include required.` See Also fncheb1 , fncheb2 , fnbes , fn2clp , fn2chp , fn2cbp , fn2cbs
``` ARGUMENTS:    INPUTS:       Norder = SCALAR. Requested order of transfer function. Coerced to                INTEGER before local processing. Norder >= 1.       b      = VECTOR, COLUMN, for return (type disregarded on input).                Numerator polynomial coefficients. Type DOUBLE.       a      = VECTOR, COLUMN, for return (type disregarded on input).                Denominator polynomial coefficients. Type DOUBLE.    RETURN: novalue. Filter functions are returned in arguments 'b' and 'a'. ```
Description ``` ```This function creates a normalized Butterworth s-domain (analog) lowpass transfer function of the form: H(s) = b(s)/a(s). The 3-dB cutoff frequency is set to 1 [radian/sec]. The requested filter order 'Norder' must be >= 1. The numerator polynomial of the transfer function is returned through argument 'b', and is a column vector where the elements form an ascending polynomial as follows: ``` ```b => b(1) + b(2)*s + b(3)*s^2 + ... ``` ```Denominator polynomial is returned in argument 'a', and is of the same form. ``` ```A Butterworth filter has a monotonically decreasing attenuation characteristic and is maximally flat in the passband. It has moderate selectivity, being lesser than the Chebyshev family but greater than a Bessel filter. ``` ```The resulting normalized embodied in polynomials 'b' and 'a' can be further scaled to different frequencies and filter types by the functions: fn2clp , fn2chp , fn2cbp , fn2cbs .

Example ``` # Design BUTTERWORTH lowpass prototype filter, fc = 1 [radian/sec] Norder  = 5;        # Filter Order b       = novalue;  # Declare numerator   polynomial a       = novalue;  # Declare denominator polynomial fnbut(Norder,b,a);  # Make prototype filter # Evaluate this filter around its cutoff. fmin    =  1d-2; # Plotting Limits fmax    =  1d0; ymax    =  10d0; ymin    = -60d0; N       = 201; # Plotting information          n       = seq(N)'-1d0; f       = logspace(log10(fmin),log10(fmax),N)'; H       = gains(b,a,f); HdB     = db20(H); fc      = 1d0/2/PI; # 3dB down at this cutoff ``` A plot of the normalized BUTTERWORTH appears as: ``` ``` ``` ```Reference
Blinchikoff ``` ```