Index-> contents reference index search Up-> SPT_HELP AnalogFilterFunctions fnbes 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 fnbes Headings-> Description Example Reference

Normalized Bessel Lowpass Filter Transfer Function
 Syntax `fnbes(`Norder, b, a`)` Include: `include spt\fnbes.oms` See Also fnbut , fncheb1 , fncheb2
``` ARGUMENTS:    INPUTS:       Norder = SCALAR. Requested order of transfer function. Coerced to                INTEGER before local processing. Norder >= 2.       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 'b' and 'a'. ```
Description ``` ```This function creates a normalized Bessel s-domain lowpass transfer function. The 3-dB cutoff frequency is set to 1 radian/sec. The requested filter order 'Norder' must be >= 2. The numerator polynomial of the transfer function is returned through argument 'b', and is a column vector where the elements form a 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. ``` ```Bessel filters approximate a maximally flat group delay characteristic. The filter's selectivity is relatively poor since it has a slow magnitude cutoff rate. But these filters have very low overshoot in their transient responses.

Example ``` include spt\fnbes.oms # Design BESSEL lowpass prototype filter, fc = 1 [radian/sec] Norder = 5;           # Filter Order b      = novalue;     # Declare numerator a      = novalue;     # Declare denominator fnbes(Norder, b, a);  # Make the prototype # 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 BESSEL filter appears as: ``` ``` ``` ```Reference
Blinchikoff ``` ```