# Gaussian

Syntax
Hd = firgauss(L,Gain,Alpha,DFormat)

Description
Designs an FIR Gaussian lowpass filter. Gaussian filters are good pulse shaping filters, and as such are typically used in communication systems, as they have no overshoot and fast transitions. The function returns a Gaussian window of length L with a standard deviation, $$\sigma$$

$$\displaystyle\sigma = \frac {L-1}{2\alpha}$$

As seen, the width of the window (standard deviation) is inversely related to alpha($$\alpha$$), i.e. a smaller value of $$\alpha$$ produces a tighter transition frequency band in the frequency domain and vice versa. A good default value is 2.5.

Hd: the firgauss method designs an FIR Gaussian lowpass filter based on the entered specifications and places the transfer function (i.e. numerator and gain) into a digital filter object, Hd. The digital filter object can then be combined with other methods if so required. For a digital filter object, Hd, calling getnum(Hd) and getgain(Hd) will extract the numerator and gain coefficients respectively – see below.

DFormat: allows you to specify the display format of resulting digital filter object.

 symbolic Display a symbolic representation of the filter object. If the order > 10, the symbolic display option will be overridden and set to numeric. numeric Display a matrix representation of the filter object void Create a filter object, but do not display output

Examples

ClearH1;  // clear primary filter from cascade
interface L = {2,100,1,14};         // filter length
interface alpha = {0.5,10,0.1,2.5};  // standard deviation = (L – 1)/(2*alpha)

Main()

Hd=firgauss(L,1,alpha,"symbolic");

Num=getnum(Hd);
Den={1};
Gain=getgain(Hd);