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3.4. SYSTEM RESPONSE FUNCTIONS 85
3.4 System Response Functions
3.4.1 Creating Time Domain Signals
The Signal Analysis Module contains several functions which are useful for building time
domain signals: gcos and gsin.Xµprovides gstep for the creation of stair-step signals.
The example below illustrates the generation of a sine wave and a step function.
# A unit step over 10 seconds
time = 0:10:.1
y1 = gstep(time)
# multiple steps over 10 seconds
sdata = [1;-2;4]
tdata = [3;5;7]
y2 = gstep(time,tdata,sdata)
# Freq: 2 Hz, Ampl: 0.5
y3 = 0.5*gsin(time,2)
Because of the native pdm data type, and the ease in which pdms can be augmented,
vector (or even matrix) valued signals are easily created. For example:
# A function depending on t
time = 0:10:.1
y1 = pdm(exp(0.1*time),time) - gsin(time,3/(2*pi))
# A function independent of t
y2 = uniform(time)
#A2x2pdm
pt = pdm(time,time)
y3 = [pt/max(time),2*Cos(3*pt+0.2));...
2+Sin(2*pt),sqrt(pt)+0.3*random(pt)]
3.4.2 Dynamic System Time Responses
In Xmath time responses can be calculated by simply multiplying a Dynamic System
by a pdm. A zero-order hold equivalent is used with the sampling interval set to the