PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

12 Practical MATLAB® Applications for Engineers

R.1.24 The analog pulse function pul(t/τ) is illustrated graphically in Figure 1.14.
The function pul(t/τ) is defi ned analytically by

pul t

t

tt

(/ )

//

//







1for

for and



 

22

02 2







R.1.25 The analog pulse pul(t/τ) is related to the analog step function u(t) by the following
relation:

pul(t/) = u(t + /2) − u(t − /2)

R.1.26 The discrete pulse sequence denoted by pul(n/N) is given by

pul n N

Nn

Nn n

(/ )

//

//

1for

for and



 

22

02 2

N

N







For example, for N = 11 (odd), the discrete sequence is given by

pul n

n

nn

(/ ) 11

15 5

05 5





for

for

and







The preceding function pul(n/11) is illustrated in Figure 1.15.

Observe that the pulse function pul(n/11) can be represented by the superposition

of two discrete step sequences as

pul(n/11) = u(n + 5) − u(n − 6)

R.1.27 The analog unit ramp function denoted by r(t) = t u(t) is illustrated in Figure 1.16.

The unit ramp is defi ned analytically by

rt

tt

t

()

for

for





0

00







A

u(n − m)

m − 1 mm + 1m + 2m + 3

n

FIGURE 1.13
Plot of u(n − m).

pul(t/)

t

−/2 0 /2

1

FIGURE 1.14

Plot of pul(t/τ).