PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 9

In general, the set of samples given by f(−n), f(−n + 1), ..., f(0), f(1), ..., f(n − 1), f(n),

can be real or complex. f(n) is called a real sequence if all its samples are real and a

complex sequence if at least one sample is complex.

Observe that any (discrete) sequence f(n) can be expressed by the equation

fn fk n k

k

()
()( )







∑

Examples of analog signals are often encountered in nature such as sound, tem-

peratures, pressure, growth, and precipitations waves.

Discrete time signals or events are usually man-made functions such as weekly

pay, monthly payment of a loan or mortgage, or the (U.S.) presidential election

every 4 years.

Discrete signals are often confused with digital signals and binary signals. A

digital signal f(nT) or in short f(n) is a discrete time signal whose values are one of

a predefi ned fi nite set of values.

A binary signal is a discrete signal whose values consist of either zeros or ones.

An analog or continuous time function or signal can be transformed into a digital

signal using an A/D. Conversely, a digital signal can be converted into an analog

signal by means of a digital to analog converter (D/A).

Digital signals are frequently encoded using binary codes such as ASCII* into

strings of ones and zeros because in this format they can be stored and processed

by digital devices such as computers, and are in general more immune to noise and

interference.

R.1.16 The discrete impulse sequence δ(n) also called the Kronecker delta sequence (named

after the German mathematician Leopold Kronecker [1823–1891]) is defi ned ana-

lytically as follows and illustrated in Figure 1.7.

()n

n

n

10

00

for

for 







Note that the discrete impulse is similar to the analog version δ(t).

R.1.17 A discrete shifted impulse δ(n − m) is illustrated in Figure 1.8.

*^ The ASCII code is defi ned in Chapter 3 of Practical MATLAB® Basics for Engineers.

1

− 2 − 1 0 123

n

FIGURE 1.

Plot of the discrete impulse δ(n).

FIGURE 1.

Plot of δ(n − m).

1

n

m − 1 m m + 1

(n − m)