Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 4

the radar is a few hertz and the target spatial contour which gets convolved with this
signal is measured in fractions of hertz.
Composite signals are very difficult to process, and demand multi-rate signal
processing techniques. A typical composite signal in the time domain is depicted in
Figure 1.3(a), which may not give total comprehension. Looking at the spectrum of
the same signal in Figure 1.3(b) provides a better understanding. These graphs are
merely representative; in reality it is very difficult to sample composite signals due
to the wide range of frequencies present at logarithmic distances.

0.08

0.6

0.4

0.06

0.2

0.04

0

0.02

− 0.2

− 0.4

0

0 200 400 600 800 1000 0 0.1 0.2 0.3 0.4 0.5

Time Frequency

(a) (b)

Figure 1.3 Composite signal x ð t Þ

1.2.2 Random Signals
Only some signals can be characterised in a deterministic way through their
spectral properties. There are some signals which need a probabilistic approach.
Random signals such as shown in Figure 1.4(a) can only be characterised by their

4

0.07

Gaussian noise

0.06

2

0.05

0.04

0

0.03

0.02

− 2

0.01

0

− 4

4 2 0 2 4

0 1000 2000 3000 4000 5000

Probability density function

Time

(a) (b)

e ð x Þ 2

2

1

Figure 1.4 Random signal x ð t Þ with pdf

p

2

2