Transforms to and from the Frequency Domain - Digital Video and Audio Broadcasting Technology - page 91

6 Transforms to and from the Frequency Domain

In this chapter, principles of transforms to and from the frequency domain
are discussed. Although it describes methods which are used quite gener-
ally throughout the field of electrical communication, a thorough knowl-
edge of these principles is of great importance to understanding the subse-
quent chapters on video encoding, audio encoding and Orthogonal
Frequency Division Multiplex (OFDM), i.e. DVB-T and DAB. Experts, of
course, can simply skip this chapter.

|U|(f)

1.0

0.5

0.5

0.2

0.1

f

0 1 2 3 4

DC

fundamental wave

Fundamental wave

t

u(t) = 0.5 + 1.0sin(t+0.2)+0.5sin(2t)+0.2sin(3t-1)+0.1sin(4t-1.5);

Fig. 6.1. Fourier Analysis of a periodic time domain signal

Signals are normally represented as signal variation with time. An oscil-
loscope, for example, shows an electrical signal, a voltage, in the time do-
main. Voltmeters provide only a few parameters of these electrical signals,
e.g. the DC component and the RMS value. These two parameters can also
be calculated from the voltage variation by using a modern digital oscillo-
scope. A spectrum analyzer shows the signal in the frequency domain. It is
possible to think of any time domain signal as being composed of an infi-