By Paul A. Lynn (auth.)

ISBN-10: 0333340302

ISBN-13: 9780333340301

ISBN-10: 1349860549

ISBN-13: 9781349860548

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Extra info for An Introduction to the Analysis and Processing of Signals

Sample text

Cos nx . dx -7t = = ~{ f Te/2 f- --:

1 Introduction In the previous chapter we have seen how a periodic signal may be expressed as the sum of a set of sinusoidal waves which are harmonically related. The spectrum of such a signal consists of a number of discrete frequencies and is known as a 'line' spectrum. Although the analysis of periodic signals gives results which can be of great practical interest, the great majority of signals are not of this type. Firstly, even signals which repeat themselves a very large number of times are generally turned 'on' and 'off.

1 t " " - - 1 t - - - - - - ="it' I j(x). sin nx . dx -1t 2 -1t Although in the majority of cases it is convenient for the interval of integration to be symmetrical about the origin, any interval equal in length to one period of the signal waveform may be chosen. Many waveforms of practical interest are either even or odd functions of time. Iff(t) is even then by definitionf(t) =f(-t), whereasifit is oddf(t) =-f(-t). If f(t) is even and we multiply it by the odd function sin nWI t the result is also odd.

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An Introduction to the Analysis and Processing of Signals by Paul A. Lynn (auth.)


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