Download e-book for kindle: An Introduction to the Analysis and Processing of Signals by Paul A. Lynn (auth.)

By Paul A. Lynn (auth.)

ISBN-10: 0333340302

ISBN-13: 9780333340301

ISBN-10: 1349860549

ISBN-13: 9781349860548

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11 Reducing the limits of integration. Waveform (a) is an odd function and dispillys halfwave symmetry. Multiplication by sine wave (b) gives the waveform in (c). 11. 2 OIoice of time origin, and WQveform power The amount of work involved in calculating the Fourier series coefficients for a particular waveform shape is reduced if the waveform is either even or odd, and this may often be arranged by a judicious choice of time origin. 12 shows three versions of a square wave which differ only in their time origin.

Conversely, a waveform known to contain any second, fourth, or other even harmonic components cannot display half-wave symmetry. 9 I Halfwave symmetry. 10. I ts average value is clearly zero, giving A 0 = 0. Also all En are zero because the wave is an even function. The cosine coefficients are given by J I Te An = 7t f(x). cos nx . dx -7t = = ~{ f Te/2 f- --:

Indeed, a spectrum G(w) may invariably be expressed 16 as the sum of two other functions of w as follows G(w) = a(w) + jb(w) where a is an even function and b is an odd function. 8(b) at positive values of w. dt . e Jwt . dw. 21t Indeed, apart from the (l/21t) multiplier in the second equation (which arises from the use of angular frequency w rather than frequency expressed in cycles per second, or hertz) and the change of sign in the exponential index, the equations are identical in form. 5), which has an even spectrum containing only cosines.

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


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