Page 276 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

Thus, by Eq. (5.74) we obtain

Let

The harmonic form of y(r) is given by [Eq. (5.15)]

where Dk is the amplitude of the kth harmonic component of y(t ). By Eqs. (5.11) and (5.16),
D, and d, are related by

Thus, from Eq. (5.167), with m = 0, we obtain
D, = 21d,I = 2 1 10

I=1.71
ja(2 + ja)
With m = 1, we obtain

5.47. The most widely used graphical representation of the frequency response H(w) is the
Bode plot in which the quantities 2010glo~H(w)l and 8,(0) are plotted versus w, with
w plotted on a logarithmic scale. The quantity 2010glolH(o)l is referred to as the
magnitude expressed in decibel! (dB), denoted by (H(o)l,,. Sketch the Bode plots for
the following frequency responses:

104(1 + jo)
(c) H(w) =
(10 + jw)(lOO + jw)

For o << 10,