By K. Sam Shanmugan
Presents a close, unified remedy of theoretical and useful facets of electronic and analog communique structures, with emphasis on electronic conversation platforms. Integrates theory—keeping theoretical info to a minimum—with over 60 useful, labored examples illustrating real-life equipment. Emphasizes deriving layout equations that relate functionality of useful blocks to layout parameters. Illustrates easy methods to exchange off among energy, band-width and kit complexity whereas preserving an appropriate caliber of functionality. fabric is modularized in order that acceptable parts might be chosen to educate a number of diversified classes. contains over three hundred difficulties and an annotated bibliography in every one bankruptcy.
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Extra resources for Digital and Analog Communication Systems
Example text
This extension is due to the periodicity of x(t). Properties of the Fourier Series. Fourier series are listed below: Some of the important properties of the 1. 16) where the asterisk denotes complex conjugate. 2. o) = 0 if x(t) is odd 3. For x(t) reat or complex, I To f T 2 oI _ToI2 1x (lW dt = n~.. oW .. 19) The preceding equation is known as Parseval's theorem. 4. 20) n=1 The coefficients of this series are real, and are related to the coefficients of the complex exponential series of x(t) by CAnfo) = VA~+B~ .
We can rewrite Cx(nlo) as Cx(nlo) = AloT (sin( 7T;/oT») = AloT sinc(nloT) 7Tn OT where the "sinc" lunction is defined as . sin 7Ty S1OC(y)=-7TY Plots of ICx(nlo)l. phase of Cx(n/o}. 3 for the value of T = T015. 2 Rectangular pulse waveform. 3 Spectra of a rectangular waveform. (a) Amplitude spectrum. (b) Phase spectrum. (e) Power spectral density. 2. Find the Fourier series of a periodic impulse train defined by 00 x(t) = ~ 8(t - kTo) "=-00 Solution. CAn/o) = T1 ~ 0 = T1 ~ 0 J T 2 oI x(t) exp(-j27Tn/ot) dt -ToI2 J T 2 oI 8(1) exp(-j27Tn/ot) dt = T1 ~ 0 -ToI2 Hence, the Fourier series for x(t) is given by 00 x(t) =~ 1 To exp(j27Tn/ot) In systems analysis, the Fourier series can be used to calculate the steady-state output of a linear time-invariant system responding to an arbitrary periodic waveform.
A singularity function that we will use quite frequently in analyzing signals in communication systems is the unit impulse or Dirac delta function 8(t). The unit impulse 8(t) is not a function in a strict mathematical sense and it is usually defined by an integral relationship. 4) has the following properties: 1. 5) 1 2. 7) ° 3. 8(at) = a¢O d 4. 8) where u(t) is the unit step function defined as u(t)={l fort>O} o for t < 0 5. Numerous conventional functions approach 8(t) in the limit. For example, .