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Note for Analog Communication Systems - ACS By Digbijay Patil

  • Analog Communication Systems - ACS
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Lecture Notes On Analogue Communication Techniques (Module 1 & 2) Topics Covered: 1. Spectral Analysis of Signals 2. Amplitude Modulation Techniques 3. Angle Modulation

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Module-I (12 Hours) Spectral Analysis: Fourier Series: The Sampling Function, The Response of a linear System, Normalized Power in a Fourier expansion, Impulse Response, Power Spectral Density, Effect of Transfer Function on Power Spectral Density, The Fourier Transform, Physical Appreciation of the Fourier Transform, Transform of some useful functions, Scaling, Time-shifting and Frequency shifting properties, Convolution, Parseval's Theorem, Correlation between waveforms, Auto-and cross correlation, Expansion in Orthogonal Functions, Correspondence between signals and Vectors, Distinguishability of Signals. Module-II (14 Hours) Amplitude Modulation Systems: A Method of frequency translation, Recovery of base band Signal, Amplitude Modulation, Spectrum of AM Signal, The Balanced Modulator, The Square law Demodulator, DSB-SC, SSBSC and VSB, Their Methods of Generation and Demodulation, Carrier Acquisition, Phase-locked Loop (PLL), Frequency Division Multiplexing. Frequency Modulation Systems: Concept of Instantaneous Frequency, Generalized concept of Angle Modulation, Frequency modulation, Frequency Deviation, Spectrum of FM Signal with Sinusoidal Modulation, Bandwidth of FM Signal Narrowband and wideband FM, Bandwidth required for a Gaussian Modulated WBFM Signal, Generation of FM Signal, FM Demodulator, PLL, Preemphasis and Deemphasis Filters. Module-III (12 Hours) Mathematical Representation of Noise: Sources and Types of Noise, Frequency Domain Representation of Noise, Power Spectral Density, Spectral Components of Noise, Response of a Narrow band filter to noise, Effect of a Filter on the Power spectral density of noise, Superposition of Noise, Mixing involving noise, Linear Filtering, Noise Bandwidth, Quadrature Components of noise. Noise in AM Systems: The AM Receiver, Super heterodyne Principle, Calculation of Signal Power and Noise Power in SSB-SC, DSB-SC and DSB, Figure of Merit ,Square law Demodulation, The Envelope Demodulation, Threshold Module-IV (8 Hours) Noise in FM System: Mathematical Representation of the operation of the limiter, Discriminator, Calculation of output SNR, comparison of FM and AM, SNR improvement using preemphasis, Multiplexing, Threshold in frequency modulation, The Phase locked Loop. Text Books: 1. Principles of Communication Systems by Taub & Schilling,2nd Edition.Tata Mc Graw Hill. Selected portion from Chapter1, 3, 4, 8, 9 & 10 2. Communication Systems by Siman Haykin,4th Edition, John Wiley and Sons Inc. References Books: 1. Modern digital and analog communication system, by B. P. Lathi, 3rd Edition, Oxford University Press. 2. Digital and analog communication systems, by L.W.Couch, 6th Edition, Pearson Education, Pvt. Ltd.

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Spectral Analysis of Signals A signal under study in a communication system is generally expressed as a function of time or as a function of frequency. When the signal is expressed as a function of time, it gives us an idea of how that instantaneous amplitude of the signal is varying with respect to time. Whereas when the same signal is expressed as function of frequency, it gives us an insight of what are the contributions of different frequencies that compose up that particular signal. Basically a signal can be expressed both in time domain and the frequency domain. There are various mathematical tools that aid us to get the frequency domain expression of a signal from the time domain expression and vice-versa. Fourier Series is used when the signal in study is a periodic one, whereas Fourier Transform may be used for both periodic as well as non-periodic signals. Fourier Series Let the signal x(t) be a periodic signal with period T0. The Fourier series of a signal can be obtained, if the following conditions known as the Dirichlet conditions are satisfied: 1. x(t) is absolutely integrable over its period, i.e.   x (t) dt  0  2. The number of maxima and minima of x(t) in each period is finite. 3. The number of discontinuities of x(t) in each period is finite. A periodic function of time say v(t) having a fundamental period T0 can be represented as an infinite sum of sinusoidal waveforms, the summation being called as the Fourier series expansion of the signal.  v (t)  A 0   n 1  2 n t  An c o s    T0   B n n 1  2 n t  sin    T0  Where A0 is the average value of v(t) given by: A0  1 T0 T0 / 2  v (t) d t  T0 / 2 And the coefficients An and Bn are given by 2 An  T0 Bn  2 T0 T0 / 2  2 nt  v (t) cos   dt  T0   T0 / 2  T0 / 2  2 nt v (t) sin   T0  T0 / 2    dt  Alternate form of Fourier Series is

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 v (t)  C 0   C n n 1 C 0  A0 C n   n An2  B  ta n 1  2 n t cos     T0 n    2 n Bn An The Fourier series hence expresses a periodic signal as infinite summation of harmonics of fundamental frequency f0  1 . The coefficients T0 C n are called spectral amplitudes i.e. C n is the amplitude of the  2 nt  spectral component C n cos    n  at frequency nf0. This form gives one sided spectral  T0  representation of a signal as shown in1st plot of Figure 1. Exponential Form of Fourier Series This form of Fourier series expansion can be expressed as :  v (t)  Ve j 2  nt / T0 n n  1 Vn  T0 T0 2   v (t)e j 2  nt / T0 dt T0 2 The spectral coefficients Vn and V-n have the property that they are complex conjugates of each other Vn  Vn* . This form gives two sided spectral representation of a signal as shown in 2nd plot of Figure1. The coefficients Vn can be related to Cn as : V0  C0 Vn  Cn  jn e 2 The Vn’s are the spectral amplitude of spectral components Vne j 2 ntf0 .

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