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Laxmi Institute of Technology, Sarigam DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING STUDENT REFERENCE MANUAL B.E COURSE SEMESTER- VII (Jul-Dec 2014) Address: Post Bag No. 15, Shrigam P. O Valsad, Gujarat 0260 278 6661 Website:www.litsarigam.co.in
Vision Laxmi Institute of technology endowed with awareness on abundance of human resources particularly concentrated in the band of aspiring youth making them reach the technical standards par global achievements, achievable through a balanced blend of impregnated tradition giving rooms to the indispensable evolutionary changes taking place in present scenario, through a structure of basic ethical values, dedication of the staff and high standards of technological infrastructural support. To evolve a system of education - the needs of the youthful India, to foster the creative individual and collective intelligence getting to surface the individualist latent talents without distorting the impregnated cultural, ethical and basic characteristic values. Mission The diversified curriculum of education under one umbrella, prioritized to reach the deserving, capacitated youth assorted from socio economic backgrounds making them a promising product of our visionary institution. To provide education of high global standards with the able guidance of dedicated professionals and a state of art ambience and to produce an unparalleled group of technocrats and engineers with high acumen and expertise. To be in consonance with the national needs to reach the highest standards of quality education to those socio economically backward but deserving strata of youth yearning for their due share of participation in this field of education, breaking through the geographical proximities.
Why Laxmi Institute of Technology? Premier Institute of higher Education & Research. Excellent track record for conduction campus placement events year after year. Dynamism in Curriculum. State of the art infrastructure, laboratories, libraries, classrooms. Highly qualified & experienced faculty. Leadership in quality education. Excellent boarding & lodging facilities. Round the clock high class perimeter security. University ensures absolutely ragging free environment. Strong industry-university interface ensuring excellent placement and training of students. Leadership in quality education. The pedagogy policy of university has its root in slogan, “Empowering India through Education”
ACADEMIC CALENDAR (AY 2015-2016) Activity Tentative Date th th th Starting of 5 & 7 semester 15 JUNE 2015 Workshop on Smart City 27 JUNE 2015 th rd nd Starting of 3 semester 2 JULY 2015 th th Class Test-1 of 5 & 7 Semester 1 Week of JULY 2015 st th Parents Teacher meeting 11 JULY 2015 th rd Class Test-1 of 3 Semester 4 Week of JULY 2015 th th th Class Test-2 of 5 & 7 Semester 4 Week of JULY 2015 rd Starting of Bridge Course 3 AUGUST 2015 Orientation Program for First Year students 5 AUGUST 2015 th th Class Test-2 of 3 Semester 5 AUGUST 2015 rd th th Mid Semester Exam for 3 , 5 and 7 Semester 17 – 25 AUGUST 2015 th rd th End of Bridge Course 28 AUGUST 2015 th st Starting of 1 Semester 31 AUGUST 2015 st rd th th Result to be displayedfor bridge course, 3 , 5 and 7 Sem. rd Mid Semester Exams 3 SEPTEMBER 2015 rd th Class Test-1 for 1 Semester Class Test-3 for 3 , 5 and 7 nd th st Semester 2 Week of SEPTEMBER 2015 th Parents – Teachers Meeting 19 SEPTEMBER 2015 st th Students Feedback Week 21 – 24 SEPTEMBER 2015 th PUT & Internal Practical/Viva for 5 & 7 Semester 1 – 9 OCTOBER 2015 th st th st Class Test-2 for 1 Semester th th th Final Detention List for 5 & 7 Semester 6 OCTOBER 2015 th th th Term End and Result to be displayed of 5 & 7 Semester 15 OCTOBER 2015 PUT & Internal Practical/Viva for 3 Semester 26 – 30 NOVEMBER 2015 th rd th Mid Semester Exam for 1 Semester 26 – 30 NOVEMBER 2015 st th th Final Detention List for 3 Semester 28 NOVEMBER 2015 th rd rd th Term End and Result to be displayed of 3 Semester 4 NOVEMBER 2015 st Class Test-3 for 1 Semester Last Week of NOVEMBER 2015 PUT & Internal Practical/Viva for 1 Semester 7 – 11 DECEMBER 2015 th st th st Final Detention List for 1 Semester 8 DECEMBER 2015 th Term End and Result to be displayed of 1 Semester 14 DECEMBER 2015 st th
TABLE OF CONTENTS Sr. No. NAME OF TOPICS 1 SCHEME AND SYLLABUS 2 LECTURE PLAN 3 REFERENCES 4 PRACTICAL LECTURE PLAN WITH REFERENCES 5 UNITWISE BLOW-UP 6 QUESTION BANK 7 PREVIOUS YEAR QUESTION PAPER
Course of Study and Scheme of Examination for Batch Starting from July 2015 B. Tech (ELECTRONICS AND COMMUNICATION ENGINEERING) Teaching Scheme(Hours) University University Continuous Subject Subject Name Credits Exam Exam Evaluation Practical Total Branch Code Theory Tutorial Practical (I) Marks Code (Theory) (E) (Practical) (E) Process (M) 171003 Digital Signal Processing 4 0 2 6 70 30 30 20 150 11 171007 Satellite communication 3 0 2 5 70 30 30 20 150 11 171002 Power Electronics 2 0 2 4 70 30 30 20 150 11 171004 Wireless Communication 4 0 2 6 70 30 30 20 150 11 171001 Microwave Engineering 3 0 2 5 70 30 30 20 150 11 TOTAL 16 0 14 30
171003 Digital Signal Processing
(i) Course Content Course Title Course Course Semester Theory Paper L T P Theory Paper Course Code Max.Marks:70 Digital Signal EC VII Sem 171003 4 0 2 Min. Marks:23 Processing Duration :2.30 hours UNIT 1 Introduction: Signals, systems and signal processing, classification of signals, elements of digital signal processing system, concept of frequency in continuous and discrete time signals, Periodic Sampling, Frequency domain representation of sampling, Reconstructions of band limited signals from its samples, general applications of DSP UNIT II Discrete-Time Signals and Systems: Discrete-Time Signals, Discrete-Time Systems, LTI Systems, Properties of LTI Systems, linear convolution and its properties, Linear Constant Coefficient Difference equations,. Frequency domain representation of Discrete-Time Signals & Systems, Representation of sequences by discrete time Fourier Transform, (DTFT), Properties of discrete time Fourier Transform, and correlation of signals, Fourier Transform Theorems. UNIT III The Z- Transform and Analysis Linear Time-of Invariant System: Z-Transform, Properties of ROC for Z-transform, the inverse Z-transform methods, Z- transforms properties, Analysis of LTI systems in time domain and stability considerations. Frequency response of LTI system, System functions for systems with linear constant- coefficient Difference equations, Freq. response of rational system functions relationship between magnitude & phase, All pass systems, inverse systems, Minimum/Maximum phase systems, systems with linear phase. UNIT IV: Structures for Discrete Time Systems: Block Diagram and signal flow diagram representations of Linear Constant-Coefficient Difference equations, Basic Structures of IIR Systems, Transposed forms, Direct and cascade form Structures for FIR Systems, Effects of Co-efficient quantization. UNIT V: Filter Design Techniques: Design of Discrete-Time IIR filters from Continuous-Time filters- Approximation by derivatives, Impulse invariance and Bilinear Transformation methods; Design of FIR filters by windowing techniques, Illustrative design examples of IIR and filters. Unit VI Discrete-Fourier Transform:
Representation of Periodic sequences: The discrete Fourier Series and its Properties Fourier Transform of Periodic Signals, Sampling the Fourier Transform, The Discrete-Fourier Transform, Properties of DFT, Linear Convolution using DFT. Unit VII Fast Fourier Transform: FFT-Efficient Computation of DFT, Goertzel Algorithm, radix2 and radix 4 Decimation-in- Time and Decimation-in-Frequency FFT Algorithms. Unit VIII Architecture of DSP Processors- : Harward architecture, pipelining, Multiplier-accumulator (MAC) hardware, architectures of fixed and floating point (TMSC6000) DSP processors.
(ii)Lecture Plan with References Subject Title: - Digital signal Session :- July – Dec 2015 processing Subject Code :- 171003 Semester :- VII Department :- ECE Branch :– ECE Lect. Topics to be Covered References No. Introduction 1 Signals, systems and signal processing T1: 2-6 2 Classification of signals T1:6-11 3 Elements of digital signal processing system, concept of T1: 12-18 frequency in continuous and discrete time signals 4 Periodic Sampling, Frequency domain representation of sampling T1: 26 5 Reconstructions of band limited signals from its samples, T1:410-426 general applications of DSP 6 Discrete-Time Signals, Discrete-Time Systems T1: 42-50 &54-67 Unit II - Discrete-Time Signals and Systems: 7 Linear convolution R6:2.51-2.61 8 linear convolution and its properties R6:2.54-2.56 9 Linear Constant Coefficient Difference equations,. T2:60-66 10 Frequency domain representation of Discrete-Time Signals & T2:66-74 Systems, 11 Representation of sequences by discrete time Fourier Transform, T2:74 (DTFT 12 Properties of discrete time Fourier Transform, and correlation of T2:81 signals, 13 Fourier Transform Theorems. T2:84-87 Unit III :The Z- Transform and Analysis Linear Time-of Invariant System 14 Z-Transform, Properties of ROC for Z-transform T2:130-131 15 the inverse Z-transform methods, Z- transforms properties T2:137-142 16 Analysis of LTI systems in time domain and stability T1: 193-200 considerations 17 Frequency response of LTI system T2:66-74 18 System functions for systems with linear constant-coefficient R6:3.49 Difference equations 19 Freq. response of rational system functions relationship between T2:300-05 magnitude & phase, All pass systems Unit IV:Structures for Discrete Time Systems: 21 Block Diagram and signal flow diagram representations of Linear T2:367 Constant-Coefficient Difference equations 22 Basic Structures of IIR Systems, T2:374 23 Direct Form I T2:380 24 Direct Form II T2:381 25 Parallel form T2:385 26 Cascade form T2:382
Unit V: Filter Design Techniques: 27 Design of Discrete-Time IIR filters from Continuous-Time filters- T2:465 Approximation by derivatives 28 Impulse invariance and Bilinear Transformation methods T2:469 29 Design of FIR filters by windowing techniques, Illustrative design T2:491-504 examples of IIR and filters. 30 Design of FIR filters by windowing techniques, Illustrative design T2:491-504 examples of IIR and filters. 31 Design of FIR filters by windowing techniques, Illustrative design T2:491-504 examples of IIR and filters. 32 Design of FIR filters by windowing techniques, Illustrative design T2:491-504 examples of IIR and filters. 33 The discrete Fourier Series and its Properties Fourier Transform of R6:4.1 Periodic Signals, Unit 6: Discrete-Fourier Transform: 34 The discrete Fourier Series and its Properties Fourier Transform R6: 4.2-13 of Periodic Signals, 35 Sampling the Fourier Transform R6:4.63 36 Sampling the Fourier Transform R6:4.63 37 The Discrete-Fourier Transform R6:5.1-5.4 38 The Discrete-Fourier Transform R6:5.1-5.4 39 Properties of DFT R6-5.9 40 Properties of DFT R6-5.9 41 Linear Convolution using DFT R6:5.12 42 Linear Convolution using DFT R6:5.12 43 Linear Convolution using DFT R6:5.12 44 Circular Convolution using DFT R6:5.16 45 Circular Convolution using DFT R6:5.16 46 Unit 7: Fast Fourier Transform: 47 FFT-Efficient Computation of DFT T2:511 48 Goertzel Algorithm T2:542 49 radix2 and radix 4 Decimation-in-Time T2:519 50 radix2 and radix 4 Decimation-in-Frequency FFT Algorithms T2:532 Unit 8 : Architecture of DSP Processors 51 Harward architecture, pipelining, Multiplier-accumulator (MAC) R5:`326 hardware 52 architectures of fixed and floating point (TMSC6000) DSP R5:329 processors Abbreviations used in the reference column are explained at the end of the Lecture Plan. Reference Books: Text Books: 1. “Digital Signal Processing: Principles, Algorithm & Application”,4th edition,Proakis, Manolakis, Proakis, Manolakis, Pearson 2. “Discrete Time Signal Processing”:Oppeheim, Schafer, Buck Pearson education publication, 2nd Edition, 2003. Reference Books: 1. Digital Signal Processing fundamentals and applications, Li Tan , Elsevier 2. Fundamentals of digital Signal Processing –Lonnie c.Ludeman, Wiley
3. Digital Signal processing-A Practical Approach ,second edition, Emmanuel feacher, and Barrie W..Jervis, Pearson Education. 4. Digital Signal Processing, S.Salivahanan, A.Vallavaraj, C.Gnapriya TMH 5. Digital Signal Processors, Architecture, programming and applications by B. Venkatramani, M Bhaskar, Mc-Graw Hill 6: Digital Signal Processing by Nagoor Kani, Second Edition, TMH publication
PRACTICAL PLAN Subject Title: - Digital signal Session :- July – Dec 2015 processing Subject Code :- 171003 Semester :- VII Department :- ECE Branch :– ECE Sr. List of Experiment References No. 1 Matlab Basics R1: 2.118 2 Generation Of Basic Signals Using Matlab R1: 2.118 3 Generation Of Basic Discrete Signals R1:2.119 4 Even And Odd Signal R1:2.119 5 Verification Of Sampling Theorem W1 6 Impulse Response Of An LTI System W3 7 Linear Convolution Using Matlab W2 8 De Convolution Using Matlab W2 9 Circular Convolution Using Matlab R1:5.58 10 Z Transform And Inverse Z Transform R1:3.117 11 DFT And IDFT R1:5.58 12 FFT And IFFT R1: Digital Signal Processing by Nagoor Kani, Second Edition, TMH publication W1: https://matlabcodes.wordpress.com/2013/02/02/sampling-theorem/ W2: http://in.mathworks.com/help/signal/ug/linear-and-circular-convolution.html W3: http://in.mathworks.com/help/control/ref/linearsystemanalyzer.html
(iii) UNIT WISE (BLOW: UP) UNIT I - INTRODUCTION A signal is a description of how one parameter varies with another parameter. For instance, voltage changing over time in an electronic circuit, or brightness varying with distance in an image. A system is any process that produces an output signal in response to an input signal. This is illustrated by the block diagram in Fig. 5-1. Continuous systems input and output continuous signals, such as in analog electronics. Discrete systems input and output discrete signals, such as computer programs that manipulate the values stored in arrays. Signals and systems are frequently discussed without knowing the exact parameters being represented. This is the same as using x and y in algebra, without assigning a physical meaning to the variables. This brings in a fourth rule for naming signals. If a more descriptive name is not available, the input signal to a discrete system is usually called: x[n], and the output signal: y[n]. For continuous systems, the signals: x(t) and y(t) are used. UNIT – II: Discrete-Time Signals and Systems: A discrete-time system is a device or algorithm that, according to some well-defined rule, operates on a discrete-time signal called the input signal or excitation to produce another discrete-time signal called the output signal or response. LTI SYSTEMS: An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal DTFT In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to the uniformly-spaced samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data (samples) whose interval often has units of time. PROPERTIES OF DTFT – Periodicity, Linearity, Conjugation, Time Reversal, Symmetry, Time shifting and frequency shifting, Differencing and summation, Time and frequency scaling, Diffentiation in frequency domain, Passeval’s relation. CONVOLUTION Convolution is a mathematical way of combining two signals to form a third signal. It is the single
most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response. Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response. This chapter presents convolution from two different viewpoints, called the input side algorithm and the output side algorithm. Convolution provides the mathematical framework for DSP. FOURIER TRANSFORMS: The Fourier transform is a reversible, linear transform with many important properties. For any function f(x) (which in astronomy is usually real-valued, but f(x) may be complex), the Fourier transform can be denoted F(s), where the product of x and s is dimensionless. Often x is a measure of time t (i.e., the time-domain signal) and so s corresponds to inverse time, or frequency UNIT III - The Z- Transform and Analysis Linear Time-of Invariant System The Fourier transform does not converge for all sequences. Specifically, depending on the definition of convergence used, the sequence is required to be either absolutely summable or have finite energy. It is useful to note that for an LSI system the condition for stability corresponds to the condition for convergence of the Fourier transform of the unit-sample response (i.e. the frequency response). The z-transform represents a generalization of the Fourier transform to include sequences for which the Fourier transform doesn't converge; and can be interpreted as the Fourier transform of the sequence modified by multiplication with a complex exponential. Associated with the z-transform is a region of convergence, i.e. a set of values of z for which the transform converges. As illustrated in the lecture two different sequences can have z- transforms of the same functional form and thus for which the z-transforms are distinguished only by their regions of convergence. This emphasizes the importance of the region of convergence in specifying the z-transform. Based on the properties of the region of convergence it is often possible to indicate implicitly the region of convergence for the z- transform. For example an indication that a sequence is right-sided implies that the region of convergence lies outside the outermost pole in the z-plane. Corresponding statements can be made about left-sided and two-sided sequences. Also, for a 'stable' sequence, the region of convergence includes the unit circle in the z-plane. Thus if it is indicated that a z-transform corresponds to a stable sequence then its region of convergence is implied. UNIT IV - Structures for Discrete Time Systems: A system structure is a pictorial representation of it which servers as basis for two possible goals: Software development targeted for general purpose computer or DSP ; Hardware architecture design targeting VLSI components Direct form I Recall the difference equation
Direct form – II By switching the order of the two sub-systems of the direct form I we get the Direct Form II (the 2 delay lines in the middle have been merged Cascade form: A rational system function with M1 real zeros N1 real poles M2 complex-conjugate pairs of zeros N2 complex-conjugate pairs of poles is written as Parallel forms It is possible to write a rational system function as sum (hence parallel) of SOSs:
UNIT V - Filter Design Techniques Filter is a system that passes certain frequency components and totally rejects all others. FIR filters are filters having a transfer function of a polynomial in z - and is an all-zero filter in the sense that the zeroes in the z-plane determine the frequency response magnitude characteristic. UNIT VI - Discrete-Fourier Transform: Fourier analysis is a family of mathematical techniques, all based on decomposing signals into sinusoids. The discrete Fourier transform (DFT) is the family member used with digitized signals. This is the first of four chapters on the real DFT, a version of the discrete Fourier transform that uses real numbers to represent the input and output signals. The complex DFT, a more advanced technique that uses complex numbers, will be discussed in Chapter 29. In this chapter we look at the mathematics and algorithms of the Fourier decomposition, the heart of the DFT. UNIT VII - Fast Fourier Transform: There are several ways to calculate the Discrete Fourier Transform (DFT), such as solving simultaneous linear equations or the correlation method described in Chapter 8. The Fast Fourier Transform (FFT) is another method for calculating the DFT. While it produces the same result as the other approaches, it is incredibly more efficient, often reducing the computation time by hundreds. This is the same improvement as flying in a jet aircraft versus walking! If the FFT were not available, many of the techniques described in this book would not be practical. While the FFT only requires a few dozen lines of code, it is one of the most complicated algorithms in DSP UNIT VIII - Architecture of DSP Processors- : Filter circuits are used in a wide variety of applications. In the field of telecommunication, band- pass filters are used in the audio frequency range (0 kHz to 20 kHz) for modems and speech processing. High-frequency band-pass filters (several hundred MHz) are used for channel selection in telephone central offices. Data acquisition systems usually require anti-aliasing low-pass filters as well as low-pass noise filters in their preceding signal conditioning stages. System power supplies often use band-rejection filters to suppress the 60-Hz line frequency and high frequency transients. Types: Butterworth Low-Pass Filters, Tschebyscheff Low-Pass Filters, Bessel Low-Pass Filters
QUESTION BANK S.N Unit I Mark Year o s 1 Check the following systems for time invariance and linearity 06 Nov’ 2 i) y(n) = n[x(n)] ii) y(n) = x(n)cos(nπ/4) 11 2 Define the following with respect to discrete time systems: 04 Jan (i) Linear Shift Variant System (ii) Recursive system (iii)Stable 13 System (iv) Causal system 3 Check for the shift invariance and stability of an accumulator 04 Jan 13 4 For each of the following systems, determine whether the 07 June system is (1) Stable (2) Causal (3) Linear (4) Time 12 invariant (i) y[n] = x[n]+ 3u[n+1] (ii) y[n] = x[Mn] M is an integer, greater than 1. 5 Find if following systems are linear, causal, stable, time-invariant and 07 May Memoryless 13 6 A discrete-time signal is defined as 07 May 13 (i) Find the values of x(n) and sketch the sequence (ii) Find x(-n+4)and sketch (iii) Find x(n-4) and sketch 7 State and explain the conditions followed by all LTI (Linear Time 07 June Invariant) 13 systems in general giving one example each of LTI and non-LTI systems. 8 Define impulse response of LTI system. Explain how from the impulse 07 June response 13 the frequency response of the LTI system can be determined. 9 Derive the criterion for sampling a continuous time signal, using 07 June Fourier 13 Transform. Also explain the aliasing effect where the criterion is not followed. 10 Prove that convergence of absolute sum of the impulse response is a 07 June sufficient 13 condition for BIBO (bounded input bounded output) stability of a LTI system. Show that this condition is also the necessary condition for BIBO stability. 11 a)Check whether the following signal is periodic or not. If a signal is 08 June periodic, find its fundamental period. 14
n b) X (n) = (-0.5) u (n). State whether it is energy or power signal. Justify c) Define and explain the convolution and correlation. d) Determine if the following system describe by, Y(t) = Sin [ x (t+2) ] ; is memory less, causal ,linear ,time invariant, stable. Unit II 1 Find convolution of two sequences 08 Nov’ i) x(n) = (-1)n u(n) and h(n) = u(n) 11 ii) x(n) = [1,2,4] and h(n) = [1,1,1,1] 2 Explain impulse response and step response of a system. Find the step 07 Nov’ response of a system whose impulse response is h[n] = a—nu( --n) for 0 11 < a < 1 3 Define Stability of Discrete Time System. Derive the necessary and 07 Nov’ sufficient condition to test the stability. Test the stability of a system 11 whose Impulse response is h[n] = an u[n]. 4 Define DTFT. Using DTFT, find impulse response of a LTI system 07 Nov’ described by difference equation y(n) – 1/2 y(n – 1) = x(n) – ¼ x(n – 1) 11 5 Calculate DTFT of following signals i) x(n) = [ ¼ ¼ ¼ 1/4 ] ii) x(n) = 2( 08 Nov’ 3/4 )n u(n) 11 6 What is circular convolution? How is it different from linear 07 Nov’ convolution? Determine the circular convolution of two sequences x(n) 11 = cos(πn/2) for n=0,1,2,3 n h(n) = 2 for n= 0,1,2 7 Find inverse DFT of X(k) = [1 2 3 4 ] 07 Nov’ 11 8 Justify the following statements with respect to discrete time systems. 04 Jan (any 13 TWO) (i)An impulse input to an accumulator yields a unit step output (ii) For a causal LTI system impulse response h(n)=0 for n