COURSE NAME DIGITAL SIGNAL PROCESSING COURSE CODE: EC 701 Dr. Mrutyunjay Rout Dept. of Electronics and communication Engineering NIT Jamshedpur NIT Jamshedpur 1 Course Description UNIT-I: DSP Preliminaries, Sampling, DT signals, sampling theorem in time domain, sampling of analog signals, recovery of analog signals, and analytical treatment with examples, mapping between analog frequencies to digital frequency, representation of signals as vectors, concept of Basis function and orthogonality. Basic elements of DSP and its requirements, advantages of Digital over Analog signal processing. UNIT-II: Discrete Fourier Transform, DTFT, Definition, Frequency domain sampling , DFT, Properties of DFT, circular convolution, linear convolution, Computation of linear convolution using circular convolution, FFT, decimation in time and decimation in frequency using Radix-2 FFT algorithm, Linear filtering using overlap add and overlap save method, Introduction to Discrete Cosine Transform UNIT-III: Z transform, Need for transform, relation between Laplace transform and Z transform, between Fourier transform and Z transform, Properties of ROC and properties of Z transform, Relation between pole locations and time domain behaviour, causality and stability considerations for LTI systems, Inverse Z transform, Power series method, partial fraction expansion method, Solution of difference equations. UNIT-IV: IIR Filter Design, Concept of analog filter design (required for digital filter design), Design of IIR filters from analog filters, IIR filter design by approximation of derivatives filter design by impulse invariance method, Bilinear transformation method, warping effect. Characteristics of Butterworth filters, Chebyshev filters and elliptic filters, Butterworth filter design, IIR filter realization using direct form, cascade form and parallel form, Finite word length effect in IIR filter design. UNIT-V: FIR Filter Design, Ideal filter requirements, Gibbs phenomenon, windowing techniques, characteristics and comparison of different window functions, Design of linear phase FIR filter using windows and frequency sampling method. FIR filters realization using direct form, cascade form and lattice form, Finite word length effect in FIR filter design, Multirate DSP, Introduction to DSP Processor Concept of Multirate DSP, Sampling rate conversion by a non-integer factor, Design of two stage sampling rate converter, General Architecture of DSP, Introduction to Code composer studio, Application of DSP to Voice Processing, Music Processing, Image processing and Radar processing 2 NIT Jamshedpur Books Text Books: 1. John G Proakis and Manolakis, “Digital Signal Processing Principles, Algorithms and Applications”, Pearson, Fourth Edition, 2007. 2. S.Salivahanan, A. Vallavaraj, and C. Gnanapriya, “Digital Signal Processing”, TMH/McGraw Hill International, 2007. Reference Books: 1. S.K. Mitra, “Digital Signal Processing, A Computer-Based Approach”, Tata Mc Graw Hill, 1998. 2. Ifaeachor E.C, Jervis B. W., “Digital Signal processing: Practical approach”, Pearson publication, Second edition, 2002. 3. Johny R. Johnson, Introduction to Digital Signal Processing, PHI, 2006. NIT Jamshedpur 3 Lecture: 1-8 Introduction to Digital Signal Processing NIT Jamshedpur 4 Lecture: 1-8 ➢ Signal processing emerged soon after World War I in the form of electrical filtering. ➢ With the invention of the digital computer and the rapid progress in VLSI technology during the 1960s, a new way of processing signals the signal processing is term as digital signal processing. ➢ Digital signal processors take the real world signals like audio, video, speech etc., that have been sampled and quantized and then mathematically manipulate them. ➢ Signals need to be processed so that the information that they contain can be displayed, analyzed, or converted to another type of signal that may be of use. NIT Jamshedpur 5 Lecture: 1-8 What is Signal? • Anything that carries information and represents as a function of independent variables such as time, space, temperature, pressure, etc. • Any physical quantity that can be varied in such a way as to convey information. • A signal is any quantity that depends on one or more independent variables. NIT Jamshedpur 6 Lecture: 1-8 Example of Signal • A radio signal represents the strength of an electromagnetic wave that depends on one independent variable, namely time is a 1-D signal. • Image is a 2-D signal. • A video signal is a 3-D signal. • Natural signals: ✓ Signals produced by the brain and heart ✓ Signals originating in galaxies, astronomical images etc. ✓ Speech signals, sounds made by dolphins ✓ Signals produced by lightning, the atmospheric pressure etc. • Man-made signals: ✓ Signals originating from satellites, radio, telephone, TV ✓ Signals due to ECG, EEG etc. ✓ signals generate from musical instruments NIT Jamshedpur 7 Lecture: 1-8 • Signal Processing: Process of operation in which the characteristics of a signal such as amplitude, shape, phase, frequency, etc. undergoes a change. OR Signal processing is the analysis, interpretation and manipulation of any signals like sound, images etc. • Types of signal processing: ✓ Analog Signal Processing ✓ Digital Signal Processing Analog Signal Analog Signal Analog Output X(t) Processing Signal y(t) Analog Input Sample and A/D Digital Signal D/A Analog Signal Hold Converter Processor Converter Output X(t) Signal y(t) • Digital Signal processors (DSP) take real-world signals like audio, video, pressure, temperature etc. that have been digitized and then mathematically manipulate them NIT Jamshedpur 8 Lecture: 1-8 Components of a DSP System NIT Jamshedpur 9 Lecture: 1-8 • Advantages of Digital Signal Processing: ✓Greater Accuracy ✓Cheaper ✓Ease of Data storage ✓Easy Operation ✓Flexibility ✓Multiplexing • Limitations of Digital Signal Processing: ✓Antialiasing Filter ✓Bandwidth limited by Sampling Rate ✓Quantization Error NIT Jamshedpur 10 Lecture: 1-8 • Applications of Digital Signal Processing: ✓In Communication ✓Consumer Application (e.g., TV, FM radio etc.) ✓Image processing ✓In Biomedical ✓In Radar and Sonar ✓In Speech and Music NIT Jamshedpur 11 Lecture: 1-8 • Any unwanted signal interfering with the main signal is termed as noise. So, noise is also a signal but unwanted. • Classification of Signals: Depending on the independent variables and the value of the function defining the signal. 1. Continuous-Time (CT) and Discrete-Time(DT) Signals 2. Continuous-valued and Discrete-valued Signals 3. Multichannel and Multidimensional Signals 4. Deterministic and Random Signals NIT Jamshedpur 12 Lecture: 1-8 Continuous-Time (CT) and Discrete-Time (DT) Signals: • Continuous-Time (CT) Signal: ➢ A CT Signal is a signal that is defined at each and every instant of time. It can be represented as x(t), where t is the independent variable. ➢ This type of signal shows continuity both in amplitude and time. These will have values at each instant of time. Sine and cosine functions are the best example of Continuous time signal. NIT Jamshedpur 13 Lecture: 1-8 Continuous-Time (CT) and Discrete-Time (DT) Signals: • Discrete-Time (DT) Signals: ➢ A DT signal is a signal that is defined at discrete instant of time. It can be represented as x(nT), where n is an integer and T is the time interval between two consecutive signal values (Sampling period). ➢ This type of signal shows continuity in amplitude but discrete in time. ➢ Relationship between time variables t and n of CT and DT signals. NIT Jamshedpur 14 Lecture: 1-8 Representation of Discrete-Time (DT) Signals: • Graphical Representation • Functional Representation • Tabular Representation n … -3 -2 -1 0 1 2 3 … X[n] … 0 0 0 1 1 1 1 … • Sequence Representation . 0 0 0 ณ1 1 1 1 . ↑ NIT Jamshedpur 15 Lecture: 1-8 • Continuous Valued and Discrete Valued Signals: ➢ Values of CT or DT signals can be continuous or discrete. ➢ If the signal takes on all possible values on a finite or an infinite range, it is said to be a Continuous valued signal. ➢ If the signal takes a set of discrete values, it is called Discrete valued signal. ➢ Continuous time and continuous valued : Analog signal. ➢ Continuous time and discrete valued: Quantized signal. ➢ Discrete time and continuous valued: Sampled signal. ➢ Discrete time and discrete values: Digital signal. NIT Jamshedpur 16 Lecture: 1-8 Multichannel and Multidimensional Signals: • Multichannel Signal: ➢ Signal is generated from multiple sources. ➢ For example: Electrocardiography (ECG) 3 lead and 12 lead signal. 푥1(푡) 푥 푡 = 푥2(푡) 푥3(푡) • Multidimensional Signal: ➢ If the signal is function of one independent variable is called one dimension signal otherwise the signal is called M-dimensional signal ➢ For example: Video signal, I(x,y,t) is a 3-Dimensional signal because I is the function of three independent variables (x,y,t). NIT Jamshedpur 17 Lecture: 1-8 Deterministic and Random Signals: • Deterministic Signal: ➢ A signal is said to be deterministic if there is no uncertainty with respect to its value at any instant of time. Or, signals which can be defined exactly by a mathematical formula are known as deterministic signals. ➢ This signal is predicted at any time. • Random Signal: ➢ A signal is said to be Random if there is uncertainty with respect to its value at some instant of time ➢ Random signals cannot be described by a mathematical equation. ➢ Random signals are modelled in probabilistic terms. NIT Jamshedpur 18 Lecture: 1-8 Standard Discrete-Time Signals: • Unit Step Sequence: ➢ The unit step sequence can be