EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING M.I.E.T. ENGINEERING COLLEGE (Approved by AICTE and Affiliated to Anna University Chennai) TRICHY – PUDUKKOTTAI ROAD, TIRUCHIRAPPALLI – 620 007 DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL EE6403 & DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING II YEAR- IV Semester M.I.E.T 3 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING M.I.E.T. ENGINEERING COLLEGE (Approved by AICTE and Affiliated to Anna University Chennai) Sub.code:EE6403 TRICHY – PUDUKKOTTAI ROAD, TIRUCHIRAPPALLIBranch/Year/Sem – 620 :EEE/II/IV 007 Sub Name: DISCRETE TIME SYSTEM AND SIGNAL PROCESSING Staff Name: Ms.P.Delphine Mary _____________________________________________________________________________ UNIT I INTRODUCTION 9 Classification of systems: Continuous, discrete, linear, causal, stable, dynamic, recursive, time variance; classification of signals: continuous and discrete, energy and power; mathematical representation of signals; spectral density; sampling techniques, quantization, quantization error, Nyquist rate, aliasing effect. UNIT II DISCRETE TIME SYSTEM ANALYSIS 9 Z-transform and its properties, inverse z-transforms; difference equation – Solution by z-transform, application to discrete systems - Stability analysis, frequency response – Convolution – Discrete Time Fourier transform , magnitude and phase representation. UNIT III DISCRETE FOURIER TRANSFORM & COMPUTATION 9 Discrete Fourier Transform- properties, magnitude and phase representation - Computation of DFT using FFT algorithm – DIT &DIF using radix 2 FFT – Butterfly structure. UNIT IV DESIGN OF DIGITAL FILTERS 9 FIR & IIR filter realization – Parallel & cascade forms. FIR design: Windowing Techniques – Need and choice of windows – Linear phase characteristics. Analog filter design – Butterworth and Chebyshev approximations; IIR Filters, digital design using impulse invariant and bilinear transformation - Warping, prewarping. UNIT V DIGITAL SIGNAL PROCESSORS 9 Introduction – Architecture – Features – Addressing Formats – Functional modes - Introduction to Commercial DSProcessors. TOTAL : 45 PERIODS OUTCOMES: Ability to understand and apply basic science, circuit theory, Electro-magnetic field theory control theory and apply them to electrical engineering problems. TEXT BOOKS: 1. J.G. Proakis and D.G. Manolakis, ‗Digital Signal Processing Principles, Algorithms and Applications‘, Pearson Education, New Delhi, PHI. 2003. 2. S.K. Mitra, ‗Digital Signal Processing – A Computer Based Approach‘, McGraw Hill Edu, 2013. 3. Robert Schilling & Sandra L.Harris, Introduction to Digital Signal Processing using Matlab‖, Cengage Learning,2014. REFERENCES: 1. Poorna Chandra S, Sasikala. B ,Digital Signal Processing, Vijay Nicole/TMH,2013. 2. B.P.Lathi, ‗Principles of Signal Processing and Linear Systems‘, Oxford University Press, 2010 3. Taan S. ElAli, ‗Discrete Systems and Digital Signal Processing with Mat Lab‘, CRC Press, 2009. M.I.E.T 4 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING 4. Sen M.kuo, woonseng…s.gan, ―Digital Signal Processors, Architecture, Implementations & Applications, Pearson,2013 5. Dimitris G.Manolakis, Vinay K. Ingle, applied Digital Signal Processing,Cambridge,2012 6. Lonnie C.Ludeman ,‖Fundamentals of Digital Signal Processing‖,Wiley,2013 M.I.E.T 5 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING M.I.E.T. ENGINEERING COLLEGE (Approved by AICTE and Affiliated to Anna University Chennai) TRICHY – PUDUKKOTTAI ROAD, TIRUCHIRAPPALLI – 620 007 DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING Sub.code:EE6403 Branch/Year/Sem :EEE/II/IV Sub Name: DISCRETE TIME SYSTEM AND SIGNAL PROCESSING Staff Name: Ms.P.Delphine Mary Course Objectives To Classify signals and systems & their mathematical representation To analyze the discrete time systems Able to differentiate various transformation techniques & their computation Able to Study about filters and their design for digital implementation Study about a programmable digital signal processor & quantization effects Implement Digital filters using various structures. Course Outcomes On completion of course the students will be able to: Apply the concept of analyzing discrete time signals & systems in time and frequency domain. Classify the different types of systems. Apply z-transform and inverse Z transform to analyze discrete time systems Apply Radix-2 Algorithm to Compute Discrete Fourier Transform Explain different types of filters Explain various architectures of Digital signal processors Prepared by Verified by Ms.P.Delphine Mary HoD Approved by Principal M.I.E.T 6 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING Unit I INTRODUCTION 9 Classification of systems: Continuous, discrete, linear, causal, stable, dynamic, recursive, time variance; classification of signals: continuous and discrete, energy and power; mathematical representation of signals; spectral density; sampling techniques, quantization, quantization error, Nyquist rate, aliasing effect. 1. SIGNALS AND SYSTEM 1.0 PREREQISTING DISCUSSION A Signal is defined as any physical quantity that changes with time, distance, speed, position, pressure, temperature or some other quantity. A Signal is physical quantity that consists of many sinusoidal of different amplitudes and frequencies. Ex x(t) = 10t X(t) = 5x2+20xy+30y A System is a physical device that performs an operations or processing on a signal. Ex Filter or Amplifier. 1.1 CLASSIFICATION OF SIGNAL PROCESSING 1) ASP (Analog signal Processing) : If the input signal given to the system is analog then system does analog signal processing. Ex Resistor, capacitor or Inductor, OP-AMP etc. Analog ANALOG Analog Input SYSTEM Output 2) DSP (Digital signal Processing) : If the input signal given to the system is digital then system does digital signal processing. Ex Digital Computer, Digital Logic Circuits etc. The devices called as ADC (analog to digital Converter) converts Analog signal into digital and DAC (Digital to Analog Converter) does vice-versa. Analog ADC DIGITAL DAC Analog signal SYSTEM signal M.I.E.T 7 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING Most of the signals generated are analog in nature. Hence these signals are converted to digital form by the analog to digital converter. Thus AD Converter generates an array of samples and gives it to the digital signal processor. This array of samples or sequence of samples is the digital equivalent of input analog signal. The DSP performs signal processing operations like filtering, multiplication, transformation or amplification etc operations over this digital signals. The digital output signal from the DSP is given to the DAC. 1.1.1 ADVANTAGES OF DSP OVER ASP 1. Physical size of analog systems are quite large while digital processors are more compact and light in weight. 2. Analog systems are less accurate because of component tolerance ex R, L, C and active components. Digital components are less sensitive to the environmental changes, noise and disturbances. 3. Digital system are most flexible as software programs & control programs can be easily modified. 4. Digital signal can be stores on digital hard disk, floppy disk or magnetic tapes. Hence becomes transportable. Thus easy and lasting storage capacity. 5. Digital processing can be done offline. 6. Mathematical signal processing algorithm can be routinely implemented on digital signal processing systems. Digital controllers are capable of performing complex computation with constant accuracy at high speed. 7. Digital signal processing systems are upgradeable since that are software controlled. 8. Possibility of sharing DSP processor between several tasks. 9. The cost of microprocessors, controllers and DSP processors are continuously going down. For some complex control functions, it is not practically feasible to construct analog controllers. 10. Single chip microprocessors, controllers and DSP processors are more versatile and powerful. 1.1.2 Disadvantages Of DSP over ASP 1. Additional complexity (A/D & D/A Converters) 2. Limit in frequency. High speed AD converters are difficult to achieve in practice. In high frequency applications DSP are not preferred. 1.2 CLASSIFICATION OF SIGNALS 1. Single channel and Multi-channel signals 2. Single dimensional and Multi-dimensional signals 3. Continuous time and Discrete time signals. 4. Continuous valued and discrete valued signals. 5. Analog and digital signals. 6. Deterministic and Random M.I.E.T 8 DEPT OF ECE EE6403 DISCRETE TIME SYSTEMS & SIGNAL PROCESSING signals 7. Periodic signal and Non-periodic signal 8. Symmetrical(even) and Anti-Symmetrical(odd) signal 9. Energy and Power signal 1) Single channel and Multi-channel signals If signal is generated from single sensor or source it is called as single channel signal. If the signals are generated from multiple sensors or multiple sources or multiple signals are generated from same source called as Multi-channel signal. Example ECG signals. Multi-channel signal will be the vector sum of signals generated from multiple sources. 2) Single Dimensional (1-D) and Multi-Dimensional signals (M- D) If signal is a function of one independent variable it is called as single dimensional signal like speech signal and if signal is function of M independent variables called as Multi-dimensional signals. Gray scale level of image or Intensity at particular pixel on black and white TV are examples of M-D signals. 3) Continuous time and Discrete time Ssig. Nonals. Conti nuous Time (CTS)