Contents

• 1. Introduction to Discrete-Time Signals and Systems

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  Objectives, Introduction, Signals, Classification of Signals, Deterministic and Non Deterministic Signals, Periodic and Aperiodic Signals, Even and Odd Signals, Energy and Power Signals, Some Basic Signals, Unit Impulse Function, Unit Step Function, Ramp Function, Exponential Signal, Sinusoidal Signal, Signum Function, Sinc Function, Transformation of Independent Variable, Time Shifting, Time Scaling, Time Reversal/Folding, Steps for Transformation of The Form x[?n + ?], System, Symbols used to Represent a Discrete Time System, Adder, Constant Multiplier, Signal Multiplier, Unit Delay, Unit Advance, Basic System Properties, Causality, Time Invariance and Time Variance, Stability, Linearity, Static and Dynamic System (Memory Less and With Memory), Invertible and Inverse, Order of a System, Review Questions, Numerical Problems.
   
  2. Linear Time Invariant (LTI) Systems

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  Objectives, Introduction, Characterization of LTI Systems, Convolution Sum for Discrete Time LTI Systems, Steps for Convolution Sum for two Discrete Signals, Properties of Linear Time Invariant (LTI) Systems, The Commutative Property, The Distributive Property, Associative Property of LTI Systems, Static and Dynamic LTI System, Inveriability of LTI Systems, Causality of LTI Systems, Stability of LTI Systems, Unit Step Response of an LTI System, Linear Constant Coefficient Difference Equations, Classical Method, Iterative Method For Difference Equations, Basic Block Diagrams for Discrete Time LTI Systems used in Difference Equation, Review Questions, Numerical Problems.
   
  3. Discrete Time Fourier Transform (DTFT)

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  Objectives, Introduction, Discrete Time Fourier Transform (DTFT) for Aperiodic Signals, Convergence of the DTFT, Fourier Transform for Discrete Time Periodic Signals, Properties of Discrete Time Fourier Transform (DTFT), Periodicity, Linearity, Time Shifting Property, Frequency Shifting Property, Multiplication by n: Frequency Differentiation, Complex Conjugation and Conjugate Symmetry, Time Reversal, Convolution Property, Scaling, Multiplication in Time Domain, Parseval’s Relation, Energy Density Spectrum of Discrete Time Aperiodic Signals, Duality, Differencing and Accumulation in Time, Frequency Response of Discrete Time LTI Systems, Review Questions, Numerical Problems.
   
  4. The z-Transform

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  Objectives, Introduction, Definition of z-Transform, Two Sided or Bilateral z-Transform, Relationship between z-Transform and DTFT, One Sided or Unilaterral z-Transform, Region of Convergence (ROC), Properties of ROC for the z-Transform, Properties of z-Transform, Linearity, Time Shifting, Scaling in the z-Domain, Time Reversal, Time Expansion (Time Scaling), Differentiation in The z-Domain, Convolution of Two Discrete Time Sequences, Correlation of Two Discrete Time Sequences, Multiplication, Parseval’s Theorem or Relation, Conjugation of a Complex Sequence, Initial Value Theorem, Final Value Theorem, The Inverse z-Transform, The Inverse z-Transform by Contour Integration Method, The Inverse z-Transform by Power Series Expansion Method, The Inverse z-Transform form by long Division Method, The Inverse z-Transform by Partial Fraction Expansion Method, Applications of z-Transform In Analysis of Discrete Time LTI Systems, Causality of Discrete Time LTI System, Stability Criteria for a Discrete Time LTI Systems, Causal and Stable Discrete Time LTI Systems, The Characterization of Discrete Time LTI System by Linear Constant Coefficient Difference Equation, Determination of Poles and Zeros of Rational z-Transform, Review Questions, Numerical Problems.
   
  5. Sampling

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  Objectives, Introduction, Mathematical Theory of Sampling, Sampling, Impulse Train Sampling of A Continuous Time Signal (Ideal Sampling), Sampling Theorem, Sampling Techniques, Real Sampling, Sampling with a Zero-Order Hold, Natural Sampling, Reconstruction of Signal, Interpolation Function (Linear Interpolation) Ideal Reconstruction, Interpolation with Zero-order Hold (ZOH), Interpolation with First Order Hold (FOH), Aliasing, Sampling of Discrete Time Signals, Impulse Train Sampling of Discrete Time Signals, Review Question, Numerical Problems.
   
  6. Discrete Fourier Transform (DFT)

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  Objectives, Introduction, Different Forms of Fourier Transform, Continuous Time and Continuous Frequency, Continuous-Time and Discrete-Frequency, Discrete-Time and Continuous Frequency, Discrete-Time and Discrete-Frequency, Discrete Fourier Transform (DFT), Relationship Between DFT and Other Transforms, Relationship between DFT and Fourier Series Coefficients of a Periodic Sequence, Relation between DFT and the Spectrum of Infinite Duration (Aperiodic) Signal, Relationship of the DFT and z-transform, Properties of DFT, Periodicity, Linearity, Symmetry Properties of DFT, Circular Shift (Time-Domain Property), Time Reversal Property, Circular Shift Property (Frequency-Domain), Complex-Conjugate Properties, Circular Correlation, Parseval’s Theorem, Multiplication of two Sequences, Convolution of two Sequence, Convolution, Linear Convolution using DFT-IDFT Method, Efficient Computation of Discrete Fourier Transform (FFT Algorithms), Radix-2 FFT Algorithms, Review Questions, Numerical Problems.
   
  7. Structures For Discrete Time Systems

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  Objectives, Introduction, Block Diagram Representation of Linear Constant Coefficient Difference Equation, Advantages of Block Diagram Representation, Signal Flow Graph Representation of Linear Constant Coefficient Difference Equations, System Function From the Signal Flow Graph (SFG), Basic Structures for IIR Systems, Direct Form Structure for IIR Filter, Basic Structures For FIR Systems, Direct Form Structure, Cascade-Form Structures for FIR System, Lattice Structure for FIR System, Transposed Structures, Transposed Direct Form–II Structure for IIR System, Transposed Direct Form Structure for FIR System, Review Questions, Numerical Problems.
   
  8. Filter Design Techniques

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  Objectives, Introduction, Ideal and Practical Filters, Filter Specifications, Approximation Techniques, Butterworth Approximation, Chebyshev Filter Approximation, Analog Frequency Transformation, Normalized Low-Pass Filter to Desired Low-Pass Filter Transformation, Normalized Low-Pass Filter to Desired High-Pass Filter Transformation, Normalized Low-Pass Filter to Desired Bandpass Filter Transformation, Normalized Low-Pass Filter to Desired Band Elimination (Bandstop) Filter Transformation, Infinite Impulse Response Filter Design (IIR Filter Design), Design of Digital IIR Filters, Designing Steps For Butterworth IIR Filter Using Impulse Invariance or Bilinear z-Transform Method, Design Steps For Chebyshev IIR Filter by Using Bilinear Transformation or Impulse Invariance Transformation, Finite Impulse Response Filter (FIR Filter), Basic Fundamentals of FIR Filters, Design of Fir Filters by Windowing Techniques, Design Steps for FIR Filter with Windowing Technique (Calculation of FIR Filter Coefficients), Hamming Window, Kaiser Window, Kaiser Window Technique for Highpass Filter, Kaiser Window for Bandpass Filter, Kaiser Window for Band Stop Filter, Review Questions, Numerical Problems.
   
  P. Papers