Learn · Digital Signal Processing and its Applications

Lecture 39 of 102Week 5

Lecture 13C: Example of Z transform

Prof. V. M. Gadre · IIT Bombay

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Digital Signal Processing and its Applications, IIT Bombay (at NPTEL)
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All the lectures

  1. Lecture 1: Introduction: Digital signal processing and its objectives Video
  2. Lecture 2A: Introduction to sampling and Fourier Transform Video
  3. Lecture 2B: Sampling of sine wave and associate complication Video
  4. Lecture 3A: Review of Sampling Theorem Video
  5. Lecture 3B: Idealized Sampling, Reconstruction Video
  6. Lecture 3C: Filters And Discrete System Video
  7. Lecture 4A: Answering questions from previous lectures. Video
  8. Lecture 4B: Desired requirements for discrete system Video
  9. Lecture 4C: Introduction to phasors Video
  10. Lecture 4D: Advantages of phasors in discrete systems Video
  11. Lecture 5A: What do we want from a discrete system? Video
  12. Lecture 5B: Linearity - Homogeneity and Additivity Video
  13. Lecture 5C: Shift Invariance and Characterization of LTI systems Video
  14. Lecture 6A: Characterization of LSI system using it's impulse response Video
  15. Lecture 6B: Introduction to convolution Video
  16. Lecture 6C: Convolution:deeper ideas and understanding Video
  17. Lecture 7A: Characterisation of LSI systems, Convolution-properties Video
  18. Lecture 7B: RESPONSE OF LSI SYSTEMS TO COMPLEX SINUSOIDS Video
  19. Lecture 7C: CONVERGENCE OF CONVOLUTION AND BIBO STABILITY Video
  20. Lecture 8A: Commutativity & Associativity Video
  21. Lecture 8B: BIBO Stability of an LSI system Video
  22. Lecture 8C: Causality and memory of an LSI system. Video
  23. Lecture 8D: Frequency response of an LSI system. Video
  24. Lecture 9A: Introduction and conditions of Stability Video
  25. Lecture 9B: Vectors and Inner Product. Video
  26. Lecture 9C: Interpretation of Frequency Response as Dot Product . Video
  27. Lecture 9D: Interpretation of Frequency Response as Eigenvalues Video
  28. Lecture 10A: Discrete time fourier transform Video
  29. Lecture 10B: DTFT in LSI System and Convolution Theorem. Video
  30. Lecture 10C: Definitions of sequences and Properties of DTFT. Video
  31. Lecture 11A: Introduction to DTFT, IDTFT Video
  32. Lecture 11B: Dual to convolution property Video
  33. Lecture 11C: Multiplication Property, Introduction to Parseval's theorem Video
  34. Lecture 12A: Introduction And Property of DTFT Video
  35. Lecture 12B: Review of Inverse DTFT Video
  36. Lecture 12C: Parseval's Theorem and energy and time spectral density Video
  37. Lecture 13A: Discussion on Unit Step Video
  38. Lecture 13B: Introduction to Z transform Video
  39. Lecture 13C: Example of Z transform Video
  40. Lecture 13D: Region of Convergence Video
  41. Lecture 13E: Properties of Z transform Video
  42. Lecture 14A: Z- Transform Video
  43. Lecture 14B: Rational System Video
  44. Lecture 15A: INTRODUCTION AND EXAMPLES OF RATIONAL Z TRANSFORM AND THEIR INVERSES Video
  45. Lecture 15B: DOUBLE POLE EXAMPLES AND THEIR INVERSE Z TRANSFORM Video
  46. Lecture 15C: PARTIAL FRACTION DECOMPOSITION Video
  47. Lecture 15D: LSI SYSTEM EXAMPLES Video
  48. Lecture 16A: Why are Rational Systems so important? Video
  49. Lecture 16B: Solving Linear constant coefficient difference equations which are valid over a finite range of time Video
  50. Lecture 16C: Introduction to Resonance in Rational Systems Video
  51. Lecture 17A: Characterization of Rational LSI system Video
  52. Lecture 17B: Causality and stability of the ROC of the system function Video
  53. Lecture 18A: RECAP OF RATIONAL SYSTEMS AND DISCRETE TIME FILTERS Video
  54. Lecture 18B: SPECIFICATIONS FOR FILTER DESIGN Video
  55. Lecture 18C: FOUR IDEAL PIECEWISE CONSTANT FILTERS Video
  56. Lecture 18D: IMPORTANT CHARACTERISTICS OF IDEAL FILTERS Video
  57. Lecture 19A: Synthesis of Discrete Time Filters, Realizable specifications Video
  58. Lecture 19B: Realistic Specifications for low pass filter. Filter Design Process Video
  59. Lecture 20A: Introduction to Filter Design. Analog IIR Filter,FIR discrete-time filter, IIR discrete-time filter. Video
  60. Lecture 20B: Analog to discrete transform Video
  61. Lecture 20C: Intuitive transforms, Bilinear Transformation Video
  62. Lecture 21A: Steps for IIR filter design Video
  63. Lecture 21B: Analog filter design using Butterworth Approximation Video
  64. Lecture 22A: Butterworth filter Derivation And Analysis of butterworth system function Video
  65. Lecture 22B: Chebychev filter Derivation Video
  66. Lecture 23: Midsem paper review discussion Video
  67. Lecture 24A: The Chebyschev Approximation Video
  68. Lecture 24B: Next step in design: Obtain poles Video
  69. Lecture 25A: Introduction to Frequency Transformations in the Analog Domain Video
  70. Lecture 25B: High pass transformation Video
  71. Lecture 25C: Band pass transformation Video
  72. Lecture 26A: Frequency Transformation Video
  73. Lecture 26B: Different types of filters Video
  74. Lecture 27A: Impulse invariant method and ideal impulse response Video
  75. Lecture 27B: Design of FIR of length (2N+1) by the truncation method,Plotting the function V(w) Video
  76. Lecture 28A: IIR filter using rectangular window, IIR filter using triangular window Video
  77. Lecture 28B: Proof that frequency response of an fir filter using rectangular window function centred at 0 is real. Video
  78. Lecture 29A: Introduction to window functions Video
  79. Lecture 29B: Examples of window functions Video
  80. Lecture 29C: Explanation of Gibb's Phenomenon and it's application Video
  81. Lecture 30A: Comparison of FIR And IIR Filter's Video
  82. Lecture 30B: Comparison of FIR And IIR Filter's Video
  83. Lecture 30C: Comparison of FIR And IIR Filter's Video
  84. Lecture 31A: Introduction and approach to realization (causal rational system) Video
  85. Lecture 31B: Comprehension of Signal Flow Graphs and Achievement of Pseudo Assembly Language Code. Video
  86. Lecture 32A: Introduction to IIR Filter Realization and Cascade Structure Video
  87. Lecture 32B: Cascade Parallel Structure Video
  88. Lecture 32C: Lattice Structure Video
  89. Lecture 33A: Recap And Review of Lattice Structure, Realization of FIR Function. Video
  90. Lecture 33B: Backward recursion, Change in the recursive equation of lattice. Video
  91. Lecture 34A: Lattice structure for an arbitrary rational system Video
  92. Lecture 34B: Example realization of lattice structure for rational system Video
  93. Lecture 35A: Introductory Remarks of Discrete Fourier Transform and Frequency Domain Sampling Video
  94. Lecture 35B: Principle of Duality, The Circular Convolution Video
  95. Live Session 28-01-2021 Video
  96. Live Session 11-02-2021 Video
  97. Live Session 04-03-2021 Video
  98. Live Session 18-03-2021 Video
  99. Live Session 20-02-2024 Video
  100. Live Session 15-04-2024 Video
  101. Live Session 25-02-2025 Video
  102. Live Session 04-04-2025 Video