## Digital Signal ProcessingClassification 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, Digital signal representation, analog to digital conversion.Discrete Time System Analysisz-transform and its properties, inverse z-transforms, difference equation - Solution by z-transform, application to discrete systems - Stability analysis, frequency response - Convolution - Fourier transform of discrete sequence - Discrete Fourier series. Discrete Fourier Transform and ComputationDFT properties, magnitude and phase representation - Computation of DFT using FFT algorithm - DIT and DIF - FFT using radix 2 - Butterfly structure.Design of Digital FiltersFIR and IIR realization - Parallel and cascade forms. FIR design : Windowing Techniques - Need and choice of windows - Linear phase characteristics.IIR design : Analog filter design - Butterworth and Chebyshev approximations; digital design using impulse invariant and bilinear transformation - Warping, prewarping - Frequency transformation.Programmable DSP ChipsArchitecture and features of TMS 320C54 signal processing chip - Quantization effects in designing digital filters. |

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### Contents

Table of Contents | 1 |

Chapter 1 Introduction 11 to 1128 | 104 |

Chapter 2 Discrete Time System Analysis 21 to 2 104 | 126 |

Chapter3 Discrete Fourier Transform and Computation 31 to 3148 | 2-105 |

Chapter 3 Discrete Fourier Transform and Computation 31 to 3 148 | 2-148 |

Chapter 4 Design of Digital Filters 41 to 4 200 | 2-200 |

Chapter4 Design of Digital Filters 4 1 to 4 200 | 4-1 |

Chapter 5 Programmable DSP Chips 51 to 5 44 | 4-5 |

Appendix B zTransform and DFT Properties B1toB4 | 5-4 |

am thankful to my colleagues for their suggestions and encouragement 1 also thank | 1 |

References R1toR2 | 2 |

Useful Formulae | 15 |

### Common terms and phrases

A/D converter aliasing amplitude analog filter anticlockwise bilinear transformation butterworth filter calculate causal chebyshev filter circular convolution circularly coefficients comparing above equation complex additions complex multiplication cutoff frequency delayed DIF-FFT difference equation digital filter Digital Signal Processing discrete time systems DSP processors DT signal equation becomes Example FFT algorithms finite FIR filter fourier transform frequency response given by equation given system equation Hence above equation Hence the system IIR system impulse response input sequence linear combination linear convolution linear phase lowpass filter LTI system N-point DFT obtained passband plotted point DFT poles rad/sec sampling frequency sequence x(n shift invariant shown in Fig shows signal flow graph Similarly Solution spectrum stable summation system function Theory Questions transfer function transition band unit circle unit sample response unit step window written x(ri y(ri z-plane zero