Signal Processing Applications and Algorithms

Course Outline:

1. Introduction – Deterministic Signals
In this chapter we introduce the theory of Deterministic Signal Processing that is the basics of every DSP system.
We demonstrate the basic principles with lab examples.

• Continuous Time Signals:
  • Periodic and Non-periodic Signals
  • Spectral representation
  • Continues Fourier Transform 
• Discrete Time Signals:
  • Sampling Theorem
  • Spectral representation
  • Discrete Time Fourier Transform
  • Z Transform
• Linear Time Invariant discrete t time systems
  • The LTI discrete time system
  • The linear convolution
  • Difference Equations
  • Transfer Functions
  • Zero-Pole Map
  • Causality and Stability
• Discrete Fourier Transform
  • DFT
  • IDFT
  • FFT
  • IFFT

Lab1: Deterministic Signals and Systems

2. Statistical Signal Processing
In this chapter we develop the theory of Random Signal Processing that is based on Statistical Modeling. We show the relations between Statistical and Spectral properties. We develop algorithms for Quantization and Compression of Random and Deterministic Signals.
We demonstrate the Statistical Signal Processing Algorithms with lab examples.

• Introduction
• Random Signals:
  • Probability Density Function (PDF)
  • The Histogram
  • Gaussian Distribution
  • Expectation
  • Variance
  • White Gaussian Noise
  • Cross-Correlation and Auto-Correlation Function
  • Power Spectral Density (PSD)

Lab 2: Random Signals Generation and Analysis

• Signal and Parameter Quantization:
  • Uniform Quantization
  • Quantization Noise
  • Non-Uniform Quantization
  • Vector Quantization (Optional)
  • Lloyd Algorithm (Optional)

Lab 3: Scalar and Vector Quantization

• Signal Compression and Coding:
  • PCM – Pulse Code Modulation
  • DPCM and ADPCM algorithms
  • Speech Signals
  • LPC algorithm (Optional)
  • Levinson algorithm (Optional)

Lab 4: Speech Signal Compression and Coding

3. Advanced Signal Processing
In this chapter we develop Methods for Advanced Signal Processing. We Design and Implement Digital FIR and IIR filters. We develop algorithms Adaptive filters and Spectral Estimation.
We demonstrate Advanced Signal Processing Algorithms with lab examples.

• Digital filter Design:
  • Introduction
  • FIR – GLP filters – Type I,II,III,IV
  • IIR filters – Butterworth, Chebyshev, Elliptic 
  • Filter implementation
  • Quantization effects (Optional)