AdmBasisty / DSP

Lecture notes on digital signal processing

Lecture notes

1. Introduction

   A short review of signals and systems, convolution, discrete-time Fourier transform, and the z-transform.

2. Discrete-time random signals

   Theory on random processes and their importance in modeling complicated signals.

3. Linear and time-invariant systems

   Linear and time-invariant (LTI) systems are a particularly important class of systems. They're the systems for which convolution holds. We review their most important properties and how to analyze them.

4. Sampling and resconstruction

   The mathmatical formulation of sampling and reconstruction.

5. Resampling

   How to change the sampling rate of digital signals.

6. Quantization

   How to model quantization and its effects on digital systems.

7. Digital filter structures

   How to implement digital filters based on their difference equation.

8. Quantization in filter structures

   Effect of fix-point operations in digital filter, how to analyze it, and how to minimize its effects.

9. Filter design

   Filter design of infinite impulse response (IIR) and finite impulse response (FIR) filters.

10. Adaptive signal processing

    Introdcution to adpative signal processing using the least mean squares (LMS) algorithm.

11. Discrete Fourier transform

    The discrete Fourier transform (DFT) and its properties. This lecture also covers fast algorithms to compute the DFT known as fast Fourier transform (FFT).

12. Spectrum analysis

    Analysis of signals in the frequency domain using the DFT and FFT.

13. Power spectrum estimation

    How to estiamte the power spectrum density (PSD) of signals.

14. Parametric signal processing

    Introduction to parametric signal processing and how to use systems to represent complicated signals.

15. Review and conclusions

    Recap of the most important concepts covered throughout the course.

Homework assignments

Homework assignments and their solution can be found in this folder.