Digital signal processing (course master's degree program, Moscow State University )
Материал из MachineLearning.
Строка 28: | Строка 28: | ||
=== Part 1 Signal representation. Classical signal analysis === | === Part 1 Signal representation. Classical signal analysis === | ||
- | * Theme 1. '''Signal representation. Signal | + | * Theme 1. '''Signal representation. Signal Spaces.''' |
- | * Theme 2. '''Spectral representation ( | + | * Theme 2. '''Dynamic Representation of Signals (Time Domain)''' |
- | * Theme | + | * Theme 3. '''Spectral representation (Frequency domain).''' History. Generalized Fourier series. Trigonometric basis. Examples. Gib_bs effect. Fourier Transform. Fourier Transform Properties |
- | * Theme | + | * Theme 4. '''From Physical to Digital Signal'''. Measuring Noise. Sampling. Aliasing. Quantization |
- | * Theme | + | * Theme 5. '''Spectral Analysis''' The Discrete Fourier Transform. The inverse DFT. Power Leakage. Tradeoff Between Time and Frequency Resolution |
- | * Theme | + | * Theme 6 '''Filtering and Feedforward Filters'''. Delaying. Z-plane. Phase Response. Digital Filters. |
- | * Theme | + | * Theme 7 '''Z-Transform'''. Examples of z-trsnsform. Convolution. Properties of z-transform. Impulse Response and the Transfer Function. |
- | * Theme | + | * Theme 8 '''Feedback filters.''' Resonance. Bandwidth. Mixing Feedback and Feedforward filters. Implementation. |
- | * Theme | + | * Theme 9. '''Compression'''. Entropy Compression. Source Compression. |
+ | * Theme 10 '''Audio and Video compression'''. Audio Coding Standards. Image coding Standards. Video Coding Standards. | ||
Строка 51: | Строка 52: | ||
* An Automatic Procedure for Matching Ultrasonic Railway Defectograms | * An Automatic Procedure for Matching Ultrasonic Railway Defectograms | ||
+ | == Practical work: == | ||
+ | |||
+ | * Sounds and signals. Harmonics | ||
+ | * Non-periodic signals. Noise | ||
+ | * Autocorrelation | ||
+ | * Discrete Fourier Transform | ||
+ | * Filtering | ||
+ | * Differentiation and Integration | ||
+ | * Modulation and sampling | ||
+ | |||
+ | == Students oral presentation: == | ||
+ | Fast Fourier Transform | ||
+ | |||
+ | Filtering and Feedforward filters | ||
+ | |||
+ | Z-Tranform and Convolution | ||
+ | |||
+ | Feedback filters | ||
+ | |||
+ | Compression | ||
+ | |||
+ | Audio- Video Codecs | ||
+ | |||
+ | Statistical Signal processing | ||
+ | |||
+ | Adaptive Filtering | ||
+ | |||
+ | Inverse problem and Signal reconstruction | ||
+ | |||
+ | Time Frequency and Multirate signal processing | ||
+ | |||
+ | Speech Processing | ||
+ | |||
+ | Image and Video Processing | ||
+ | |||
+ | Nonlinear and Fractal Signal Processing | ||
+ | |||
== Textbooks: == | == Textbooks: == |
Текущая версия
|
- Master degree program, 1 year, autumn, department MMP ( ММП),
- Lectures — Thursday, 4:20 pm, room 605
- Control — exam, 14 June, 9:00, room 637
- Instructor — Krasotkina O.
- Office hours — Tuesday, Thursday, 11:00 am : 19:00 pm, or by appointment, room 532
Description:
The main goal of this course is to expose students to the mathematical theory of signal analysis, and at the same time, to some of its many applications in the finance, geophysic, image understanding, bioinformatics, and etc. Course begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. The signal is meant an experimentally acquired or mathematically simulated function of spatial coordinates and time which is to be analyzed with the purpose of studying behavior of the respective distributed dynamical system.
It was even Leonard Euler who marked that everything what happens in the world bears the sense of some minimum or maximum. The second part of course consider a wide class of signal analysis problems, which allow for treating them in unified terms of respective standard mathematical optimization problem for which there exist or can be created effective methods of solving. A signal is considered as a set of experimentally acquired values of a number of variables each of which is associated with respective node of an undirected adjacency graph that presents the fixed structure of the data set. The proposed theoretical approach is illustrated with its applications to the problems of segmentation, smoothing, fine texture analysis, matching of visual images, multi-alignment of long molecular sequences. .
Prerequisite:
Some prerequisites include linear algebra, functional analysis, optimization and probability theory. Practical work would typically involve a fair amount of scientific programming in Python or Matlab (Scilab).
Syllabus:
Introduction
Applied signal analysis problem . What is a signal? Signal analysis problems: examples .
Part 1 Signal representation. Classical signal analysis
- Theme 1. Signal representation. Signal Spaces.
- Theme 2. Dynamic Representation of Signals (Time Domain)
- Theme 3. Spectral representation (Frequency domain). History. Generalized Fourier series. Trigonometric basis. Examples. Gib_bs effect. Fourier Transform. Fourier Transform Properties
- Theme 4. From Physical to Digital Signal. Measuring Noise. Sampling. Aliasing. Quantization
- Theme 5. Spectral Analysis The Discrete Fourier Transform. The inverse DFT. Power Leakage. Tradeoff Between Time and Frequency Resolution
- Theme 6 Filtering and Feedforward Filters. Delaying. Z-plane. Phase Response. Digital Filters.
- Theme 7 Z-Transform. Examples of z-trsnsform. Convolution. Properties of z-transform. Impulse Response and the Transfer Function.
- Theme 8 Feedback filters. Resonance. Bandwidth. Mixing Feedback and Feedforward filters. Implementation.
- Theme 9. Compression. Entropy Compression. Source Compression.
- Theme 10 Audio and Video compression. Audio Coding Standards. Image coding Standards. Video Coding Standards.
Part 2 Statistical signal analysis
- Theme 1. The beyesian framework for the estimation of signal models.
- Theme 2. Hidden Markov Model of the Signal.
- Theme 3 Hidden Markov Model Estimation for Additive Loss Function
- Theme 4 Hidden Markov Model Estimation for Singular Loss Function
- Theme 5 Structural Parameters Estimation.
Selected applications:
- A mathematical and algorithmic framework for dynamic returns-based style analysis of investment portfolios
- A new method of seismic explorations for oil and gas in crystalline basement rocks
- An Automatic Procedure for Matching Ultrasonic Railway Defectograms
Practical work:
- Sounds and signals. Harmonics
- Non-periodic signals. Noise
- Autocorrelation
- Discrete Fourier Transform
- Filtering
- Differentiation and Integration
- Modulation and sampling
Students oral presentation:
Fast Fourier Transform
Filtering and Feedforward filters
Z-Tranform and Convolution
Feedback filters
Compression
Audio- Video Codecs
Statistical Signal processing
Adaptive Filtering
Inverse problem and Signal reconstruction
Time Frequency and Multirate signal processing
Speech Processing
Image and Video Processing
Nonlinear and Fractal Signal Processing
Textbooks:
- Theory and Application of Digital Signal Processing by Rabiner and Gold. A comprehensive, industrial-strength DSP reference book.
- Signal Computing:Digital Signals in the Software Domain by Michael Stiber, Bilin Zhang Stiber and Eric C. Larson. A very readable book