Course #11

Digital Signal Analysis Techniques: 

Time, Frequency, and Spatial Algorithms

Spring 2011. Location to be decided.

INSTRUCTOR
Professor S. Lawrence Marple Jr. 
Georgia Tech Research Institute, Smyrna GA, USA

TECHNOLOGY FOCUS 
Conventional tools for analyzing and extracting the feature content of signals are filters (time content), Fourier transforms (frequency content) and beamforming (spatial content). Alternative tools to these conventional techniques are able to produce signal analysis results with finer temporal detail and higher spectral and spatial resolution. This course goes beyond available textbooks and extends these signal analysis tools to higher dimensions and multiple sensor channels. 

COURSE CONTENT 
This course introduces practical implementation of the latest research approaches to time series and spectral analysis. The course uses a systematic approach based on a signal modelling theme, while focusing on fast computational procedures that make the alternative higher performance analysis techniques feasible to implement in practical applications. Of special focus are the extensions of fast computational algorithms for high performance signal analysis techniques to multichannel, multi-dimensional, and non-stationary instantaneous time-frequency analysis applications, where there is little published implementation literature. 

The first three days focus on one-dimensional data sources. The following two days cover data from multi-channel and two-dimensional sources, and single channel data with highly non-stationary features. Application examples using telecom, sonar, radar, seismic, and biomedical data have been incorporated into the course. Emerging signal processing techniques in modern time series and spectral analysis, including bandwidth extrapolation methods, non-stationary signal time-frequency analysis, and multi-resolution (wavelet-based analysis) analysis, will be covered. 

An extensive software toolbox (MATLAB and C) is provided students for all the algorithms and computational techniques introduced in the course. 

WHO SHOULD ATTEND
The expected background for students is some fundamental knowledge of Fourier transforms, basic digital signal processing (filters, convolution, Fast Fourier Transform [FFT]), basic matrix mathematical operations (matrix inverse, eigenvectors), and introductory random signals (correlation, spectral density). There is a review during the first day on these topics to introduce notation and to remind students of basic concepts. Some experience applying time and frequency domain techniques to signals would be helpful. This course provides alternative time and frequency domain analysis techniques. A number of data cases are used to demonstrate the practical use of the theoretical concepts.

Monday 

Signal Analysis Tools and Classical Spectral Analysis 
The first day reviews all the relevant concepts of traditional temporal 
and frequency domain analysis of signals. We will establish some important 
concepts for the advanced alternative temporal and frequency 
(spectral) techniques covered in sequel course days. 

• Complex Signal Representations
• Analytic Signals
• Matched Filters 
• Issues in Spectral Estimation
• Concepts from Fourier Transform Theory 
• Tutorial Review: Random Signal Theory
• Tutorial Review: Matrix Algebra Theory 
• Resolution and Time-Bandwidth Uncertainty Principle
• Autocorrelation and Cross Correlation
• Power Spectral Density
• Window Selection
• Correlogram Method
• Periodogram Method 
• Blackman-Tukey Method 

Tuesday 

Parametric and Autoregressive Methods 
The most successful high performance analysis approach is based on autoregressive and linear prediction modelling and estimation. We explore the basis for the high performance via a systematic modelling viewpoint, and illustrate the performance with actual data. 

• Parametric Time Series Models: Autoregressive (AR), Moving Average (MA), and Autoregressive Moving Average (ARMA) 
• Parameter Relationships among AR, MA, and ARMA Models 
• Autocorrelation Relationships among Parametric Models
• AR, Linear Prediction, and Lattice Filters
• Levinson-Durbin Algorithm 
• Reflection Coefficients
• Maximum Entropy Analysis
• ARMA Spectral Estimation
• MA Spectral Estimation 
• AR Spectral Estimation: Yule-Walker algorithm, Burg algorithm, least squares linear prediction algorithms
• AR Model Order Selection
• Adaptive AR Spectral Analysis Algorithms: LMS and Fast RLS 
  computational algorithms 

Wednesday 

Exponential Frequency Estimation and Minimum Variance Spectra 
Even higher performance for finding signal feature extraction is 
achieved using minimum variance and eigenanalysis approaches, at 
a computational cost increase. We explore the tradeoffs. 

• Prony’s Method 
• Damped Exponential Parameter Estimation 
• Relationship to AR Methods 
• Least Squares Prony Algorithms 
• Noise Excision by Eigenanalysis/Principal Components Analysis 
• Minimum Variance Estimation: Derivation and relationship to AR spectral estimation, signal and noise subspace concepts 
• Pisarenko’s Technique 
• MUSIC Algorithm
• ESPRIT Algorithm 

Thursday 

Multi-Channel and Two-Dimensional Spectral Analysis 
Some of the techniques discussed the first three days are extended to multi-channel (multiple sensors) and higher dimensional data situations. We cover many of the important extensions and show that higher estimation performance is achieved, sometimes with unexpected artefacts for which a user needs to be aware. 

• Multi-Channel (MC) Spectral Analysis: MC transform theory, MC random 
  process theory
• MC Classical Spectral Estimators
• MC AR/MA/ ARMA Processes
• MC Block-Levinson Algorithm
• MC AR Spectral Estimators
• MC Minimum Variance Spectral Analysis 
• Two-Dimensional (2D) Spectral Analysis: 2D transform theory, 2D random process theory
• 2D Minimum Variance Spectral Algorithm
• 2D Autoregressive and Linear Prediction
• Time Delay Estimation by Application of MC Analysis
• Bandwidth Extrapolation via Linear Prediction Methods
• Relationship of Temporal and Spatial Spectral Analysis Techniques 
• High Resolution Direction Finding and Beamformation 

Friday 

Non-Stationary Time-Frequency Analysis (TFA) 
Some additional performance tradeoffs and issues concerning non-stationary (time-varying) signal analysis will be summarized, again using actual data to illustrate the tradeoffs. 

• Time-Recursive AR Estimation
• Short Time Fourier Transform 
• Linear and Quadratic Time-Frequency Representations
• Short Time Fourier Transform (STFT)
• Wigner-Ville Distribution
• 2D Methods of TFA 
• Ambiguity Functions in TFAs 

Multi-Resolution and Deconvolution Analysis 

• Alternative Multi-Resolution Basis Functions to Fourier Transform Frequency Representation
• Scaling (time compression/time expansion) Properties of Analyzing Wavelets for Time-Frequency Analysis 
• Scalograms vs Time-Frequency Grams
• Time Domain, Least Squares, and Frequency Domain Deconvolution Techniques

Regular Course Fee: EUR 2995

Early Registration Course Fee: EUR 2725
This applies to firm registrations received 2 months before course start. 

University Student and Faculty Rate:
Two university participants are welcome to attend for one course fee if payment is to be made from university funds.

Deliverables:
The course fee covers tuition, course material, and the day conference packages (morning/afternoon refreshments, lunches etc.), paid on your behalf to the course venue. Accommodation is not included.

Payment should be made before course start.