Course 011 Digital Signal Analysis Techniques: Time, Frequency, and Spatial Algorithms
Professor Gonzalo Seco-Granados and Professor José A. López-Salcedo are teaching this 3-day course that goes beyond available textbooks and extends these signal analysis tools to higher dimensions and multiple sensor channels.
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.
Available course dates
This course has no planned course dates.
If you are interested in this course, contact us at cei@cei.se
Telecommunications
011 Digital Signal Analysis Techniques: Time, Frequency, and Spatial Algorithms
Location: Barcelona, Spain Date: April 13 - April 15, 2026 Duration: 3 days
Instructors: Professor Gonzalo Seco-Granados and Professor José A. López-Salcedo
This 3-day course that goes beyond available textbooks and extends these signal analysis tools to higher dimensions and multiple sensor channel. 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.
Read full course description including course schedule.
Early Bird
2 280,00 €2 535,00 €
Early Bird Price Ends: February 13, 2026
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.
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).
Some experience applying time and frequency domain techniques to signals would be helpful.
Daily Schedule
Signal Analysis Tools and Classical Spectral Analysis
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
- Complex Signal Representations, Analytic Signals
- Issues in Spectral Estimation
- Tutorial Review: 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
- Periodogram Method
- Blackman-Tukey Method
Parametric and Autoregressive Methods
Many real-life applications are based on autoregressive and linear prediction modelling and estimation. We explore the basis for the high accuracy 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)
- Parametric Relationships
- Autocorrelation Relationships among Parametric Models (AR)
- Linear Prediction
- Levinson-Durbin Algorithm
- Maximum Entropy Analysis
- Spectral Estimation
- Order Selection
Exponential Frequency Estimation and Minimum Variance Spectra
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
- Pisarenko’s Technique
- MUSIC and ESPRIT Algorithms
- Estimation of Number of Components
Multi-Channel and Two-Dimensional Spectral Analysis
Some of the techniques are revisited in the form of a multi-channel configuration, being representative of important applications such as array processing or the use of multiple sensors.
- Multi-Channel (MC) Spectral Analysis
- MC Classical Spectral Estimators
- Minimum Variance Spectral Analysis
- Minimum Variance Spectral Algorithm
- Autoregressive and Linear Prediction
- Relationship of Temporal and Spatial Spectral Analysis Techniques
- Spatial and Temporal Reference Beamforming
- Super-Resolution Direction Finding
Time-Frequency Analysis (TFA)
Performance tradeoffs and issues concerning time-varying signal analysis will be summarized
- Cyclostationarity,
- 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
ALL COURSE DATES FOR THE CATEGORY: Telecommunications
Telecommunications
815 O-RAN System Overview
Location: Barcelona, Spain Date: April 13 - April 14, 2026 Duration: 2 days
Instructor: Dr. Marcin Dryjanski
The course covers joint design of technology and ecosystem aspects in Open RAN networks. The technology enablers include open networking, virtualization, HW/SW disaggregation, network intelligence. The course discusses Open RAN concept, architecture, use cases, functions and interfaces. With further network densification and high sophistication of the relation between multiple layers and operators and network elements require network management solution based on Artificial Intelligence (AI). The central point is the O-RAN Alliance, but relation to other entities, like TIP (Telecom Infra Project), and 3GPP is also emphasized.
Read full course description including course schedule
Early Bird
1 560,00 €1 735,00 €
Early Bird Price Ends: February 13, 2026
Telecommunications
044 Radio Spectrum Management
Location: Gothenburg, Sweden Date: June 22 - June 24, 2026 Duration: 3 days
Instructor: Dr. Naveed Mufti
This 3-day course in Radio Spectrum Management. This topic is of ever increasing importance for Telecommunications Companies, Public Authorities as well as for Defence Forces.
This advanced course is giving participants the knowledge of rules and regulations for the utilization, also discussing analysis and planning of the Radio Spectrum.
It is necessary for the planning, implementation and operation phases of various types of technologies: Point-to-Point/Multipoint Links, Broadband Wireless Access, Cellular Systems, Radar, Navigation Systems as well as television and sound broadcasting networks, both analogue and digital.
The hierarchical process of military spectrum management has extensive needs for long-term strategic as well as short-term tactical frequency management.
Read full course description including course schedule
Early Bird
2 280,00 €2 535,00 €
Early Bird Price Ends: April 22, 2026
Telecommunications
058 Modern Digital Modulation Techniques for Wireless, Satellite, and Wireline Communications – 5G and Beyond
Location: Barcelona, Spain Date: April 13-17, 2026 Duration: 5 days
Instructor: Professor Irving Kalet
The goal of this course is to introduce the participant to those digital modulation methods and multiple access techniques presently in use in mobile wireless (e.g.,5G-NR), broadband wireless(e.g.,Wi-Fi6), cable, satellite, deep-space and wireline (and power-line) communications, as well as to those techniques, which are being considered for future or next generation systems, e.g., 6G, and Wi-Fi 7.
Modern digital modulation and multiple access techniques are basic building blocks of the physical (or radio) interface of all digital communication systems. We will describe many of these techniques during the course including those methods, which are being used in the newest systems including the Fifth Generation (5G-NR) cellular system, as well as ideas for modulations for 6G.
Objective:
- Learning about OFDM -based systems including OFDM, OFDMA, S-OFDMA, and SC-FDMA, which are integral parts of 5G-NR, 4G-LTE and the IEEE 802.11 (Wi-Fi) systems.
- Emphasis on the new modulation standard for the physical interface of 5G-NR. This OFDM standard is based on scalable subcarrier spacing.
- Discuss other modulations, such as “Faster Than Nyquist” (FTN) signaling, which are being considered for advanced wireless systems. Many of the modulations have been combined with MIMO, Massive MIMO, and BLAST, to improve spectral efficiency.
- Describe the use of constant-envelope CPM modulations (e.g., GMSK), especially for present and future broadband wireless communications and space communications. All of the modulations have been, and will be, utilized in mobile and broadband wireless systems, as well as in xDSL systems, to greatly improve both bandwidth and power efficiency.
- Discussion of one of the most important topics in communications, Shannon Information Theory.
Early Bird
3 540,00 €3 935,00 €
Early Bird Price Ends: March 13, 2026
Telecommunications
011 Digital Signal Analysis Techniques: Time, Frequency, and Spatial Algorithms
Location: Barcelona, Spain Date: April 13 - April 15, 2026 Duration: 3 days
Instructors: Professor Gonzalo Seco-Granados and Professor José A. López-Salcedo
This 3-day course that goes beyond available textbooks and extends these signal analysis tools to higher dimensions and multiple sensor channel. 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.
Read full course description including course schedule.
Early Bird
2 280,00 €2 535,00 €
Early Bird Price Ends: February 13, 2026
E-Learning Courses, Telecommunications
E-Course 606 Radio Spectrum Management for Various Services
Location: E-Course 3 months access
Instructor: Mr. Olov Carlsson
This e-learning course in Radio Spectrum Management is taught by Mr. Olov Carlsson, Senior Director – EM Solutions at Altair Engineering, Sweden. This topic is of ever increasing importance for Telecommunications Companies, Public Authorities as well as for Defence Forces. Radio Spectrum Management for Various Services This e-learning course is giving participants the knowledge in Radio Planning for various services, like Space, Mobile, Broadcasting, Radio Navigation, Radio Location and Science Services. The course includes: 214 minutes on-demand video 81 modules 3 months access This course is the third part of a series of three e-Learning courses about Radio Spectrum Management. For effective training benefit, we recommend also attending course 604 Radio Spectrum Management – Introduction, Organisations and Regulations and course 605 Radio Spectrum Management – Technical Basics. Get a better price when ordering all three courses: Bundle 604-606 Radio Spectrum Management299,00 €
E-Learning Courses, Telecommunications
E-Course 605 Radio Spectrum Management – Technical Basics
Location: E-Course 3 months access
Instructor: Mr. Olov Carlsson
This e-learning course in Radio Spectrum Management is taught by Mr. Olov Carlsson, Senior Director – EM Solutions at Altair Engineering, Sweden. This topic is of ever increasing importance for Telecommunications Companies, Public Authorities as well as for Defence Forces. Radio Spectrum Management – Technical Basics This e-learning course is giving participants the knowledge of technical basics, like Technical Characteristics, Radio Wave Propagation and Collocation Interference. The course includes: 131 minutes on-demand video 43 modules 3 months access This course is the second part of a series of three e-Learning courses about Radio Spectrum Management. For effective training benefit, we recommend also attending course 604 Radio Spectrum Management – Introduction, Organisations and Regulations and course 606 Radio Spectrum Management for various Services Get a better price when ordering all three courses: Bundle 604-606 Radio Spectrum Management199,00 €
E-Learning Courses, Telecommunications
E-Course 604 Radio Spectrum Management – Introduction, Organisations and Regulations
Location: E-Course 3 months access
Instructor: Mr. Olov Carlsson
Senior Director of EM Solutions at Altair Engineering, Sweden Mr. Carlsson is teaching this bundle e-learning course in Radio Spectrum Management. This is of ever increasing importance for Telecommunications Companies, Public Authorities as well as for Defence Forces. Radio Spectrum Management – Introduction, Organisations and Regulations This e-learning course is giving participants the knowledge of organisations and regulations, both national and international. The course includes: 100 minutes on-demand video 29 modules 3 months access This course is the first part of a series of three e-Learning courses about Radio Spectrum Management. For effective training benefit, we recommend also attending course 605 Radio Spectrum Management – Technical Basics and course 606 Radio Spectrum Management for various Services Get a better price when ordering all three courses: Bundle 604-606 Radio Spectrum Management99,00 €
E-Learning Courses, Telecommunications
E-Course Bundle 604-606 Radio Spectrum Management
Location: E-Course 12 months access
Instructor: Mr. Olov Carlsson
Senior Director of EM Solutions at Altair Engineering, Sweden Mr. Carlsson is teaching this bundle e-learning course in Radio Spectrum Management. This is of ever increasing importance for Telecommunications Companies, Public Authorities as well as for Defence Forces. This advanced course is giving participants the knowledge of rules and regulations for the utilization, also discussing analysis and planning of the Radio Spectrum. The course includes: 445 minutes on-demand video 153 modules 12 months access Course 604 – Radio Spectrum Management – Introduction, Organisations and Regulations This e-learning course is giving participants the knowledge of organisations and regulations, both national and international. Course 605 – Radio Spectrum Management – Technical Basics This e-learning course is giving participants the knowledge of technical basics, like Technical characteristics, Radio wave propagation and Collocation interference. Course 606 – Radio Spectrum Management for Various Services This e-learning course is giving participants the knowledge in Radio Planning for various services, like Space, Mobile, Broadcasting, Radionavigation, Radio Location and Science services. Read full course description including course schedule.495,00 €