Applied Signal Processing

• Apply Fourier transform properties and pairs to derive frequency-domain representations for both complex continuous-time and discrete-time signals.
• Evaluate and visualize spectra of periodic and aperiodic signals, ensuring accurate mapping to physical units such as Hz, dB, and phase.
• Utilize the z-transform to determine system characteristics, including impulse response, transfer functions, and time-frequency domain relationships.
• Assess the causality and stability of discrete-time systems through the analysis of pole-zero configurations in the z-plane.
• Design and implement filter types (low/high/band-pass, notch) using pole-zero placement, windowing methods, and bilinear transformations.
• Model and quantify the effects of quantization noise in analog-to-digital conversion and digital filtering systems.
• Analyze the statistical properties of random signals by computing auto-correlation and cross-correlation functions.
• Compute and compare power spectral density (PSD) estimates using non-parametric (e.g., Welch) and parametric (e.g., AR modeling) methods.
• Analyze analog (AM, FM) and digital (ASK, FSK, PSK, QAM) modulation techniques to evaluate their performance in communication systems.
• Apply signal processing to physiological data (ECG, Ultrasound) to extract clinical parameters like heart rate and blood flow profiles.
• Critically discuss signal processing applications across diverse domains, including telecommunications, radar, sonar, and medical diagnostics.
• Integrate GenAI to develop and debug code (MATLAB/Python), validating outputs against theory and communicating findings fluently in English.

This course delves into the essential aspects of signal processing, starting with the classification of signals and analytic signals. It covers the use of the Fast Fourier Transform (FFT) and the analysis of random signals, including correlation functions, power, and cross spectra. Additionally, it addresses errors in analog-to-digital conversion and explores digital filters and their error sources. The course introduces simple signal measures and the modulation of both analog and digital signals, along with matched filtering and spectral estimation using parametric models. Practical applications include the use of signal processing software like Matlab/Python and the processing of biomedical signals. The exercises and lectures provide comprehensive insights into various topics, ranging from the fundamentals of power and energy to advanced concepts like Z-Transform, Digital Systems, and Random Signals.

• Lecture 1: Introduction
• Lecture 2: Power and Energy
• Lecture 3: Fourier Series
• Lecture 4: Fourier Transform
• Lecture 5: Complex Signals
• Lecture 6: Analog Systems
• Lecture 7: Sampling & Digital Signals
• Lecture 8: Z-Transform and Discrete Time Fourier Transform (DTFT)
• Lecture 9: Digital Systems I
• Lecture 10: Digital Systems II
• Lecture 11: Implementation of Discrete-Time Systems (FIR Systems)
• Lecture 12: Implementation of Discrete-Time Systems (IIR Systems)
• Lecture 13: Discrete Fourier Transform (DFT)
• Lecture 14: Fast Fourier Transform (FFT)
• Lecture 15: Design of FIR Filters
• Lecture 16: Design of IIR Filters
• Lecture 17: Random Signals I – Introduction
• Lecture 18: Random Signals II – Ergodic Random Process & Parameters
• Lecture 19: Random Signals III – Filtering & Noise
• Lecture 20: Modulation I
• Lecture 21: Modulation II
• Lecture 22: Power Spectrum
• Lecture 23: Nonparametric (classical) Methods for Power Spectrum Estimation
• Lecture 24: Parametric Methods for Power Spectrum Estimation
• Lecture 25: DFT for Power Spectrum Estimation

02402/02403/02405/22050/22051, 1. Linear systems or basic signal analysis and introductory statistics.
2. Students should have prior knowledge in Matlab/Python.

Lectures and exercises

The courses 22050, 22051, and 22052 constitute a specialization track in signal processing and should be taken in said order.

Minimum: 5.

Please be aware that this course will only be held if the required minimum number of participants is met. You will be informed 8 days before the start of the course, whether the course will be held.