Applied Signal Processing

• Use Fourier transform pairs and properties to determine the Fourier transform of complex analog and digital signals.
• Relate spectra of periodic and aperiodic analog and digital signals and plot these using correct physical units such as Hertz, Amplitude, dB, Phase etc.
• Analyze zero-pole diagrams to determine the causality and stability.
• Use the z-transform to calculate the impulse response and the transfer function.
• Determine the quantization errors in analog-to-digital conversion and model error sources in filters due to finite word length.
• Design low-pass, high-pass, band-pass, band-stop and notch filters using pole-zero placement, simple windowing functions, filter transformation rules and the signal processing toolbox in Matlab/Python.
• Determine the auto-and cross correlation functions of analog and digital random signals.
• Understand the fundamentals of modulation techniques commonly used in communication systems for digital signal transmission.
• Find the power density spectra of random signals using non-parametric and parametric spectral estimation methods.
• Apply signal processing techniques to signals emanating from biological systems (ECG, ultrasound) and design procedures to estimate some parameters such as heart rate, blood velocity and profile of blood flow.
• In own words give examples of signal processing techniques applied in various applications such as telecommunications, radar and sonar and biomedical systems.
• Communicate proficiently about the signal processing topics 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

• 36 – 49 (Tues 13-17, Fri 8-12)

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.