Responsible Instructor 

Contact Hours / Week x/x/x/x 
2/0/0/0 hc; 2/0/0/0 wc; 4/0/0/0 lab

Education Period 

Start Education 

Exam Period 

Course Language 

Required for 
Image Processing. Multimedia analysis. Highly recommended for Computer Science M.Sc. track Data Science and Cybersecurity specialisation.

Expected prior knowledge 
Calculus: series, integration, complex numbers, complex exponents, Euler's formula. Linear algebra: vector and matrix manipulations. Special attention is asked for complex numbers. Selfcheck exercises and study material is provided via Blackboard.

Course Contents 
Digital signal processing is used in many modern computer sciences systems and applications. Examples are content recommenders in information systems; speech, music and image content based retrieval and searching; music and video compression; sensor data processing in embedded systems; bioinformatics and medical data analysis. This course deals with the foundations and principles of digital signal processing. The first part concentrates on acquiring digital signals (sampling) and the basic linear filtering operations and convolution. The second part of the course introduces the concept of frequency or Fourier description of signals and systems. This concept is the foundation of many of today's computer sciencebased systems and applications, and has found wide applications in the processing of a variety of sound, music, sensor, image, video and other multimedia information.

Study Goals 
1. Properties of digital signals and systems. The student is able to explain, compute and apply the properties of timediscrete linear timeinvariant systems and the inputoutput relation; explain and use the principle of superposition; write arbitrary signals in terms of the sum of impulse signals.
2. Linear timeinvariant (LTI) filters and convolution. The student is able to explain, determine and apply the impulse response of a timediscrete LTI system such as FIR or IIR filter; explain the relation between impulse response, inputoutput relation and convolution; manually (for short signals) or numerically (using Matlab, for long signals) convolve the input signal and the impulse response to compute the output signal; explain and apply the properties of convolution, including the difference between linear and circular convolution; recursively compute the output of an IIR filter; implement and visualize convolution via Matlab; implement and apply FIR filters in practical exercises and assignment, and visualize and interpret the results.
3. Sampling. The student is able to explain and apply the process of data acquisition (sampling) and Shannon's sampling theorem; explain the concepts of oversampling, undersampling and aliasing; explain how to avoid aliasing; use of zeroorder or linear interpolation for the reconstruction of timecontinuous signals; make audible (using Matlab) original and processed audio signals and interpret the results.
4. Discrete Fourier Transform (DFT). The student is able to write a periodic signal as the sum of complex exponentials; explain the concepts and differences of Fourier series, DTFT and DFT; explain and interpret the complex spectrum, magnitude spectrum and phase spectrum ; compute and visualize manually (for short signals) or numerically (for longer signals) the magnitude and phase of DTFT and DFT coefficients, and interpret the results; explain the difference between the numerical results computed using the DFT for finitelength signals and the theoretical results computed using the DTFT for infinitelength signals; explain the principles of the fast Fourier transform (FFT); apply the DTFT and DFT to practical exercises and assignments.
5. Frequency response of LTI filters. The student is able to compute manually (for short impulse responses) or numerically (for longer impulse responses) the frequency response of an LTI system using DTFT and DFT; visualize and explain the magnitude and phase response of an LTI system; evaluate convolution via product of frequency response of the filter and Fourier transform of the input signal; compute the frequency response of cascaded filters; numerically determine the impulse response of an FIR filter with desired frequency response using the inverseDFT method.
6. Applications of filters and DFT. The student is able to apply theory and practice to (simplified) versions of relevant computer sciencebased signal processing problems and assignments, such as music compression and recognition.

Education Method 
The course consists of  7 plenary lectures in which the main concepts are explained and discussed;  7 working group in which theory and practical (Matlabbased) exercises are solved and discussed;  6 handson sessions in which practical (Matlabbased)assignments need to be solved and approved by the instructor.

Computer Use 
The course includes a compulsory set of computer (Matlabbased) assignments that need to be solved and approved by the instructor during the handson sessions. Matlab software is preinstalled on the computers available during the handson sessions. Students can also install Matlab software on their own computer.

Literature and Study Materials 
The course loosely follows the book 'Signal Processing First' James H. McClellan, Ronald W. Schafer and Mark A. Yoder ISBN 0131202650 Prentice Hall. Alternatively, also online material may be used, such as 'The Scientist and Engineering´s Guide to Digital Signal Processing', S.W. Smith ( http://www.dspguide.com/pdfbook.htm ). Slides used during the lectures are made available via Blackboard. Theory and practical exercises, as well as the Matlab assignments are available for download via Blackboard. During the course several pointers to online MOOCs and video lectures will be given.

Practical Guide 
Study material and the handson assignments can be downloaded via Blackboard.

Assessment 
The first partial examination is in week 4, and deals with the materials covered in plenary lectures, working groups and Matlab assignments in week 13. The result of this partial exam counts for 30%.
The second partial examination is scheduled at the end of the quarter, and covers all course material with emphasis on the materials covered in plenary lectures, working groups and Matlab assignments in week 58. The result of this partial exam counts for 70%.
A resit exam, covering all materials of the plenary lectures, working groups and Matlab assignments, is scheduled at the end of the second quarter.
The Matlab handson assignments are integral part of the course and must be approved during the handson sessions, even if the student solves the assignments at home (using an own computer). Completion of the handson assignments are a prerequisite for entering the second partial exam or the resit exam.
The completed Matlab handson assignments are valid for an entire academic (study) year, but expire at the end of the academic (study) year. Failing to pass the course in one year implies redoing all Matlab handson assignments.

Permitted Materials during Tests 
The lecturers have prepared one page with key equations (formuleblad). This page is permitted during the examination. It is also allowed to make notes on this one printed page.

Enrolment / Application 
Enrolment is necessary for both partial examinations. Due to the cutoff dates, students are advised to immediately signup for the first partial examination in week 4. It is not necessary to enroll for the Matlab handon assignments.

Tags 
Image processing

Information & Communication

Mathematics

Modelling

Project

Signals and Systems


Judgement 
The final grade at the end of the quarter in which the course is lectured is determined as follows. 1. The grade (rounded to one decimal) of the first partial examination counts for 30%. 2. The grade (rounded to one decimal) of the second partial examination counts for 70%. 3. The Matlab handson assignments have to be completed and approved by the instructor. The approval of each assignment must be done within the week set for that assignment. In case of unforeseen circumstances (like illness) the instructor can allow for a delay of maximally one week, and only if such approval is obtained at the latest in the week the assignment should have been completed.
Validity of partial examination results and completed Matlab handson assignments. * The results of the partial examinations expire at the end of the quarter in which the course was lectured if the Matlab handson assignments have not been completed and approved by the instructor before the second partial examination. * The completed Matlab handson assignments are valid for an entire academic (study) year, but expire at the end of the academic (study) year.
The grade of the resit examination is determined as follows. 1. The grade of the resit examination. 2. The Matlab handson assignments completed before the resit examination. Students who had not yet completed the handson assignments during the regular sessions are invited to contact the instructor to make a single appointment to verify and approve all (remaining) assignments. These appointments take place in the weeks before the resit examination.

Self test 
Fourier transforms, DTFT and DFT rely heavily on the description of signals as a sum of complex exponentials. It is important that the student brings operational knowledge of complex numbers (see first years Calculus). A set of selftests is available as well as selfstudy materials. Complex exponents are assumed background knowledge and not discussed during the lectures.
