II1303 Signal Processing 7.5 credits

• Sinusoidal signals
• Amplitude, phase and frequency
• Representation on complex exponential form (phasors)
• Spectrum representation of signals
• Sinusoidal signals, harmonics
• Fourier series: synthesis and analysis
• Digital signals and sampling
• Aliasing & Folding
• Reconstruction from the samples
• FIR-filter Finite Impulse Response (FIR)
• Convolution (convolution)
• Linearity and time-invariance
• Cascading systems
• Frequency response
• Amplitude and phase response
• Lowpass, highpass and bandpass filters
• Z-transforms
• Definition and use of z-transforms
• Relationsship between the z-plane and the frequency plane
• Recursive filters
• Feedback difference equations
• Impulse response
• Z-transform for recursive filter
• The filters of the other order
• Spectrum analysis
• Fourier transform (continuous time)
• Discrete Fourier transform
• The FFT-algorithm
• Relationship between time continuous and discrete-time frequency domains

After passing the course, the student shall be able to

• describe systems for signal processing in mathematical form 
• use complex exponential notation to describe signals and systems
• use and write code in mathematical program to describe and carry out calculations on a signal processing system
• analyse signals with regard to frequency content
• describe and explain the behaviour and important properties of system with regard to frequency content and frequency response
• describe the behaviour of system with Fourier transforms
• describe, analyse and dimension mixed analogue and digital systems with sampling operations and digital filters
• use z-transforms to analyse discrete-time systems
• describe how signal processing is used in applications for example treatment of sounds and digital images.

• Knowledge in algebra and geometry, 7.5 higher education credits, equivalent completed course IX1303.
• Knowledge in mathematical analysis, 7.5 higher education credits, equivalent completed course IX1304.

Active participation in a course offering where the final examination is not yet reported in LADOK is considered equivalent to completion of the course.

Registering for a course is counted as active participation.

The term 'final examination' encompasses both the regular examination and the first re-examination.

If the course is discontinued, students may request to be examined during the following two academic years.

• LAB1 - Laboratory Work, 3.0 credits, grading scale: A, B, C, D, E, FX, F
• TEN1 - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Slimane Ben Slimane

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.