DT1130 Spectral Transforms 7.5 credits

Oscillations and complex phasors. Time-discrete signals, quantiszation and sampling. Linear systems, digital filters with and without feedback. Impluse response and step response. Frequency response and transfer function. Convolution. Z-transform. Periodic signals and fourier series. Dicrete fourier transform, FFT. Spectrum and spectrogram. Windowing. Source-filter models. Formants and fundamental frequency. Filtering, convolution and transforms in two dimensions. Discrete cosine transform and JPEG-based image compression.

The student should after the course be able to

    * analyse audio signals using spectrum/spectrogram and explain relations between spectrum, analysis window length, analysis bandwidth and resolution in time and frequency domains

    * explain and calculate the consequences of sampling and quantisation of analogue signals

    * express signals mathematically in terms of complex phasors, and utilise fourier series to describe periodic signals

    * analyse simple linear systems using the Z-transform, and calculate various properties of theese such as filter equation, transfer function, pole- and zero configuration, magnitude response and impulse response and relate these to each other

    * explain and apply convolution of signals in one and two dimensions

    * explain function and scope of use, and numerically compute the discrete fourier transform, and state the basic principle and computational properties of the FFT algorithm

    * account for basic principles and algorithms used in filtering and spectrally based compression of images

    * use Matlab for general computation and visualisation task, especially filtering and spectral treatment of sounds and images.

For single course students: completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B, English corresponding to English A. Furthermore: 15 hp in mathematics.

For those already studying at KTH: The courses SF1625 Calculus in One Variable and SF1624 Algebra and Geometry or corresponding.

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

• LABA - 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.

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

André Holzapfel

• 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.

DT2212 Speech Technology Extended Course, DT2213 Musical Communication and Music Technology, DT1410 Audio Technology.

Examination takes place as before, except for the programming task (part of LAB1) which was previously examined through a seminar, which is replaced by personal reporting for teachers.

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