DT1120 Spectral Transforms 6.0 credits

Oscillations and complex phasors. Time-discrete signals, quantization and sampling. Linear systems, digital filters with and without feedback. Impulse response and step response. Magnitude response and transfer function. Convolution. Periodic signals and fourier series. Discrete fourier transform, FFT. Spectrum and spectrogram. Windowing. Source-filter models. Formants and fundamental frequency. Filtering, convolution and transforms in two dimensions. Discrete cosine transform. 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, and calculate various properties of theese such as filter equation, transfer function, pole- and zero configuration, magnitude response and impulse response (and for two pole resonators also center frequency and bandwidth) 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
• Implement filtering and spectral treatment of actual signals (sounds/images) using Matlab

To be announced at the web page for the course at least 2 weeks before the start of the course.

• TEN1 - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, F
• LAB1 - Laboratory Work, 1.5 credits, grading scale: P, 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.

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

One written examination (4,5 university credits) and a laboratory course (1,5 university credits).

• 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.