technical university of cluj-napoca

Introduction to digital signal processing: the concept of frequency for continuous-time and discrete-time signals; normalized frequency; sampling and aliasing effects.

Discrete-time signals and systems: elementary signals, classifications, and operations; LTI systems and the convolution sum.

Analysis of discrete-time LTI systems: causality and stability; correlation; FIR and IIR systems; zero-input and zero-state responses.

Direct-form structures for discrete-time systems. LTI systems described by constant-coefficient linear difference equations: impulse response and stability.

Bilateral and unilateral z-transforms: region of convergence; poles and zeros; transfer function; inverse z-transform.

Analysis of LTI systems in the z-domain: transient and steady-state responses; causality and stability. Fourier series representation of periodic discrete-time signals.

Fourier transform of aperiodic discrete-time signals: properties and frequency-domain characteristics of LTI systems.

Discrete Fourier transform: properties; circular and linear convolution; zero-padding, frequency resolution, and spectral leakage.

Fast Fourier transform: radix-2 decimation-in-time FFT algorithm; radix-2 decimation-in-frequency FFT algorithm; split-radix algorithms.

LTI systems viewed as frequency-selective filters. Linear-phase FIR filters.

Digital filter design: filter specifications and approximation. FIR filter design: window method; frequency-sampling method. Indirect methods for IIR digital filter design: analog prototypes; impulse-invariance method, bilinear transformation, matched z-transform method, and frequency transformations.

Direct methods for IIR filter design: Padé approximation. Implementation of discrete-time FIR systems: direct-form, cascade, parallel, and lattice structures.

Implementation of discrete-time IIR systems: direct-form structures, cascade structures, parallel structures, lattice structures, and lattice-ladder structures.

Integrated review of the course content and solution of synthesis problems in preparation for the final assessment.

L1.

Brief introduction to MATLAB for digital signal processing.

L2.

Commonly used discrete-time signals in digital signal processing.

L3.

Sampling and reconstruction of analog signals. Correlation of discrete-time signals.

L4.

Linear time-invariant discrete-time systems.

L5.

The z-transform. Analysis of discrete-time LTI systems in the z-domain.

L6.

Practical Assessment 1 — Week 6

L7.

Fourier transform and discrete Fourier transform.

L8.

Linear convolution and circular convolution.

L9.

Design of finite impulse response filters.

L10.

Discrete-time LTI systems as frequency-selective filters.

L11.

Design of infinite impulse response filters.

L12.

Practical Assessment 2 — Week 12

L13.

Seminar — Solving review problems and addressing students’ questions.

L14.

Seminar — Solving review problems and addressing students’ questions.

Corneliu Rusu, Lăcrimioara Grama. Lecture Notes in Digital Signal Processing. Ed. Risoprint, 2009.

John G. Proakis, Dimitris G. Manolakis. Digital Signal Processing: Principles, Algorithms and Applications. Pearson Education, 5th ed., 2022. link1, link2, link3, link4.

Steven W. Smith. The Scientist and Engineer’s Guide to Digital Signal Processing. dspguide.com.

Corneliu Rusu. Prelucrarea numerică a semnalelor. Ed. Risoprint, 2002.

Corneliu Rusu. Prelucrări digitale de semnale. Ed. Mediamira, 2000.

Lăcrimioara Grama. Digital signal processing: laboratory guide. Ed. U.T.Press, 2014.

Sanjit K. Mitra. Digital signal processing: A Computer-Based Approach. McGraw-Hill international edition, 4th ed., 2011.

MathWork. mathworks.com.

Lăcrimioara Grama, Corneliu Rusu. Prelucrarea numerică a semnalelor - aplicații și probleme. Ed. U.T.Press, 2008.

Lăcrimioara Grama, Alin Grama, Corneliu Rusu. Filtre numerice - aplicații și probleme. Ed. U.T.Press, 2008.