Digital Signal Processing

Course in Bachelor’s program (3rd year, series E)

Teachers

Prof. Dragoș Burileanu
Lect. Șerban Mihalache

Course Description

This subject is studied within the field of Electronic Engineering, Telecommunications and Information Technologies / specialization Microelectronics, optoelectronics and nanotechnologies, and aims to familiarize students with the fundamentals of digital signal processing: specific algorithms, processing techniques, VLSI architectures, and practical considerations for implementation. The objective is to understand the phenomena that are associated with the main DSP techniques, from a system design point of view. The numerous examples and detailed explanations given in the lecture notes and chapters help both to clarify more difficult theoretical aspects and to solve practical applications and problems, relevant for engaging the students in the learning process. Additionally, the laboratory applications have as objective the practical learning of the main concepts in the field of DSP. The applications include various software simulations using a high-level programming environment (MATLAB).

The subject addresses the following basic ideas and specific concepts: the representation and analysis in the time and frequency domains of discrete signals and systems, the discrete Fourier transform and the concept of frequency resolution, fast calculation algorithms for the discrete Fourier transform, the synthesis and analysis of digital filters, concepts related to finite arithmetic in DSP, VLSI structures used in the hardware implementation of DSP systems. All these contribute to providing students with an overview of the methodological and procedural benchmarks related to the DSP field.

Contents

Course

  • “Introduction” – Generalities. Examples; comparison with analog solutions. Performance and limitations in digital signal processing
  • “Time-domain representation of discrete signals and systems” – Discrete-time signals: definition, examples, notation conventions; properties, fundamental operations. Discrete-time systems: linearity and time invariance, convolution; causality and stability; digital filters
  • “Frequency-domain representation of discrete signals and systems” – Basic concepts of Fourier analysis. Frequency response of a discrete system; the Fourier transform for discrete-time, aperiodic signals. Sampling and reconstruction of analog signals. Time – frequency duality in digital signal processing
  • “Analysis of discrete systems using the z-transform” – The z-transform for discrete-time signals. The inverse z-transform. Characterization of digital filters: transfer function, stability, frequency response; examples
  • “The discrete Fourier transform (DFT)” – Fourier representation of finite-duration sequences. The connection between the discrete Fourier transform and the z-transform; “frequency sampling”. The discrete Fourier transform for unlimited duration signals. Window functions. Frequency resolution. DFT properties
  • “The fast Fourier transform (FFT)” – Discrete Fourier transform computation complexity. Basics of the fast Fourier transform; efficient computation of the DFT. The Cooley-Tukey (decimation-in-time) algorithm. Practical aspects of FFT implementation and optimization techniques
  • “Digital filter design” – Basic concepts, classification, frequency domain specifications; from the requirements of an application to the development and testing of a digital filter. Infinite impulse response (IIR) digital filter design. Finite impulse response (FIR) digital filter design. Digital filter structures and representation. Computation complexity of digital filters
  • “Finite-precision arithmetic in digital signal processing” – Numerical issues and data formats. Fixed-point representation in digital signal processors. Floating-point representation in digital signal processors. Comparison between numerical implementations. Finite word-length effects in digital filter implementation
  • “Hardware implementation of DSP systems. VLSI architectures” – Generalities: hardware implementations, objectives and performance; applications. Digital signal processors (DSPs): general characteristics; Harvard and Super-Harvard architectures; performance, levels of integration; processor families, typical examples. Development systems and practical considerations of DSP algorithm implementation

Laboratory

  • Presentation of the MATLAB software package; examples. Generation and time-domain representation of discrete sequences
  • Time-domain representation of discrete systems: convolution, impulse response, stability; the digital filtering concept
  • Frequency-domain representation of discrete signals. The discrete Fourier transform (DFT) and the fast Fourier transform (FFT): applications, spectral analysis
  • Digital filters: synthesis, analysis, implementation
  • Digital filters for audio applications
  • Miscellaneous issues in digital signal processing
  • Laboratory assessment

Grading

Laboratory evaluation (colloquium): 25%
Course midterm exam (written): 25%
Course final exam (written): 50%