Digital Signal Processing
In this course the student will acquire fundamental theoretical knowledge of digital signal processing and will study the basic concepts of signal representation and of signal filtering.
The following topics are covered: Time discrete signals and systems. Representation of signals and systems in transform domain (Fourier, Laplace and Z transforms). Signal decomposition. Signal sampling and reconstruction. The sampling theorem. Spectral analysis of signals. Invertible systems and deconvolution. Types of linear time-invariant systems. Phase and group delay. Linear phase systems. Filtering. Selective filters. All-pass filters. Minimum and maximum phase filters. Phase correctors. Classical design of digital filters. Computer-aided design of optimal digital filters. Implementation of digital filters. Digital biquad section. Filter structures. Number representation and overflow. Dynamic range scaling. Quantization of filter coefficients. Finite world-length effects. Digital signal processors. Fast Fourier transform. Multirate digital signal processing. Decimation and interpolation. Filter banks.
- define the basic concepts of digital signal processing
- state and explain the Nyquist-Shannon sampling theorem
- apply the fast Fourier transform as a signal analysis and processing tool
- identify a filter type and determine its frequency response
- compare digital filter structures
- select which digital filter to use depending on the application and the specification
- design optimal digital filter using a computer
- analyze and implement time-discrete and digital system using block diagrams and signal-flow graphs
- combine basic blocks of multirate systems to realize a multirate filter bank
Forms of Teaching
Lectures present theoretical concepts.Exercises
Recitations include solving practical tasks and discussing solving procedures.Laboratory
Laboratory exercises introduce students to digital signal processing hardware.
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Laboratory Exercises||50 %||20 %||50 %||20 %|
|Homeworks||0 %||5 %||0 %||0 %|
|Mid Term Exam: Written||0 %||25 %||0 %|
|Final Exam: Written||0 %||30 %|
|Final Exam: Oral||20 %|
|Exam: Written||50 %||50 %|
|Exam: Oral||30 %|
Mandatory prerequisites for the final oral exam are at least 50% achieved on the midterm and on the final exam combined, and at least 50% on the laboratory.
The mandatory prerequisite for the comprehensive written exam is at least 50% achieved on the laboratory.
A minimum of 5 points is required to pass the final oral exam.
A minimum of 7 points is required to pass the comprehensive oral exam.
Week by Week Schedule
- Introduction. Review: time discrete signals and systems; Fourier transforms (DFT, DTFT and CTFT).
- Review: representation of signals and systems in transform domain (Fourier, Laplace and Z transforms).
- Signal decomposition. Signal sampling and reconstruction. The sampling theorem.
- Convolution and deconvolution. Invertible systems. Minimum phase and maximum phase systems. Relation between amplitude and phase reposnse for minimum phase systems.
- Interpretation of magnitude and phase responses. Phase delay. Group delay. Phase distortions. Linear phase systems. Negative group delay.
- Relation between time-continuous and time-discrete systems. Euler transform. Bilinear transform.
- Filtration. Digital filter specification. Filter types: selective filters; all-pass filters; minimum phase filters; and phase correctors.
- Midterm exam
- FIR filter design: window method; least-squares design; Parks-McClellan FIR filter design.
- IIR filter design: impulse invariance method; bilinear transform; Yule-Walker IIR filter design.
- Implementation of digital filters. Digital biquad section. Filter structures.
- Number representation and overflow. Dynamic range scaling. Quantization of filter coefficients. Finite world-length effects. Digital signal processors.
- Multirate digital signal processing. Decimation and interpolation. Filter banks.
- Fast Fourier transform. Efficient computation of convolution and of correlation between finite duration signals.
- Final exam