Course Identification

Mathematical knowledge in linear algebra (Vector spaces, Matrices, Complex numbers, Inner Product) and ordinary differential equations (with fixed coefficients).
Working knowledge of Matlab programming (many self-reading materials can we found over the Internet).

Subjects
Motivation and Introduction to Digital Signal Processing
Short Mathematical reminder – Vector spaces and inner products. Orthogonal families. Example: Fourier series
Continuous time Signals and Systems - The Dirac impulse function, System characterization: memory, linearity, time-dependence, causality, Fourier and Laplace analysis, Impulse response and Convolution, Differential equations as an I/O system. Time and Frequency domains
Discrete time Signals and Systems - System characterization: memory, linearity, time-dependence, causality, FIR vs. IIR, Fourier and Z analysis, Unit sample response and Convolution, Difference equations as an I/O. Time and Frequency domains
Sampling – Shannon-Nyquist sampling and  reconstruction. Practical considerations. A/D, D/A, Quantization.
The Discrete Fourier Transform and the FFT algorithms. Spectral Analysis for random and deterministic signals. Windows
Filtering – Concepts and design methods
FIR filters – Linear phase, Window design methods, Park McLellan algorithm.
IIR filters – Families: Butterworth, Chebychev, Elliptic, Bessel. Bilinear transform design method
If time permits – Short Time Fourier Transform, Gabor Transform, Wavelets and Multi resolution analysis, Multi-rate systems

Upon successful completion of this course students should be able to:
1. Understand and utilize signal representation for continuous time and discrete time signals in both time and frequency domain.
2. Characterize and analyze systems in the time domain (differential and difference equations, impulse response) and in the frequency domain (Fourier, Laplace, Z).
3. Understand signal sampling and reconstruction, practical sampling and quantization.
4. Understand and utilize the discrete Fourier transform and the FFT algorithm. Implement the windowed/averaged transform for spectral analysis of signals.
5. Utilize digital filters and design both finite impulse response and infinite impulse response filters.
6. Gain proficiency with Matlab, and utilize this language to solve problems on a wide-range of signal processing scenarios
7. Optional – be able to understand and utilize advanced time-frequency transforms

B. Porat, A Course in Digital Signal Processing, J. Wiley, 1997

"מבוא לעיבוד ספרתי של אותות" חוברת עזר להרצאות מאת ד. מלאך וש. רז, טכניון 2005

מבוא לעיבוד ספרתי של אותות הרצאות של גל בן דוד, Youtube Technion channel