Signal processing is a technology that spans an immense set of disciplines including entertainment, communication, robotics, space exploration, medicine, seismology, just to name a few. Sophisticated signal processing algorithms and hardware are prevalent in a wide range of systems, from highly specialized military systems through industrial applications to consumer electronics. The present course covers the concepts and techniques of modern digital signal processing which are fundamental to all the above applications. The course starts with a detailed overview of discrete-time signals and systems, representation of the systems by means of differential equations, and their analysis using Fourier and z-transforms. The sampling theory of continuous-time signals is explained next, followed by exploring the transform-based analysis of linear time-invariant (LTI) systems and their structures. Subsequently, the notion of discrete Fourier transform is introduced, followed by an overview of fast algorithms for its computation. The methods for spectral analysis of discrete-time signals are discussed next. Finally, principal methods for design of FIR and IIR filters are covered, followed by a discussion of their use for construction of filter banks as the first step into the theory of wavelet analysis.

This course makes extensive use of MATLAB as an analysis, design, and visualization tool.

WEEK	TOPICS
1	Discrete-time signals and systems, linear time-invariant systems and their properties, linear constant-coefficient difference equations, frequency-domain representation of discrete-time signals and systems, symmetry properties of the Fourier transform, Fourier transform theorems.
2	The z-transform, properties of the region of convergence for the z-transform, the inverse z-transform, z-transform properties.
3	Frequency-domain representation of sampling, reconstruction of a band-limited signal from its samples, discrete-time processing of continuous-time signals, changing the sampling rate using discrete-time processing.
4	The frequency response of LTI systems, frequency response for rational system functions, relationship between magnitude and phase, all-pass systems, minimum-phase systems, linear systems with generalized linear phase.
5	Block diagram representation of linear constant-coefficient difference equations, basic structures for IIR systems, finite-precision numerical effects, the effects of coefficient quantization, effects of roundoff noise in digital filters.
6	Representation of periodic sequences, the discrete Fourier series, the Fourier transform of periodic signals, sampling the Fourier transform, the discrete-Fourier transform (DFT), properties of the DFT, linear convolution using the DFT, the discrete cosine transform (DCT).
7	Efficient computation of the DFT, decimation-in-time FFT algorithms, decimation-in-frequency FFT algorithms, implementation of DFT using convolution.
8	Fourier analysis of signals using DFT, DFT analysis of sinusoidal signals, the time-dependent Fourier transform, block convolution, Fourier analysis of non-stationary signals, Fourier analysis of stationary random signals, the periodogram.
9	Real and imaginary part sufficiency of the Fourier transform for causal sequences, sufficiency theorems for finite-length sequences, relationships between magnitude and phase, Hilbert transform relations for complex sequences.
10	Design of FIR filters by windowing, examples of FIR filter design by using the Kaiser window method, optimum approximations of FIR Filters, FIR equiripple approximation.
11	Continuous-time filters, Butterworth low-pass filters, Chebyshev filters, elliptic filters, design of discrete-time IIR filters from continuous-time filters.
12	Downsampling and upsampling of discrete signals, perfect reconstruction, quadrature mirror filters, recursive implementation of filter banks and its relation to discrete wavelet transforms.

A. Oppenheim and R. Schafer, Discrete-Time Signal Processing, Second Edition, Prentice Hall, 1998.

• 5 biweekly home projects: 15%
  
• Midterm exam: 35%
  
• Final exam: 50%
  

Grading policy: only one question will be marked for each project. Still, answers to all question should be submitted.

• Project #1. Solutions to the project are available here.
• Project #2. The sound file for Q-4 can be found here. Solutions to the project are available here.
• Project #3. The sound file for Q-4 can be found here. Solutions to the project are available here.
• Project #4. The mat file for Q-2 can be found here. Solutions to the project are available here. Matlab solution can be found here.
• Project #5. The mat file for Q-1 can be found here. The mat file for Q-2 can be found here. Solutions to the project are available here.

• The lecture notes for the first week of classes are available here.
• The lecture notes for the second week of classes are available here.
• The lecture notes for the third week of classes are available here.
• The lecture notes for the fourth week of classes are available here.
• The lecture notes for the fifth week of classes are available here.
• The lecture notes for the sixth week of classes are available here.
• The lecture notes for the seventh week of classes are available here.
• The lecture notes for the eighth week of classes are available here.
• The lecture notes for the ninth week of classes are available here.
• The lecture notes for the tenth week of classes are available here.

• Tutorial 1.
• Tutorial 2.
• Tutorial 3.
• Tutorial 4.
• Tutorial 5.
• Tutorial 6.
• Tutorial 7.
• Tutorial 8.
• Tutorial 9.
• Tutorial 10.
• Tutorial 11.
• Tutorial 12.
• Tutorial 13.

• The midterm exam (Spring'09) is available here. Solutions to the exam can be found here.
• The final exam (Spring'09) is available here. Solutions to the exam can be found here.

• Learn more about some recent developments in the sampling theory from this paper.
• A summary of the properties of z-transform can be downloaded from here.
• A summary of the properties of DTFT can be downloaded from here.
• The homeworks for Spring'08 can be download from here.
• The exams given in Spring'08 can be download from here.
• The exams given in Spring'07 can be download from here.