Learning Outcomes and Objectives
It is the intent of this course that students will:
- be able to describe signals mathematically and understand how to perform mathematical operations on signals.
- be familiar with commonly used signals such as the unit step, ramp, impulse function, sinusoidal signals and complex exponentials, and be able to classify signals as continuous-time or discrete-time, as periodic or non-periodic, as energy or power signals, and as having even or odd symmetry.
- be able to describe linear time invariant systems either using linear constant coefficient differential equations or using their impulse response and be able to find a state space representation of a system from a block diagram and vice versa.
- understand various system properties such as linearity, time invariance, presence or absence of memory, causality, bounded-input bounded-output stability and invertibility and be able to identify whether a given system exhibits these properties and its implication for practical systems.
- understand the process of convolution between signals, its implication for analysis of linear time invariant systems and the notion of an impulse response.
- be able to solve a linear constant coefficient differential equation using Laplace transform techniques.
- understand the intuitive meaning of frequency domain and the importance of analyzing and processing signals in the frequency domain.
- be able to compute the Fourier series or Fourier transform of a set of well-defined signals from first principles, and further be able to use the properties of the Fourier transform to compute the Fourier transform (and its inverse) for a broader class of signals.
- understand the application of Fourier analysis to ideal filtering, amplitude modulation and sampling.
- be able to process continuous-time signals by first sampling and then processing the sampled signal in discrete-time.
- develop basic problem solving skills and become familiar with formulating a mathematical problem from a general problem statement.
- be able to use basic mathematics including calculus, complex variables and algebra for the analysis and design of linear time invariant systems used in engineering.
- develop a facility with MATLAB programming to solve linear systems and signal problems.
Text Book and Relevant Sections
These course resources make use of the following text:
Simon Haykin and Barry Van Veen, Signals and Systems 2005 JustAsk! Edition, John Wiley & Sons, Inc.
The following text book sections are covered.
- Chapter 1: 1.4, 1.5, 1.6 (1.6.2, 1.6.3, 1.6.5, 1.6.6, 1.6.8), 1.8
- Chapter 2: 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.14
- Chapter 3: 3.2, 3.3, 3.5, 3.7, 3.8
- Chapter 4: 4.2
- Chapter 3: 3.9, 3.10, 3.11, 3.12, 3.14, 3.15, 3.16, 3.17, 3.18
- Chapter 8: 8.2
- Chapter 4: 4.5, 4.6
Supplemental Notes
Problem Sets and Solutions
Relevant Text Sections | Problem Set | Solutions |
1.4 | 1.1(c, d), 1.5 (a,c,d,e,f,g), 1.6, 1.7, 1.8, 1.9 (a,b,c,f,h), 1.43, 1.44, 1.45, 1.49 | |
1.5 | 1.10, 1.11, 1.12, 1.13, 1.14 (a,b,c,d,e,f), 1.15, 1.51, 1.52(f), 1.53, 1.56 (b,c,d,f,k) |
|
1.6 | 1.17, 1.18, 1.22, 1.57, 1.58, 1.59, 1.61 | |
1.8 | 1.26, 1.27, 1.28, 1.29, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.64 (a,b,d,e,f,i,j), 1.68, 1.72, 1.73, 1.75, 1.76 | |
2.2, 2.3, 2.4, 2.5 | 2.1, 2.2, 2.3, 2.5, 2.6, 2.32, 2.33 (a,c), 2.34(a,e,k), 2.39(a,b,n), 2.40(a,k,p) | PDF, errata |
2.6, 2.7, 2.8, 2.9 | 2.44, 2.47, 2.48, 2.49, 2.50(a,b,h), 2.51 | |
3.2, 3.3, 3.5 | 3.7, 3.8, 3.9, 3.10, 3.50(a,b,f), 3.51, (a,b,c,e) | |
3.7 | 3.14, 3.15, 3.54, 3.55 | |
4.2, 3.9, 3.10 | 4.1 (a,b), 4.16 (a,d), 3.16 (a), 3.17 (a,d), 3.18(a), 3.20(b), 3.21(a) | |
3.11, 3.12, 3.14, 3.15, 3.16, 3.17, 3.18 | 3.22, 3.23, 3.25, 3.26, 3.29, 3.34, 3.40(b), 3.41 3.43, (a), 3.44, 3.58 (a,b,e,g), 3.59 (a,c,e) | |
8.2, 4.5, 4.6 | 8.1, 4.10, 4.12, 4.25(a) |
Note: Problem set solutions are courtesy of Sanjay Nair.