Course Objectives

At the end of the course, the student should

1. Be able to describe signals mathematically and understand how to perform mathematical operations on signals. The operations should include operations on the dependent as well as independent variables.
2. Be familiar with commonly used signals such as the unit step, ramp, impulse function, sinusoidal signals and complex exponentials.
3. Be able to classify signals as continuous-time vs. discrete-time, periodic vs. non-periodic, energy signal vs. power signal, odd vs. even, conjugate symmetric vs anti-symmetric
4. Be able to describe systems using linear constant coefficient differential equations and using their impulse response.
5. Understand system properties - linearity, time invariance, presence or absence of memory, causality, bounded-input bounded-output stability, and invertibility. Be able to identify whether a given system exhibits these properties and its implication for practical systems.
6. Be able to perform the process of convolution between signals and understand its implication for analysis of linear time-invariant systems. Understand the notion of an impulse response.
7. Be able to compute the output of an LTI system given the input and the impulse response through convolution sum and convolution integral.
8. Be able to solve a linear constant coefficient differential equation using Laplace transform techniques.
9. Understand the intuitive meaning of frequency domain and the importance of analyzing and processing signals in the frequency domain.
10. Be able to compute the Fourier series or Fourier transform of a set of well-defined signals from first principles. 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.
11. Understand the application of Fourier analysis to ideal filtering.
12. Understand the Nyquist sampling theorem and the process of reconstructing a continuous-time signal from its samples.
13. Be able to process continuous-time signals by first sampling and then processing the sampled signal in discrete-time.
14. Develop basic problem-solving skills and become familiar with formulating a mathematical problem from a general problem statement.
15. Use basic mathematics including calculus, complex variables and algebra for the analysis and design of linear time invariant systems used in engineering.