Course Objectives

At the end of the course, the student should

- 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.
- Be familiar with commonly used signals such as the unit step, ramp, impulse function, sinusoidal signals and complex exponentials.
- 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
- Be able to describe systems using linear constant coefficient differential equations and using their impulse response.
- 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.
- 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.
- Be able to compute the output of an LTI system given the input and the impulse response through convolution sum and convolution integral.
- 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. 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.
- Understand the Nyquist sampling theorem and the process of reconstructing a continuous-time signal from its samples.
- 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.
- Use basic mathematics including calculus, complex variables and algebra for the analysis and design of linear time invariant systems used in engineering.

page revision: 6, last edited: 14 Nov 2018 17:16