Course Outline

Overview

The course has three sections. The first section looks at describing signals and linear systems in the time domain, which is the most intuitive perspective for most people. Signals are continuously varying waveforms, like audio or radio signals.

The second part of the course introduces the idea of representing signals in the frequency domain using the Fourier series and Fourier transform. This is a tremendously powerful perspective that greatly simplifies the understanding of communication systems, and signal processing.

This will be used to show how signals can be represented as a sequence of samples, and still be perfectly reconstructed, given reasonable conditions. Sampled signals can be processed by computers, and are the basis of all of the modern hand-held devices we all know and love. The third section of the course will show why and how this works.

Each week new material will be introduced during the Monday and Wednesday classes. Most Fridays will be devoted to describing systems that are based on the concepts we are discussing.

Outline

Section 1: Signals and Linear Systems in the Time Domain

• Signals and systems

• Linear systems

• Convolution

• Examples from radar, cell phones

Section 2: Continuous Time Signals in the Frequency Domain

• Fourier Series

• Fourier Transform

• Modulation and Communications

• Signal Sampling and Reconstruction

• Examples from doppler ultrasound imaging and broadcast radio

Section 3: Discrete Time Signals in the Frequency Domain

• Discrete Time Fourier Transform

• Discrete Time Fourier Series

• Examples from Magnetic Resonance Imaging (MRI)