Linear Systems for Communication

Aim

The course will give basic knowledge about time and frequency analysis of continuous-time signals and continuous-time linear systems. In particular, the course focuses on analog electrical circuits and applications in analog and digital communication. The course will also give knowledge about the mathematical tools used in the course. In short, after completed course the student should be able to:

For Electrical Circuits: Calculate, with structured methods, currents, voltages, and power in general dc and ac circuits. Calculate the voltage gain for circuits with operational amplifiers. Describe the construction and the function of electrical filters. Calculate and in practice measure the cutoff frequencies and center frequency for electrical filters.

For Linear Systems: Determine, interpret and mathematically handle time domain properties of deterministic signals and linear systems. By using Fourier series, the Fourier transform and the Laplace transform determine, interpret and mathematically handle frequency domain properties and general transform representations of both signals and systems. Define various properties of linear systems and, in connection with problem solving, handle the consequences of these properties. By using appropriate methods, for a given input signal calculate the output signal from a linear time-invariant system, and also give an account of the possibilities and limitations of different methods. With some precision, perform time and frequency analysis of various analog and digital modulation methods.

General: Give a well structured and logically coherent account - using adequate terminology - of the connections between different concepts in the course.

Content

For Electrical Circuits: Electric circuit fundamentals. Thévenin’s and Norton’s theorems. Node-voltage analysis. Sinusoidal steady-state analysis, phasors, impedance, power. Introduction to electrical filters. Ideal operational amplifiers.

For Linear Systems: Signal properties, system properties. Differential equation representation of linear systems. Linearization of non-linear systems. Impulse response and step response. Convolution. Fourier series analysis of periodic signals. Fourier transform analysis of signals and systems. Frequency spectrum. The frequency response function. Laplace transform analysis of signals and systems. The transfer function, Pole-zero diagrams. Time-continuous passive frequency selective filters.

For Communication: Principles of analog and digital communication, from a linear systems perspective. Amplitude modulation, frequency and phase modulation. Digital modulation methods.