Single-Course Danish 5 ECTS

# Continuous time signals and linear systems

## Overall Course Objectives

The overall goal of the course is to enable the student to build mathmatical models for simple linear electrical AC-circuits and use these models to characterize and improve their properties in both time domain, Fourier domain, and Laplace domain. Applications focus on measurement systems with an AC-coupled instrumentation amplifier and low- and highpass filters to amplify a target signal and suppress secondary DC and AC signals.

Learning Objectives

• identify and categorize deterministic/stochastic, analog/digital, causal/noncausal, periodic/aperiodic signals and signals with finite energy/power.
• identify and categorize systems according to linearity, stability, causality, time invariance and order.
• analyse linear physical systems and build corresponding mathematical models.
• investigate strengths and weaknesses in a system or filter design according to the systems differential equation, transfer function, frequency response, and pole-zero diagram and convert between these representations.
• use and define the mathematical properties of the Fourier and the Laplace transform and the conditions for their use.
• calculate output signals for known input signals using convolution, Fourier, and Laplace transformation.
• calculate the impulse, step, and ramp responses and their steady state error.
• calculate the frequency and amplitude spectrum of deterministic signals.
• investigate and explain the influence of the damping ratio and the natural frequency on the position of poles, step response, and amplitude characteristic for second order systems.
• design the transfer function for Butterworth filters based on the outcome of a sensitivity analysis.
• use computer tools for signal and systems analysis.

Course Content

This course concerns signals and linear systems in continuous time. Review of circuit theory, classification of signals and systems, derivation and solutions of system equations, impulse/step response, convolution, Fourier transformation of aperiodic and periodic signals, amplitude and phase spectra, Bode plot, pole-zero diagrams, Laplace domain derivation of impulse and step response, Butterworth filters, frequency scaling, impedance scaling, and applications of Maple and circuit simulators.

Recommended prerequisites

31003/34601/22437/01005/01034/01035/01037

Teaching Method

Lectures, exercises, computer exercises.

Faculty

Remarks

Lectures on theory can be reviewed in pre-recorded videos. The Discussion tool in DTU Learn provides a Question and Answer platform.

See course in the course database.

## Registration

Language Danish 13 weeks Health Tech DTU Lyngby Campus 22050 Bachelor Week 5 Week 19 Tues 8-12
Price 7.500,00 DKK