2011 | OriginalPaper | Chapter

# Introduction to invariant linear systems

Recognise a system as a process whereby an input (either continuous or discrete) is converted to an output, also called the response of the system Distinguish between linear and non-linear systems and recognise time-invariant and shift-invariant systems Determine the zero-input response and the zero-state response Appreciate why zero valued boundary conditions give rise to a time-invariant system Demonstrate that the response of a continuous, linear, time-invariant system to an arbitrary input is the convolution of the input with response of the system to a unit impulse Understand the role of the exponential function with respect to a linear, time-invariant system Use the convolution theorem to find the response of a continuous, linear, time-invariant system to an arbitrary input Derive the system transfer function of a constant coefficient linear differential equation and use it to solve the equation Demonstrate that the response of a discrete, linear, shift-invariant system to an arbitrary input is the convolution sum of the input with response of the system to a unit impulse Understand the role of the exponential function with respect to a discrete linear, shift-invariant system Derive the system transfer function of a constant coefficient linear difference equation and use it to solve the equation Derive the constant coefficient difference equation from knowledge of its unit impulse response.