The first aim of this course is to provide the student with further calculus basedtechniques so as to have completed a broad range of methods for the solution of engineeringproblems. A second aim of the module is to develop the student’s power of judgement inthe selection of appropriate techniques for problem solving and the evaluation of results.Finally the module aims to complete the process of putting in place a firm mathematicalfoundation for future development of the student.
Summation notation. Review of complex numbers, polar and exponential form. Fourier's Theorem and Fourier coefficients. Fourier series for piecewiseconstant and piecewise linear signals. Fourier Series for even and odd functions.Fourier Series for functions of arbitrary period. Complex form of Fourier series. Parseval’s theoremand power spectra.
Introduction to Fourier Transforms
Definition of the Fourier transform and simple examples. Table of Fourier Transforms of common functions. Linearity of the Fourier Transform. Inverting Fourier Transforms using partial fractions. Properties of the Fourier Transform. Amplitude and phasespectra. Transfer functions and filters for simple systems.
Review of sequences. Sampling and discrete time signals.Definition of the z-Transform. Simple examples and table of common z-Transforms. Linearity and shift theorems. Inverting z-Transforms. Use of the z-Transform to solve first- and second-order linear difference equations withconstant coefficients.
|Module Content & Assessment