The first aim of Mathematics 6 is provide the student with further transform based techniques so as to have completed a broad range of methods for the solution of engineering problems. A second aim of the module is to apply numerical implementations of transforms to sampled signals and data. Finally the module aims to complete the process of putting in place a firm mathematical foundation for future development of the student.
Fourier Series
Classification of signals. Piecewise linear signals. Periodic signals. Even and odd signals.Fourier synthesis – superposition of sinusoidal waves. Fourier’s Theorem and Fourier coefficients. Fourier series for piecewise constant and piecewise linear signals. Fourier Series for even and odd functions and even and odd extensions. Fourier Series for functions of arbitrary period. Review of complex numbers, polar and exponential form. converting from real to omplex form of Fourier series. Parseval’s theorem and power spectra.
Introduction to Fourier Transforms
The Fourier transform. Amplitude and phase spectra. Transfer functions and filters for simple systems. Fast Fourier Transform in Matlab and sampling.
z-Transforms
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 find transfer functions and to solve first and second-order, linear difference equations with constant coefficients.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |