AMATH 242/CS 371 Spring 2018: Assignment 4|with a detailed answer key

AMATH 242/CS 371 Spring 2018: Assignment 4 Instructor: Sverrir Thorgeirsson SOLUTIONS Important: Apart from correctness, marks are allocated for explanations, clarity, brevity and general quality of presentation. Marks are deducted for handwritten solutions that are hard or impossible to read. Make sure that your pdf-file is self-contained and contains all answers, tables and graphs that are asked for. The answers should not be hidden in the submitted code; the code should only show how you found your answers. Total number of marks: 40 1. (10 marks) (a) (2 marks) Create a computer function in MATLAB or Python which generates one thousand evenly spaced samples of one second of a Gaussian white noise1 drawn from the distribution N(0, 1). Plot the result of your function. Make sure that your function is deterministic (i.e. that it always return the same output) so that it can be tested. Remark: If you use Python, you can use the numpy library function l. In MATLAB, you can use the wgn function. Answer: Figure 1: Example of Gaussian noise as specified. (b) (8 marks) Create another function which smooths the Gaussian white noise by taking the convolution of its Fourier transform with a rectangular function. Let the function take one integer argument which determines the maximum frequency of the resulting signal in Hz. Plot your function for the arguments 2, 5 and 20 on the same graph. 1See