# Mathematics of Signal Representations

## Math4355 - Spring 2013 - Homework

Assignment 1, due Thursday, January 24

• Review Sections 0.1-0.3, memorize properties of an inner product, definitions of convergence in square norm (Definition 0.7), pointwise and uniform convergence (Definition 0.8).
• Do Exercises in Chapter 0, p. 34-35: 1; 3; 6; 7;
• Show that the sequence of functions given by fn(x)= x e-nx converges uniformly on the interval [0,1] to zero. Hint: Use calculus to find where the function maximally deviates from zero.
• (Matlab project) Define a variable with the command "x=0:0.001:1;" in Matlab. This is just a row vector with values ranging from 0 to 1 in steps of 0.001 increment. Now plot the functions fn(x) = x e-nx for n=2, n=5, and n=10. Refer to Matlab Help on arithmetic (element by element product) and elementary functions (exponential) if needed. You may want to call the resulting vectors of function values f2, f5, and f10. Plotting the functions is simply done by "plot(x,f2);" and similarly for f5 and f10. Export (save) the plots and print them. Attach a printout of your plots to your homework, together with the Matlab code you used to generate the function values.