Please see the attached file for the fully formatted problems. The convolution of two functions f and g is defined to be the new function f * g. whenever the integral converges. (a)Is it true that f*g = g*f? Why? (b) If F(k) = (i//) f°° exp (?ikx) f(x) dx and G(k) = (i//) f°° exp (?ikx) g(x) dx are the Fourier tra
Please see the attached file for the fully formatted problem. 2. Let p be a fixed and given square integrable function, i.e. 0 < S g(x)g(x) dx = ||g^2|| < inf The function g must vanish as |x| ---> inf. Consequently, one can think of g as a function whose non-zero values are concentrated in a small set around the origin x
Please see the attached file for the fully formatted function. Find the Fourier series, sketch the graph of the function for 3 periods. Is this a discontinuous graph? Is it an even or odd function, I know there are Fourier series rules for them.
(a) Explain the relationship between the spectral components indicated above and the corresponding graph showing the motion of the surface of the motor plotted as a function of time. What do they represent? (b) Given the amplitudes indicated in the above diagram, copy and complete the table below for the amplitude of the vib