Expand in Fourier series:
Expand in fourier sine and fourier cosine series of: f(x) =
x(L-x), 0<x<L
Expand in fourier cosine series: f(x) = sinx, 0<x<pi
Expand in fourier series f(x) = 2pi*x-x^2, 0<x<2pi,
assuming that f is periodic of period 2pi, that is,
f(x+2pi)=f(x)
Both the Fourier Series and the Discrete Fourier Transform are
calculated using summation. Explain the key differences in what the
inputs each of the Fourier Series and the DFT are AND the
requirements the inputs.
Given the following functions, can you have the corresponding a)
Fourier series, b) Fourier transform and c) Laplace transform? If
yes, find them, if not, explain why you can not.
A, x(t) = -1+cos(2t) +
sin(pai*t+1)
(4-1)
B, x(t) = 2d(t) cos(2t) +d(t-1.5p)
sin(2t)
(4-2)
C, x(t) = 1+cos(1.5t) +
cos(4t)
(4-3)
Given the following functions, can you have the corresponding a)
Fourier series, b) Fourier transform and c) Laplace transform? If
yes, find them, if not, explain why you can not.
A, x(t) = -1+cos(2t) +
sin(pt+1) (4-1)
B, x(t) =2d(t) cos(2t) +d(t-1.5p)
sin(2t) (4-2)
C, x(t) = 1+cos(1.5t) +
cos(4t) (4-3)