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)
Using Matlab Simulink, find Fourier transform of the following
signal;
?(?) = 2 + ∑
1 ?
sin (20???)
4
?=1
.
Set simulation stop time = 20 seconds, sample time = (1/1024)
seconds, buffer size =1024, and frequency range in Hz for the
vector scope is −100 ≤ ? ≤ 100
Use the Fourier transform to find the solution of the following
initial boundaryvalue Laplace equations
uxx + uyy = 0, −∞ < x < ∞ 0 < y < a,
u(x, 0) = f(x), u(x, a) = 0, −∞ < x < ∞
u(x, y) → 0 uniformlyiny as|x| → ∞.
4 a) Find the Fourier Integral representation of ?(?) = 1 ?? |?|
< 1
0 ?? |?| > 1
b) Find the Fourier Sine Transform of ?(?) = ? −|?| . Hence
evaluate ∫ ?????? 1+?2 ??.