In: Electrical Engineering

Based on fourier series

Q1: how to determine if a signal function x(t) is periodic and ac. And what happens if there is x(t) = sint + cost + sint? How would we know if ac/periodic?

Q2: What is fourier series and fourier coefficients?

Q3: What is Fourier Trigonometric Series?

Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1.
Determine and plot the spectrum Fourier Transform of signal x(t) (
For plot : Use only interval n=-2 to n=2). 2. Based on the result
obtained in part one. Determine Complex Exponential Fourier Series,
and trigonometric Fourier Series. 3. Evaluate the energy spectral
density of the periodic signal x(t) in rang (n=-2 to n=2)

find Fourier series of periodic function ?(?) = { −?, −1 ≤ ? ≤ 0
with the period 2
{ ?, 0 ≤ ? ≤ 1

. Given the
following non-periodic signal:
x(t) = 3 e-5t cos(12t)
u(t)
Find the Fourier transform expression X(ω) without
using Table.
Calculate the magnitude spectrum of X(ω) for ω = π/8, π/4, and
π/2

Find the real Fourier series of the piece-wise continuous
periodic function
f(x) = x+sin(x) -pi<=x<pi

Find the Fourier series expansion of the function f(t) = t + 4 ,
0 =< t < 2pi

Find the real Fourier series of the piece-wise continuous
periodic function
f(x)=1+x+x^2 -pi<x<pi

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)

Calculate the fourier series of these periodic functions f(x) =
cosh(2πax + πa), x ∈ [0, 1) and f(x) = cos(2πax − aπ) x ∈ [0, 1).
The period of these functions is 1.
1-periodic

Fourier Series Approximation Matlab HW1:
You are given a finite step function
x(t)=-1, 0<t<4
1, 4<t<8
.
Hand calculate the FS coefficients of x(t) by assuming
half- range expansion, for each case below and modify the
code.
Approximate x(t) by cosine series only (This is
even-half range expansion). Modify the below code and plot the
approximation showing its steps changing by included number of FS
terms in the approximation.
Approximate x(t) by sine series only (This...

Given a sinusoidal signal:
x(t) = Asin(2πft)
Find Fourier Transform (FT) of the sinusoidal x(t) given above
and plot the spectrum with:
a. A = 2, f = 1000Hz
b. A = 2, f = 9000Hz
c. A = 5, f = 1000Hz
d. A = 10, f = 10000Hz

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