Question

The sketch of the following periodic function *f(t)*
given in one period,

f(t) = {**(3t+1)**, -1 < t <= 1 and
**0**, -3 < t <= -1

**a)** Find period of the function, 2p?

**b)** Find Fourier coeff, a0, an **(n
=>1)**, bn?

**c)** Fourier series representation of f(t)?

**d)** Result from **(c)**, find the
first four non-zero term?

Answer #1

For the periodic function y(t) with period 12, y(t) = (0 if −6
< t < −3, 4 if −3 < t < 3, 0 if 3 < t < 6)
(a) determine the real Fourier series of y(t): y(t) = a0 + ∞ Sum
n=1 (an cos(2πfnt) + bn sin (2πfnt))
The ns are subscripts

Find the Fourier series of the periodic function given on one
period of length 2 by
f(x) = x2, - 1 < x < 1:

In the interval −π < t <
0, f(t) = 1; and for 0 < t
< π, f(t) = 0. f(t) = f(t+2 π)
Find the following for f(t) as associated with the Fourier
series:
a0 =?
an =?
bn =?
ωo =?

f(t)is an odd, periodic function with period 1 and
f(t)=3−6t
for 0≤t≤0.5
(I)
Find the Fourier coefficient an.
Put in this value only ie. Omit the "an = "
This question accepts numbers or formulas.
Plot | Help | Switch to Equation Editor | Preview
(II)
Find the Fourier coefficient b5.
Put in this value only ie. Omit the "b5 = "
Give your answer to AT LEAST FOUR PLACES OF DECIMALS.
This question accepts numbers or formulas.
Plot | Help...

Find the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

Given that: f(x) = { cos x , 0 < x < 2π
(a) Sketch extended periodic f(x) from -4π <x < 4π, and
justify whether f (x) is even function, odd function or
neither.
(b) Produce f (x) in a Fourier series.

State whether the given function is even or odd. Then, showing
the details of your work, find the Fourier series of the function,
with period 2pi. Result should be in closed form. Plot using Octave
or Matlab the first few non-zero partial sums for each case.
f(x)=x for -pi/2<x<pi/2
f(x)=pi-x for pi<x<3pi/2

sketch the function f and obtain fourier series
1. f(x)=|x|, -2pi<x<2pi

Given signal x(t) = sinc(t):
1. Find out the Fourier transform of x(t), find X(f), sketch
them.
2. Find out the Nyquist sampling frequency of x(t).
3. Given sampling rate fs, write down the expression of the
Fourier transform of xs(t), Xs(f) in terms of X(f).
4. Let sampling frequency fs = 1Hz.
Sketch the sampled signal xs(t) = x(kTs) and the Fourier
transform of xs(t), Xs(f).
5. Let sampling frequency fs = 2Hz. Repeat 4.
6. Let sampling frequency...

Find the Fourier series of f(x) as given over one period.
1.
f(x) =(0 if −2 < x < 0 and
2 if 0 < x < 2 )

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