deduce the coefficients C_n, Cn from the fourier series justifying the steps and determine the form...
Find Fourier series coefficients a0,
an, bn and cn
(ALL of these coefficients) for the following
periodic signals. You can use symmetry to determine whether
an or bn is zero – observe
carefully. However, you are NOT allowed to extract
a0, an and bn
from the expression of cn. That is to say, you
need to find a0, an and
bn exclusively from symmetry or by
integration.
Problem 5: Determine all of the complex Fourier series coefficients, cn, for the function shown. f(t) 2T -T T2T 0 for - T<t<0 (t) = t eat, for 0 < t < T
Show that the Fourier Series with an and bn can be written as rS n Sin Cn eXp nO0O where cn are complex coefficients. What is their value?
Show that the Fourier Series with an and bn can be written as rS n Sin Cn eXp nO0O where cn are complex coefficients. What is their value?
f) Calculate the coefficients of the trigonometric form of the Fourier series
numerically in MATLAB and graphically represent the one-sided spectrum
(width and phase) frequency for n up to 10 compared to the analytics results.
g) From the coefficients of the trigonometric form of the Fourier series ,
calculate the coefficients of the exposure series and present the two-sided spectrum (width and phase) frequency.
h) Find the average and active value of the signal from the Fourier expansion.
i) Check...
5. Determine the complex Fourier series coefficients of the following waveform: 10 6. Determine the complex Fourier series coefficients of the following waveform: x4(t) = 14(t + 10) Л Л 12 3
Let \(\left.x_{(} t\right)=\left\{\begin{array}{rr}t, & 0 \leq t \leq 1 \\ -t, & -1 \leq t \leq 0\end{array}\right.\), be a periodic signal with fundamental period of \(T=2\) and Fourier series coefficients \(a_{k}\).a) Sketch the waveform of \(x(t)\) and \(\frac{d x(t)}{d t}\) b) Calculate \(a_{0}\) c) Determine the Fourier series representation of \(g(t)=\frac{d x(t)}{d t}d) Using the results from Part (c) and the property of continuous-time Fourier series to determine the Fourier series coefficients of \(x(t)\)
1. (a) Evaluate the Fourier coefficients a, an, ba for the function defined as f)-2 cos() for-π/2 s sn2 and zero else over the period of 2T, do NOT use MATLAB or a calculator for integrations. All the steps should be shown. Write a few terms of the Fourier series expansion Plot 2 or 3 cycles of the Fourier series using MATLAB and verify whether the plot matches the given waveform Find Co and Cn and plot the amplitude spectrum...
Determine the fundamental period To, and the Fourier series coefficients af of the plot. ak = 1) c(t)e-jk (24pi/T)t dt 11/213
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
Determine if the signal is periodic (4 points each) and plot the Fourier series coefficients if the signal is periodic. (16 points) xt=3cos10πt+2cos25t xt=3+8cos8πt+2cos12πt+40°