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1. For the signal represented in the figure, answer the following questions. a. b. What is...
2- In cach of the following, we specify the Fourier series coefficients of a CT signal...
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
You have a periodic signal, which period is T = 4π seconds, represented by the next complex...
You have a periodic signal, which period is T = 4π
seconds, represented by the next complex Fourier Exponential Series
of truncated
Find the coefficients a4, b2 and b4 Fourier's Trigonometric
Series of that signal.
| (0) + +)---+-+(-1)
-3 -2 -1 0 23 4 Given the pecriodc signal (O0 as showninabove, find 1) 2)...
-3 -2 -1 0 23 4 Given the pecriodc signal (O0 as showninabove, find 1) 2) 3) The period To, the fundamental angular frequency w The harmonic functions of trigonometric Fourier series The values of first 2 none zero an (coefficients of cos term) and bn (coefficients of sin term) 4) The expression of ft)
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Four...
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Fourier Series 3) 4) Graph the even extension of the function 5) Find the Fourier series and Fourier coefficients for the even extension 6) Write out the first three non-zero terms of the even Fourier series 7) Graph the odd extension of the...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Consider the following signal that is periodic with period T=2 a) Draw a picture of this signal ...
Consider the following signal that is periodic with period T=2 a) Draw a picture of this signal for . b) For which values of t will the Fourier series provide a good approximation for this signal? Justify based on part a c) Find the complex Fourier coefficients Cn from the definition. (integrate through using a table of integrals) d) Find the real Fourier coefficients an, bn. You may use your knowledge of Cn to do this, without integrating. Alternatively, you...
Determine the trigonometric Fourier series coefficients an and bn for signal x(t) sin(3m + 1) +...
Determine the trigonometric Fourier series coefficients an and bn for signal x(t) sin(3m + 1) + 2 cos(7m-2) . Determine also the signal's fundamental radian frequency wo. No integration is required to solve this cos( ( ? problem
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2...
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
Problem 1: Consider the continuous-time signal r(t) as shown in Figure 1. r(t) Figure 1: A...
Problem 1: Consider the continuous-time signal r(t) as shown in Figure 1. r(t) Figure 1: A continuous-time signal r(t) (a) Determine the fundamental period and the fundamental angular frequency of r(). 5 (b) Write down the equation for z(0) as the Fourier Series in exponential form and identify (c) Sketch the spectrum of this signal indicating the complex amplitudes and the frequen- points the Fourier Series coefficients. (15 points cies. [10 points
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
You have a periodic signal, which period is T = 4π
seconds, represented by the next complex Fourier Exponential Series
of truncated
Find the coefficients a4, b2 and b4 Fourier's Trigonometric
Series of that signal.
| (0) + +)---+-+(-1)
-3 -2 -1 0 23 4 Given the pecriodc signal (O0 as showninabove, find 1) 2) 3) The period To, the fundamental angular frequency w The harmonic functions of trigonometric Fourier series The values of first 2 none zero an (coefficients of cos term) and bn (coefficients of sin term) 4) The expression of ft)
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Fourier Series 3) 4) Graph the even extension of the function 5) Find the Fourier series and Fourier coefficients for the even extension 6) Write out the first three non-zero terms of the even Fourier series 7) Graph the odd extension of the...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Determine the trigonometric Fourier series coefficients an and bn for signal x(t) sin(3m + 1) + 2 cos(7m-2) . Determine also the signal's fundamental radian frequency wo. No integration is required to solve this cos( ( ? problem
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
Problem 1: Consider the continuous-time signal r(t) as shown in Figure 1. r(t) Figure 1: A continuous-time signal r(t) (a) Determine the fundamental period and the fundamental angular frequency of r(). 5 (b) Write down the equation for z(0) as the Fourier Series in exponential form and identify (c) Sketch the spectrum of this signal indicating the complex amplitudes and the frequen- points the Fourier Series coefficients. (15 points cies. [10 points
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