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2. Consider a periodic signal shown below (20 points) i(t) -7 -6 -5 -4 -3 -2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N....
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1...
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1 3 2 - - 1 1 0 1 2 3 4 5 6 t A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
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 periodic signal x(t) shown in the Figure below: x(t) . 3 2 0 1...
Consider the periodic signal x(t) shown in the Figure below: x(t) . 3 2 0 1 2 3 4 5 6 t A. Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the...
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the exponential Fourier series representation f(t) = Σ Dnejuont . where wo 2T/To and 1. (2 points) When f(t) is a real-valued, show that DD This is known as the complex conjugate symmetry property or the Hermitian property of real signals. 2. (2 points) Show that when f(t) is an even function of time that Dn is an even function of n 3. (2 points)...
Question 5: [Basic] Consider three periodic signals xi(t) and x2(t). xi(t) has period 2 and its...
Question 5: [Basic] Consider three periodic signals xi(t) and x2(t). xi(t) has period 2 and its Fourier series coefficients are ai = a_1 = 2 and Ak = 0 for all k + +1. x2(t) has period 3 and its Fourier series coefficients are di = j, a-1 = -j and Ak = 0 for all k # £1. Answer the following questions. 1. Plot xi(t) and x2(t). 2. Suppose y(t) = xi(t) + 22(t). Find out the Fourier series...
Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a)...
Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a) Determine the fundamental period for each signal. b) Determine the fundamental period and fundamental frequency of the signal: y(t) = x;(C)x(0) (t) and x2(c) when the fundamental frequency is c) Determine the Fourier Series coefficients of defined as determined in part (b). d) Using Parseval's relation, determine the power of xy(t) and xy(t) e) Determine and plot the Fourier Series Coefficients of y(t). Show...
3. For the periodic signal shown below, find the period T and compute the main harmonics....
3. For the periodic signal shown below, find the period T and
compute the main harmonics. For our purposes, “main” means having
at least 2% of the amplitude of the fundamental harmonic. Use
MATLAB to plot the signal for two periods. Also plot
approximations to the signal using finitely many harmonics..
For the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, "main" means having at least 2% of the amplitude of the...
Consider the following CT periodic signals x(t), y(t) and z(t) a(t) 5 -4 y(t) 5/-4 z(t)...
Consider the following CT periodic signals x(t), y(t) and z(t) a(t) 5 -4 y(t) 5/-4 z(t) 5 4 (a) [2 marks] Find the Fourier series coefficients, ak, for the CT signal r(t), which is a periodic rectangular wave. You must use the fundamental frequency of r(t) in constructing the Fourier series representation (b) [2 marks] Find the Fourier series coefficients, bk, for the CT signal y(t) cos(t) You must use the fundamental frequency of y(t) in constructing the Fourier series...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1 3 2 - - 1 1 0 1 2 3 4 5 6 t A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
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 periodic signal x(t) shown in the Figure below: x(t) . 3 2 0 1 2 3 4 5 6 t A. Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the exponential Fourier series representation f(t) = Σ Dnejuont . where wo 2T/To and 1. (2 points) When f(t) is a real-valued, show that DD This is known as the complex conjugate symmetry property or the Hermitian property of real signals. 2. (2 points) Show that when f(t) is an even function of time that Dn is an even function of n 3. (2 points)...
Question 5: [Basic] Consider three periodic signals xi(t) and x2(t). xi(t) has period 2 and its Fourier series coefficients are ai = a_1 = 2 and Ak = 0 for all k + +1. x2(t) has period 3 and its Fourier series coefficients are di = j, a-1 = -j and Ak = 0 for all k # £1. Answer the following questions. 1. Plot xi(t) and x2(t). 2. Suppose y(t) = xi(t) + 22(t). Find out the Fourier series...
Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a) Determine the fundamental period for each signal. b) Determine the fundamental period and fundamental frequency of the signal: y(t) = x;(C)x(0) (t) and x2(c) when the fundamental frequency is c) Determine the Fourier Series coefficients of defined as determined in part (b). d) Using Parseval's relation, determine the power of xy(t) and xy(t) e) Determine and plot the Fourier Series Coefficients of y(t). Show...
3. For the periodic signal shown below, find the period T and
compute the main harmonics. For our purposes, “main” means having
at least 2% of the amplitude of the fundamental harmonic. Use
MATLAB to plot the signal for two periods. Also plot
approximations to the signal using finitely many harmonics..
For the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, "main" means having at least 2% of the amplitude of the...
Consider the following CT periodic signals x(t), y(t) and z(t) a(t) 5 -4 y(t) 5/-4 z(t) 5 4 (a) [2 marks] Find the Fourier series coefficients, ak, for the CT signal r(t), which is a periodic rectangular wave. You must use the fundamental frequency of r(t) in constructing the Fourier series representation (b) [2 marks] Find the Fourier series coefficients, bk, for the CT signal y(t) cos(t) You must use the fundamental frequency of y(t) in constructing the Fourier series...
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