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Problem 1: A signal f(t) is said to be periodic if for some positive constant To...
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]....
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
For the continuos-tine periodic signal π x(t)-1 + sin(wot) + 2cos(wot) + cm(2.01 + ), which...
For the continuos-tine periodic signal π x(t)-1 + sin(wot) + 2cos(wot) + cm(2.01 + ), which has fundamental frequency wo Determine the Fourier series coefficients a such that A continuous-time periodic signal with fundamental frequency wo-2m is expressed as +3 al-a-l = 4 Use Euler's relation to express r(t) as sum of cosine and sine functions of time
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...
(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic,...
(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic, find its fundamental period. (a) x(t) = 4, a constant signal. (b) x(t) = 28ej (400#t) (c) x[n] = 28ej(1007n) (d) x(t) = 10 sin(5t) - 4 cos(7t) (e) x[n] = 10 sin(5n) - 4 cos(7n) (f) r(t) = cos(Ft) sin(ft) (g) x(t) = teit (h) x[n] = e(m/v2) (1) x[n] = cos(km2) (Pay attention to the square) (j) x[n] = {X- 8[n -...
For the continuous-tine periodic signal 4nt (-), 2mt x(t) = 2 + cos (-) + sin...
For the continuous-tine periodic signal 4nt (-), 2mt x(t) = 2 + cos (-) + sin determine the fundamental frequency wo and the Fourier series coefficients ak such that kwot k=-oo
Chapter 1: Problem 1. Determine whether or not each of the following signals is periodic. In...
Chapter 1: Problem 1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its fundamental period. a.X (n) = 3 cos (5n + 4) b. x(n) = 2 exple-t) C. x(n) = cos () cos (4) d. "(m) = cos (3)- sin (a) + 3 cost 8 cos )
3. Determine whether or not each of the following signals is periodic. If a signal is...
3. Determine whether or not each of the following signals is periodic. If a signal is periodic fundamental period x(t)=cos(2t+4 Determine whether the following signals are Energy signals or Power signals a. 4.
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and...
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
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)...
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
For the continuos-tine periodic signal π x(t)-1 + sin(wot) + 2cos(wot) + cm(2.01 + ), which has fundamental frequency wo Determine the Fourier series coefficients a such that A continuous-time periodic signal with fundamental frequency wo-2m is expressed as +3 al-a-l = 4 Use Euler's relation to express r(t) as sum of cosine and sine functions of time
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...
(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic, find its fundamental period. (a) x(t) = 4, a constant signal. (b) x(t) = 28ej (400#t) (c) x[n] = 28ej(1007n) (d) x(t) = 10 sin(5t) - 4 cos(7t) (e) x[n] = 10 sin(5n) - 4 cos(7n) (f) r(t) = cos(Ft) sin(ft) (g) x(t) = teit (h) x[n] = e(m/v2) (1) x[n] = cos(km2) (Pay attention to the square) (j) x[n] = {X- 8[n -...
For the continuous-tine periodic signal 4nt (-), 2mt x(t) = 2 + cos (-) + sin determine the fundamental frequency wo and the Fourier series coefficients ak such that kwot k=-oo
Chapter 1: Problem 1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its fundamental period. a.X (n) = 3 cos (5n + 4) b. x(n) = 2 exple-t) C. x(n) = cos () cos (4) d. "(m) = cos (3)- sin (a) + 3 cost 8 cos )
3. Determine whether or not each of the following signals is periodic. If a signal is periodic fundamental period x(t)=cos(2t+4 Determine whether the following signals are Energy signals or Power signals a. 4.
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
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)...
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