![e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i) An (ii) Fourier series representation of x 4 marks] 3 marks Question 6 (20 marks) continuous time signal is represented by: x)-2cos 200a +sin 300 a) Explain the flow of converting a continuous time signal into a discrete time signal. (b) Determine the Nyquist frequency of the signal xtt). 3 marks] 3 marks] Explain why the minimum sampling frequency must be at least twice the Nyquist (o) [4 marks] 5 marks] [5 marks frequency. (d) Find the discrete-time signal xin] obtained by sampling the signal x(0) given above 250 Hz. at the sampling rate f Determine the signal that yields samples identical to those obtained in (d) at the sampling rate f-250 Hz. (e)](http://img.homeworklib.com/questions/079c9460-c2de-11ea-80f1-670fa7d524df.png?x-oss-process=image/resize,w_560)
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e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i)...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t)...
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...
(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...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
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...
An analog signal is given as below x(t) = 10sin 4rtt The signal is sampled by...
An analog signal is given as below x(t) = 10sin 4rtt The signal is sampled by two different frequencies f, = 1Hz, f, = 10Hz respectively, and the output are yı, Yz. (i) Sketch signal x(t) in the time domain. (3 marks) (ii) Sketch frequency spectrum of x(t). (3 marks) (iii) After sampling, the continuous signal is converted to a discrete signal. Draw the two discrete signals Yı, Y2: (4 marks) (iv) Discuss whether f1, f, can successfully sample the...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal...
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)
Insted of the equation on the pic, use this equation please 5e^-4t 3r x(t)-10e' for t,t...
Insted of the equation on the pic, use this equation
please
5e^-4t
3r x(t)-10e' for t,t 20 Assume 0-0 for I<0. Sketch the signal showing the major points of interest a) Calculate the Continuous Time Fourier Transform of *C b) Calculate the total energy of ( c) Using Parseval's theorem, compute the energy spectral density, ESD of"C) d) Sketch the ESD of "showing the major features. e) Using the ESD obtained from c), now calculate the essential bandwidth B Hz...
A. Find the Fourier series for the given function. G b. Let en(x)-f(x) - Sn(x). Find the least up...
a. Find the Fourier series for the given function. G b. Let en(x)-f(x) - Sn(x). Find the least upper bound or the maximum value (if it exists) of len(x) 1 for n = 10, 20, and 40 c. If possible, find the smallest n for which len(x)| s 0.01 for all x f(x +2) = f(x) x2 , 0£1〈1; ㄑㄨ
a. Find the Fourier series for the given function. G b. Let en(x)-f(x) - Sn(x). Find the least upper bound...
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. ...
Please explain why. Thank you.
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. For each of the given sampling rates in F, Hz or in T period, (i) determine the spectrum x(eM) of x[n]; (ii) plot its magnitude and phase as a function of w in and as a function of sampling frequency Fs in HZ; and (iii explain whether e(t) can be recovered from rn] (a) re(t) 8 +12e-3207e-j0(+), with sampling rate...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...
(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...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
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...
An analog signal is given as below x(t) = 10sin 4rtt The signal is sampled by two different frequencies f, = 1Hz, f, = 10Hz respectively, and the output are yı, Yz. (i) Sketch signal x(t) in the time domain. (3 marks) (ii) Sketch frequency spectrum of x(t). (3 marks) (iii) After sampling, the continuous signal is converted to a discrete signal. Draw the two discrete signals Yı, Y2: (4 marks) (iv) Discuss whether f1, f, can successfully sample the...
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)
Insted of the equation on the pic, use this equation
please
5e^-4t
3r x(t)-10e' for t,t 20 Assume 0-0 for I<0. Sketch the signal showing the major points of interest a) Calculate the Continuous Time Fourier Transform of *C b) Calculate the total energy of ( c) Using Parseval's theorem, compute the energy spectral density, ESD of"C) d) Sketch the ESD of "showing the major features. e) Using the ESD obtained from c), now calculate the essential bandwidth B Hz...
a. Find the Fourier series for the given function. G b. Let en(x)-f(x) - Sn(x). Find the least upper bound or the maximum value (if it exists) of len(x) 1 for n = 10, 20, and 40 c. If possible, find the smallest n for which len(x)| s 0.01 for all x f(x +2) = f(x) x2 , 0£1〈1; ㄑㄨ
a. Find the Fourier series for the given function. G b. Let en(x)-f(x) - Sn(x). Find the least upper bound...
Please explain why. Thank you.
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. For each of the given sampling rates in F, Hz or in T period, (i) determine the spectrum x(eM) of x[n]; (ii) plot its magnitude and phase as a function of w in and as a function of sampling frequency Fs in HZ; and (iii explain whether e(t) can be recovered from rn] (a) re(t) 8 +12e-3207e-j0(+), with sampling rate...
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