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For the time signal shown: (a) What is the highest frequency present?...
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in thi...
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[...
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
Question 1 If we need to have a frequency resolution of 50 Hz or better and a time resolution of 10 microsecond or better, and we want the number of data points to be a power of 2, what is the minimu...
Question 1
If we need to have a frequency resolution of 50 Hz or better and a time resolution of 10 microsecond or better, and we want the number of data points to be a power of 2, what is the minimum number of data points necessary for a Discrete Fourier Transform of a signal? What is the resulting sampling and Nyquist frequency? (9 pts)
If we need to have a frequency resolution of 50 Hz or better and a...
question 2 Question 2: (10 points) A narrowband signal has a bandwidth of 8 kHz centered on a carrier frequency of 150 kHz. It is proposed to represent this signal in discrete-time form by samplin...
question 2
Question 2: (10 points) A narrowband signal has a bandwidth of 8 kHz centered on a carrier frequency of 150 kHz. It is proposed to represent this signal in discrete-time form by sampling its in-phase and quadr ature components individually. What is the minimum sampling rate that can be used for this representation? tify you Jus answer. How would you reconstruct the original narrowband sig ampled versions of its in-phase and quadrature components?
Question 2: (10 points) A...
The continuous signal x(t) = 3 cos(2pi 70 t) is converted to a discretized signal. What...
The continuous signal x(t) = 3 cos(2pi 70 t) is converted to a discretized signal. What is the expression for the discrete signal if the sampling frequency is 200 Hz? What is the frequency of the discrete signal if it is sampled at 3Hz?
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist...
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
7. Based on the following frequency spectrum plot, what frequency components are in the time domain...
7. Based on the following frequency spectrum plot, what frequency components are in the time domain signal? Frequency Spectrum Amplitude 10 20 50 60 70 30 40 Frequency (Hz) 8. Based on the following frequency spectrum plot, what frequency components are in the time domain signal? Frequency Spectrum Amplitude 100 200 300 400 500 600 700
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...
13]. 5.21 a. The periodic signal gp(t) is shown in Figure P5.21. Find and sketch Go(w)....
13]. 5.21 a. The periodic signal gp(t) is shown in Figure P5.21. Find and sketch Go(w). b. How would the frequency spectrum change if the period of the waveform was doubled? Sp(o) 3 -30 -10 10 20 30 40 50 60 70 80 90 100 120 140 160 (ms) Figure P5.21
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoi...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
Question 1
If we need to have a frequency resolution of 50 Hz or better and a time resolution of 10 microsecond or better, and we want the number of data points to be a power of 2, what is the minimum number of data points necessary for a Discrete Fourier Transform of a signal? What is the resulting sampling and Nyquist frequency? (9 pts)
If we need to have a frequency resolution of 50 Hz or better and a...
question 2
Question 2: (10 points) A narrowband signal has a bandwidth of 8 kHz centered on a carrier frequency of 150 kHz. It is proposed to represent this signal in discrete-time form by sampling its in-phase and quadr ature components individually. What is the minimum sampling rate that can be used for this representation? tify you Jus answer. How would you reconstruct the original narrowband sig ampled versions of its in-phase and quadrature components?
Question 2: (10 points) A...
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
7. Based on the following frequency spectrum plot, what frequency components are in the time domain signal? Frequency Spectrum Amplitude 10 20 50 60 70 30 40 Frequency (Hz) 8. Based on the following frequency spectrum plot, what frequency components are in the time domain signal? Frequency Spectrum Amplitude 100 200 300 400 500 600 700
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...
13]. 5.21 a. The periodic signal gp(t) is shown in Figure P5.21. Find and sketch Go(w). b. How would the frequency spectrum change if the period of the waveform was doubled? Sp(o) 3 -30 -10 10 20 30 40 50 60 70 80 90 100 120 140 160 (ms) Figure P5.21
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
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