A signal contains 4 components, 10 Hz, 30 Hz, 65 Hz, and 105 Hz. If use...
A signal contains 4 components, 10 Hz, 30 Hz, 65 Hz, and 105 Hz. If use a sampling frequency 50 Hz to sample the signal, are these components sampled correctly? Please draw in frequency domain of what you observed
Homework Answers
Answer:
The components given are as follows:
10 Hz, 30 Hz, 65 Hz, and 105 Hz.
The frequency domain of the given components is shown below:
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A signal contains 4 components, 10 Hz, 30 Hz, 65 Hz, and 105 Hz.
If use...
An analog signal, bandlimited to 10 Hz is corrupted by high-frequency noise. The spectrum of the...
An analog signal, bandlimited to 10 Hz is corrupted by high-frequency noise. The spectrum of the noise is from 30 Hz to 50 Hz. The noisy analog signal is sampled at 70 Hz. A digital lowpass filter is to be designed so as to remove the noise from the signal. For the filter design problem, what would you choose for the desired frequency response D(?)? Sketch the function for 0 ? ? ? ? where ? is normalized frequency (radians/sample)....
Consider the signal y(t) = 10cos(30ft) +15cos(80nt). c) If a sampling frequency of 30 Hz is...
Consider the signal y(t) = 10cos(30ft) +15cos(80nt). c) If a sampling frequency of 30 Hz is used to sample y(t), the resulting discrete signal y(n) will also have two components, one from sampling 10 cos(30nt), the other from sampling 15cos(80ft). Calculate the frequencies of the two components in y(n) (10pts)
1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume...
1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume any arbitrary spectrum for this signal. (Note that this signals also has frequencies from 0 to \(-10 \mathrm{KHz} .)\) a) Draw the frequency spectrum of the signal after it has been sampled with a sampling frequency \(\mathrm{F}_{\mathrm{s}}=25 \mathrm{kHz}\) b) What range of sampling frequencies allows exact reconstruction of this signal from its samples? c) How is the original signal reconstructed from the sampled signal?...
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sa...
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sampled at the rate of fs400 Hz, show the resulting spectrum of the ideally sampled signal. (b) If we attempt to reconstruct gi (t) from the samples in Part (a), what will be the recovered analog signal in both time and frequency domains? (c) Determine another analog signal G2(f) in frequency domain such that its samples at = 400 Hz will lead to the same...
Consider a message signal m(t) that contains frequency components at 100, 200, and 400 Hz. This...
Consider a message signal m(t) that contains frequency components at 100, 200, and 400 Hz. This signal is used to modulate a carrier at 100 kHz to obtain an SSB modulated signal. At the receiver, in the coherent detector is used to recover m(t), the oscillator supplies a sine wave of frequency 100.02 kHz instead of a cosine wave of frequency 100 kHz. (a) Determine the frequency components of the detector output if the SSB signal transmits the upper sideband....
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal ; c. Determine the frequency/frequencies of aliasing noise . Q2)...
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...
Problem 3 For the following signals, 345 points were sampled. a) 3.75 Hz signal sampled at...
Problem 3 For the following signals, 345 points were sampled. a) 3.75 Hz signal sampled at 10 Hz b) 24.8 Hz signal sampled at 20 Hz c) 175 Hz signal sampled at 30 Hz Determine: i) The Nyquist frequency and whether the signal is aliased. ii) The values for Af and the uncertainty in the frequency ur (round to the nearest 0.001 Hz). If aliased, what is the aliased frequency (include a marked-up folding diagram, available on Canvas for Quiz...
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
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at a sampling rate fs = 180 Hz. Sketch the spectrum X (f) of the sampled signal x (t). Properly label x-axis and y-axis. 2) Now suppose we will use an ideal lowpass filter of gain 1/fs with a cutoff frequency 90 Hz for the sampled signal xs(t). What is the output of the filter x,(t)? 3) Now let's take samples of x(t) at sampling...
Consider the signal y(t) = 10cos(30ft) +15cos(80nt). c) If a sampling frequency of 30 Hz is used to sample y(t), the resulting discrete signal y(n) will also have two components, one from sampling 10 cos(30nt), the other from sampling 15cos(80ft). Calculate the frequencies of the two components in y(n) (10pts)
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sampled at the rate of fs400 Hz, show the resulting spectrum of the ideally sampled signal. (b) If we attempt to reconstruct gi (t) from the samples in Part (a), what will be the recovered analog signal in both time and frequency domains? (c) Determine another analog signal G2(f) in frequency domain such that its samples at = 400 Hz will lead to the same...
Consider a message signal m(t) that contains frequency components at 100, 200, and 400 Hz. This signal is used to modulate a carrier at 100 kHz to obtain an SSB modulated signal. At the receiver, in the coherent detector is used to recover m(t), the oscillator supplies a sine wave of frequency 100.02 kHz instead of a cosine wave of frequency 100 kHz. (a) Determine the frequency components of the detector output if the SSB signal transmits the upper sideband....
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...
Problem 3 For the following signals, 345 points were sampled. a) 3.75 Hz signal sampled at 10 Hz b) 24.8 Hz signal sampled at 20 Hz c) 175 Hz signal sampled at 30 Hz Determine: i) The Nyquist frequency and whether the signal is aliased. ii) The values for Af and the uncertainty in the frequency ur (round to the nearest 0.001 Hz). If aliased, what is the aliased frequency (include a marked-up folding diagram, available on Canvas for Quiz...
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
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at a sampling rate fs = 180 Hz. Sketch the spectrum X (f) of the sampled signal x (t). Properly label x-axis and y-axis. 2) Now suppose we will use an ideal lowpass filter of gain 1/fs with a cutoff frequency 90 Hz for the sampled signal xs(t). What is the output of the filter x,(t)? 3) Now let's take samples of x(t) at sampling...
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