An analog signal ?? (?) = 6sin(280??) + 3 sin(720??) − 7cos 260(? − 1)? is...
An analog signal ?? (?) = 6sin(280??) + 3 sin(720??) − 7cos 260(? − 1)? is sampled 400 times per second.
(a) Determine the Nyquist sampling rate for ?? (?).
(b) What are the frequencies, in radians, in the resulting discrete-time signal ?(?).
(c) What is the quantization step size? (assume L=10)
(d) What is the dynamic range of the signal.
Homework Answers
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An analog signal ?? (?) = 6sin(280??) + 3 sin(720??) − 7cos
260(? − 1)? is...
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...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting sampl...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
For an analog signal E(t) = 4 + 2 sin 47t + 3 sin 16t V...
For an analog signal E(t) = 4 + 2 sin 47t + 3 sin 16t V which sampled at a sample rate of 32 Hz. What are the criteria to properly construct its discrete time series. Discuss the results when using fs = 16 Hz and at fs = 45 Hz.
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that ...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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...
blem 1. A signal varies as y(t) 1000sin(40Tt) + 500 sin(150rt). 1. Compu signal Compute Nyquist...
blem 1. A signal varies as y(t) 1000sin(40Tt) + 500 sin(150rt). 1. Compu signal Compute Nyquist frequency for the signal. Does aliasing show up in the sampled signal provided a sampling frequency of 100 H Support your answer with appropriate calculations & using folding plot below. Compute the aliasing frequency. te the maximum frequency that can be represented in the resulting discrete 2. 3. 4. Sin 3.2 2.8 In-phase tofsf 2.6 2.4 2.2 Out-of phase 1.8 1.6 1.4 0.4 0.8...
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?...
1. A mono audio signal has a bit rate (sampling rate times bits per sample) of...
1. A mono audio signal has a bit rate (sampling rate times bits per sample) of 35 MB/sec. How many seconds of such audio can be stored on a CD of 700 MB? 2. An audio signal is sampled at a rate of 256 samples per second and 8 bits are assigned to each sample. Calculate the file size of 4 seconds of stereo audio. 3. Following is(are) advantages of digital audio as compared to analog audio duplication flexibility environmental...
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
Ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is s...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
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...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
For an analog signal E(t) = 4 + 2 sin 47t + 3 sin 16t V which sampled at a sample rate of 32 Hz. What are the criteria to properly construct its discrete time series. Discuss the results when using fs = 16 Hz and at fs = 45 Hz.
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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...
blem 1. A signal varies as y(t) 1000sin(40Tt) + 500 sin(150rt). 1. Compu signal Compute Nyquist frequency for the signal. Does aliasing show up in the sampled signal provided a sampling frequency of 100 H Support your answer with appropriate calculations & using folding plot below. Compute the aliasing frequency. te the maximum frequency that can be represented in the resulting discrete 2. 3. 4. Sin 3.2 2.8 In-phase tofsf 2.6 2.4 2.2 Out-of phase 1.8 1.6 1.4 0.4 0.8...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
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