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1. A signal, x(t) = 2 cos(21fmt), is applied to the ideal sampling circuit in the...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of t...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
Don't need to do #1. Please go into detail on how you solved #2 and #3 The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
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)...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling intervals: [30 points] • Ts= 0.5 sec. • Ts= 0.75 sec • Ts =1 sec. (a) For each case, also sketch the reconstructed continuous time signal from the samples using linear interpolation (i.e. connecting samples by straight lines). (b) In which case the sampled signal has aliasing distortion? What is the minimal sampling frequency and the corresponding sampling interval needed to avoid aliasing? 3....
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
Digital Signal Processing Sampling
Non-linear system If x1(n)=1*sin(2*pi*n*ts), x2(n)=0.5*sin(2*pi*2*n*ts) & y(n)=x(n)*x(n) What is the spectral representation of Ysum(m)? Sampling of a signal x(t)=sin(1000 t)+ sin (6280 t) What is the minimum sampling frequency? If fs=10 kHz, draw the spectrum (frequency domain) of the sampled signal
MATLAB Fourier transform. Suppose that a signal x(t) is sampled with sampling frequency fs =100Hz. The sequence x[n] obtained after the sampling is given below: Take the DFT of the sampled sequence a...
MATLAB Fourier transform. Suppose that a signal x(t) is sampled
with sampling frequency fs =100Hz.
The sequence x[n] obtained after the sampling is given below:
Take the DFT of the sampled sequence and plot
its magnitude and phase.
What is the frequency resolution (Δf) of your plot?
N= 20, 100 Hz
N= 20, 100 Hz
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
Let x(t) be the signal with Fourier transform Xjw) shown below x(j) Let Xs(t) be obtained...
Let x(t) be the signal with Fourier transform Xjw) shown below x(j) Let Xs(t) be obtained by sampling x(t) with sampling period Td let xdin]- x(nT) for all integer n. Which option is the plot of Xd(e the Fourier transform of xdinj? Instructions: First sketchXs ω which is the Fourier transtorm of xs nt is going to be infinite number of replicas of Sketch on 3 e cas. You need to n he span between heep as he )and Xole...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
MATLAB Fourier transform. Suppose that a signal x(t) is sampled
with sampling frequency fs =100Hz.
The sequence x[n] obtained after the sampling is given below:
Take the DFT of the sampled sequence and plot
its magnitude and phase.
What is the frequency resolution (Δf) of your plot?
N= 20, 100 Hz
N= 20, 100 Hz
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
Let x(t) be the signal with Fourier transform Xjw) shown below x(j) Let Xs(t) be obtained by sampling x(t) with sampling period Td let xdin]- x(nT) for all integer n. Which option is the plot of Xd(e the Fourier transform of xdinj? Instructions: First sketchXs ω which is the Fourier transtorm of xs nt is going to be infinite number of replicas of Sketch on 3 e cas. You need to n he span between heep as he )and Xole...
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