The function x(t)=cos(2, where f is the sinusoidal frequency, sampled by replacing t with nT, where...
The function x(t)=cos(2, where f is the sinusoidal frequency,
sampled by replacing t with nT, where T is
the sampling period and n is an integer. The results is the
sequence x[n]=cos(2If f=1 MHz=1,000,000, and
T is 0.1 microseconds. Write expression for x[n]. Plot x[n] over -8
< n < 8
Homework Answers
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The function x(t)=cos(2, where f is the sinusoidal frequency,
sampled by replacing t with nT, where...
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 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t)...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
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
6. Let Xc(r) = cos 2π450t. This signal is sampled with f, = 1 .5kHz: x[n]...
6. Let Xc(r) = cos 2π450t. This signal is sampled with f, = 1 .5kHz: x[n] = xe (nT), n = 0,±1, . . . where T, = 1/f, we have 512 samples of x[n]. (a) Plot X (el") of x[n], n = 0, ± 1 , ±2, . . . (b) Approximately plot the DFT magnitude |x(kl. The DFT size is N = 512.
The signal x(t) 10 cos(2t (3300) t +0.2x)) is sampled at fs 8 kHz (a) Determine...
The signal x(t) 10 cos(2t (3300) t +0.2x)) is sampled at fs 8 kHz (a) Determine the sampled signal x[n]. (b) What would be the lowest possible sampling frequency for reconstructing x(0)? 4.
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut...
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut + ?) N. The differential equation of the displacement x(t) is Use phasor techniques to solve for the displacement phasor Xin terms of the excitation frequency ? , and the mechanical elements M = 0.1 kg, D = 8 N-s/m , and K = 2,000 N/m . If Fi-10 N and ?? = 30°, determine the excitation frequency w (in rad/s) at which the...
1. A signal, x(t) = 2 cos(21fmt), is applied to the ideal sampling circuit in the...
1. A signal, x(t) = 2 cos(21fmt), is applied to the ideal sampling circuit in the Figure below (left) where fm = 1 kHz. A sampling function, p(t), whose characteristic is given in the Figure below (right), is used when Ts = 0.25 ms. a) (5p) Plot the sampled signal, xs(t), in time domain for at least one period. b) [10p] Express the Fourier transform of sampled signal, xs(t), denoted by Xs , in frequency domain. c) [10p] Plot the...
a. Consider the following signal xi(t)= cos(2aft) The signal is sampled with the sampling frequency Fs....
a. Consider the following signal xi(t)= cos(2aft) The signal is sampled with the sampling frequency Fs. Answer the following: for a given sampling frequency Fs, what is the range of f so that the continuous time signal has a unique sampled signal? What happens if f is outside this range? Show you result using a number of illustrative Matlab plots (with suitably chosen Fs and f, try for example (some of) F=0.1Fs, 0.2Fs,..., 2Fs – but don't include all plots...
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples...
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples would be stored after 60 ms? (b) If x(t) = 4 cos(2π250t + 2n/7), what is the period of this signal? (c) For CDs, the sampling rate is 44,100 samples per second. How often (in seconds) must the ADC sample the signal?
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Fi...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Find and plot the Fourier Transform of x(t) (b) (10 pts) What is the Nyquist frequency and period for sampling? (c) (10 pts) Find and plot the Fourier Transform of xp(t) using the Nyquist rate.
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t)...
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 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
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
6. Let Xc(r) = cos 2π450t. This signal is sampled with f, = 1 .5kHz: x[n] = xe (nT), n = 0,±1, . . . where T, = 1/f, we have 512 samples of x[n]. (a) Plot X (el") of x[n], n = 0, ± 1 , ±2, . . . (b) Approximately plot the DFT magnitude |x(kl. The DFT size is N = 512.
The signal x(t) 10 cos(2t (3300) t +0.2x)) is sampled at fs 8 kHz (a) Determine the sampled signal x[n]. (b) What would be the lowest possible sampling frequency for reconstructing x(0)? 4.
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut + ?) N. The differential equation of the displacement x(t) is Use phasor techniques to solve for the displacement phasor Xin terms of the excitation frequency ? , and the mechanical elements M = 0.1 kg, D = 8 N-s/m , and K = 2,000 N/m . If Fi-10 N and ?? = 30°, determine the excitation frequency w (in rad/s) at which the...
1. A signal, x(t) = 2 cos(21fmt), is applied to the ideal sampling circuit in the Figure below (left) where fm = 1 kHz. A sampling function, p(t), whose characteristic is given in the Figure below (right), is used when Ts = 0.25 ms. a) (5p) Plot the sampled signal, xs(t), in time domain for at least one period. b) [10p] Express the Fourier transform of sampled signal, xs(t), denoted by Xs , in frequency domain. c) [10p] Plot the...
a. Consider the following signal xi(t)= cos(2aft) The signal is sampled with the sampling frequency Fs. Answer the following: for a given sampling frequency Fs, what is the range of f so that the continuous time signal has a unique sampled signal? What happens if f is outside this range? Show you result using a number of illustrative Matlab plots (with suitably chosen Fs and f, try for example (some of) F=0.1Fs, 0.2Fs,..., 2Fs – but don't include all plots...
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples would be stored after 60 ms? (b) If x(t) = 4 cos(2π250t + 2n/7), what is the period of this signal? (c) For CDs, the sampling rate is 44,100 samples per second. How often (in seconds) must the ADC sample the signal?
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Find and plot the Fourier Transform of x(t) (b) (10 pts) What is the Nyquist frequency and period for sampling? (c) (10 pts) Find and plot the Fourier Transform of xp(t) using the Nyquist rate.
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t)...
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