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a) Find E.(s)for T= 0.1s for the 2 functionse(t) = cos(4m),and e2 (1)-cos(16m) Explain why the...
Show all steps for upvote! l. The 2 functions e(I)-cos(4π), e2 (t)-cos(16m) are sampled every T seconds. (4+5+6-15 pts) (i) In order that that they both be reconstructible from their samples, how lar...
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l. The 2 functions e(I)-cos(4π), e2 (t)-cos(16m) are sampled every T seconds. (4+5+6-15 pts) (i) In order that that they both be reconstructible from their samples, how large can Tbe? (ii) If T= 0.1, explain why the 2 transforms E(c) and E2(z) are equal, without actually computing the transforms. Note that cos(2/V-θ)-cos(θ). (iii) If T-0.1, mention how you will design a filter to include as part of the sampler in order to ensure that aliasing...
Write a Matlab code to generate the signal y(t)=10*(cos(2*pi*f1*t)+ cos(2*pi*f2*t)+ cos(2*pi*f3*t)), where f1=500 Hz, f2=750 Hz...
Write a Matlab code to generate the signal y(t)=10*(cos(2*pi*f1*t)+ cos(2*pi*f2*t)+ cos(2*pi*f3*t)), where f1=500 Hz, f2=750 Hz and f3=1000 Hz. Plot the signal in time domain. Sketch the Fourier transform of the signal with appropriately generating frequency axis. Apply an appropriate filter to y(t) so that signal part with frequency f1 can be extracted. Sketch the Fourier transform of the extracted signal. Apply an appropriate filter to y(t) so that signal part with frequency f2 can be extracted. Sketch the Fourier...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse ...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n)
Problem 2 In each step to follow...
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...
Please finish these questions. Thank you Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is giv...
Please finish these questions. Thank you
Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each sign...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
1. Draw frequency domain representations (sketches of the real and imaginary parts of the Fourier transform)...
1. Draw frequency domain representations (sketches of the real and imaginary parts of the Fourier transform) for both cos(2*pi*fc*t) and sin(2*pi*fc*t), for a carrier waveform. ____________________ Now suppose we have a sinusoidal signal of frequency fi, where fi << fc. Let the signal be m(t)=cos(2*pi*fi*t) and the carrier be cos(2*pi*fc*t). Say we mix m(t) up to carrier frequency fc when we multiply m(t) by the carrier to create the modulated signal, s(t) = m(t) * cos(2*pi*fc*t). Draw the real part...
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...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
1-Can we calculate the Fourier Transform for a function represented by Fourier Series? Elaborate. 2-What happens...
1-Can we calculate the Fourier Transform for a function represented by Fourier Series? Elaborate. 2-What happens if we sample with a frequency that is less than half the maximum frequency of the sampled signal? 3-Describe in your words what is Fourier Series and its relation to periodic signals. Mention whether it is a time domain or frequency domain representation
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l. The 2 functions e(I)-cos(4π), e2 (t)-cos(16m) are sampled every T seconds. (4+5+6-15 pts) (i) In order that that they both be reconstructible from their samples, how large can Tbe? (ii) If T= 0.1, explain why the 2 transforms E(c) and E2(z) are equal, without actually computing the transforms. Note that cos(2/V-θ)-cos(θ). (iii) If T-0.1, mention how you will design a filter to include as part of the sampler in order to ensure that aliasing...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n)
Problem 2 In each step to follow...
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...
Please finish these questions. Thank you
Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
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...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
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