Please answer the following fully with detailed justification/explanation. Thank you.
![Consider the signal e(t) (60m sin (50t) (a) Determine Xc(jw), the Fourier transform of e(t). Plot (and label) Xe(ju) b) What is the Nyquist rate for re(t)? (c) Consider processing the signal re(t) using the system shown below: Conversion to a Ideal to an e(t) y(t) impulse train Filter H-(ju) The sampling rate for this system is f DT filter is shown below 150 Hz. The frequency response of the H(e) Determine and sketch the Fourier transforms of rp(t), r[n], y[n], yp(t), and y(t). In other words, sketch Xp(jw), X(e2), Y(e), Y(jw), and Y(jw)](http://img.homeworklib.com/questions/d6d74770-6bda-11eb-af98-9129f006d0ab.png?x-oss-process=image/resize,w_560)
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Please answer the following fully with detailed
justification/explanation. Thank you.
Consider the signal e(t) (60m sin...
3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? ...
3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with...
Question2: (40 points]: Consider the system shown in the figure with the input signal xc(t) =...
Question2: (40 points]: Consider the system shown in the figure with the input signal xc(t) = 3 cos(100t) + 2 cos(200t), sampling frequency ws = 600 rad/s, and final filter cutoff frequency w1 = 400 rad/s. The filter has an impulse response given byha[n] = 8[n – 1] + 8[n] + 8[n + 1]. a) [10 points] Find and plot the signal Xa(ein) b) [10 points] Find and plot the signals Ya(ejn) and yo (jw) c) [10 points] Find and...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero ou...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
7.21. A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate where T = 10-4. For each of the following sets of constraints on x(t) and/or X(j), does the sampling theo...
7.21. A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate where T = 10-4. For each of the following sets of constraints on x(t) and/or X(j), does the sampling theorem (see Section 7.1.1) guarantee that x(t) can be recovered exactly from xp(t)? (a) X(jo) = 0 for lal > 5000π (b) x(ja)-0 for lol > 15000m (c) Re(X(jw)} = 0 for lal > 5000m (d) x(t) real and X(ju)-0 for ω > 5000TT (e) x(t) real and...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
Please provide a detailed answer, Thank you A Signal xt) with a Fourier Transform Rads/sec. X(92)...
Please provide a detailed answer, Thank you
A Signal xt) with a Fourier Transform Rads/sec. X(92) shown below is sampled with sampling Frequency 100 X(02) -2020 20 brad/sec) a- Plot the Fourier Transform of the sampled signal X.(2) b- What is the Nyquist Frequency C- What is the minimum sample rate we can use? d- What filter we can use to reconstruct the signal and what is its impulse response. e- If we decide to sample the signal at 50...
Points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sam...
points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sample s) at a frequency o, rads/second, e signal sa(t). Can you find a finite sampling frequency o such that ly recover s(t) from so()? If so, find it. If not, explain why not. a) (5 pts) In ting in the can perfectly you s (t) sa(t) →| Impulse sample at- rate o b) (5 pts) Now suppose we filter the signal s() with an...
Please explain your steps. I really don't understand this. Exercise 2. Consider the continuous-time signal x(t)...
Please explain your steps. I really don't
understand this.
Exercise 2. Consider the continuous-time signal x(t) = ejwot. Signal x(t) is sent to the input of a first LTI system (System 1) with frequency response Hi(jw) = e-jwA. Let A and wo be constant positive real values. Let y(t) be the output signal of System 1. Signal y(t) is then sent to the input of a second LTI system (System 2) with frequency response H2(jw) = w. Let z(t) be...
A Digital Signal Processing system is taking at its input the following analogue signal s(t); s(t)...
A Digital Signal Processing system is taking at its input the following analogue signal s(t); s(t) - 20+ 20 cos(24xt)cos(xt), Where time t is expressed in ms. Part 1 - Setting the sampling frequency: (11 Marks) As a start, the system comprises only a sampler and an ideal analogue reconstructor as follows: w(t) s(t) Sampler Analogue Reconstructor s,(t) Figure a) Find the frequency spectrum S(t) of s(t) and deduce its bandwidth. You may directly use the table provided at 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...
3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with...
Question2: (40 points]: Consider the system shown in the figure with the input signal xc(t) = 3 cos(100t) + 2 cos(200t), sampling frequency ws = 600 rad/s, and final filter cutoff frequency w1 = 400 rad/s. The filter has an impulse response given byha[n] = 8[n – 1] + 8[n] + 8[n + 1]. a) [10 points] Find and plot the signal Xa(ein) b) [10 points] Find and plot the signals Ya(ejn) and yo (jw) c) [10 points] Find and...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
7.21. A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate where T = 10-4. For each of the following sets of constraints on x(t) and/or X(j), does the sampling theorem (see Section 7.1.1) guarantee that x(t) can be recovered exactly from xp(t)? (a) X(jo) = 0 for lal > 5000π (b) x(ja)-0 for lol > 15000m (c) Re(X(jw)} = 0 for lal > 5000m (d) x(t) real and X(ju)-0 for ω > 5000TT (e) x(t) real and...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
Please provide a detailed answer, Thank you
A Signal xt) with a Fourier Transform Rads/sec. X(92) shown below is sampled with sampling Frequency 100 X(02) -2020 20 brad/sec) a- Plot the Fourier Transform of the sampled signal X.(2) b- What is the Nyquist Frequency C- What is the minimum sample rate we can use? d- What filter we can use to reconstruct the signal and what is its impulse response. e- If we decide to sample the signal at 50...
points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sample s) at a frequency o, rads/second, e signal sa(t). Can you find a finite sampling frequency o such that ly recover s(t) from so()? If so, find it. If not, explain why not. a) (5 pts) In ting in the can perfectly you s (t) sa(t) →| Impulse sample at- rate o b) (5 pts) Now suppose we filter the signal s() with an...
Please explain your steps. I really don't
understand this.
Exercise 2. Consider the continuous-time signal x(t) = ejwot. Signal x(t) is sent to the input of a first LTI system (System 1) with frequency response Hi(jw) = e-jwA. Let A and wo be constant positive real values. Let y(t) be the output signal of System 1. Signal y(t) is then sent to the input of a second LTI system (System 2) with frequency response H2(jw) = w. Let z(t) be...
A Digital Signal Processing system is taking at its input the following analogue signal s(t); s(t) - 20+ 20 cos(24xt)cos(xt), Where time t is expressed in ms. Part 1 - Setting the sampling frequency: (11 Marks) As a start, the system comprises only a sampler and an ideal analogue reconstructor as follows: w(t) s(t) Sampler Analogue Reconstructor s,(t) Figure a) Find the frequency spectrum S(t) of s(t) and deduce its bandwidth. You may directly use the table provided at 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...
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