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1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T...
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...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the s...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts)...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered?
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....
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...
PROBLEM 8.5: (This problem is based on a problem from MIT's course 6.003, found on OpenCourseWare...
PROBLEM 8.5: (This problem is based on a problem from MIT's course 6.003, found on OpenCourseWare.) Suppose a continuous-time signal rc(t) is multiplied by an impulse train with alternating signs: (a) Find P(jw), the Fourier transform of p(t). (Hint: notice that p(t) is periodic with period 2T, and recall the expression for a Fourier transform of a periodic signal in terms of its Fourier series coefficients) (b) Assume that the Fourier transform of xe(t) is the Xc(ju) shown below Xe(jw)...
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in...
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies Suppose we impulse-train sample x(t) at the rate of 500 samples/second. 200 400 600 800 1000 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000 Hz....
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
Please answer the following fully with detailed justification/explanation. Thank you. Consider the signal e(t) (60m sin...
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...
Consider the complex-valued signal c(t) with Fourier transform as shown in the figure. Keep in mind...
Consider the complex-valued signal c(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies. Suppose we impulse-train sample o(t) at the rate of 500 samples/second. FOURIER TRANSFORM 200 600 800 1000 400 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000...
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...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered?
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....
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...
PROBLEM 8.5: (This problem is based on a problem from MIT's course 6.003, found on OpenCourseWare.) Suppose a continuous-time signal rc(t) is multiplied by an impulse train with alternating signs: (a) Find P(jw), the Fourier transform of p(t). (Hint: notice that p(t) is periodic with period 2T, and recall the expression for a Fourier transform of a periodic signal in terms of its Fourier series coefficients) (b) Assume that the Fourier transform of xe(t) is the Xc(ju) shown below Xe(jw)...
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies Suppose we impulse-train sample x(t) at the rate of 500 samples/second. 200 400 600 800 1000 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000 Hz....
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
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...
Consider the complex-valued signal c(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies. Suppose we impulse-train sample o(t) at the rate of 500 samples/second. FOURIER TRANSFORM 200 600 800 1000 400 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000...
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