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Problem A: Suppose you want to sample the signal f(t) = 100sinc(100nt). Determine the sampling rate...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that ...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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?
need problem 6.13 done. 12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms...
need problem 6.13 done.
12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms. Write an analytical expression for the Fourier transform Xa (w) and sketch it. Find an analytical expression for X, () the Fourier transform of the naturally- sampled signal T, (t). a. c. Sketch the transform X, (w). 613. Repeat...
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...
Consider the signal y(t)=5+10cos(32πt)+15cos(180πt). Determine 1.The frequencies contained in the signal 2.The minimum sampling rate to...
Consider the signal y(t)=5+10cos(32πt)+15cos(180πt). Determine 1.The frequencies contained in the signal 2.The minimum sampling rate to avoid aliasing
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5)...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
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)...
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....
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sa...
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sampled at the rate of fs400 Hz, show the resulting spectrum of the ideally sampled signal. (b) If we attempt to reconstruct gi (t) from the samples in Part (a), what will be the recovered analog signal in both time and frequency domains? (c) Determine another analog signal G2(f) in frequency domain such that its samples at = 400 Hz will lead to the same...
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...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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?
need problem 6.13 done.
12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms. Write an analytical expression for the Fourier transform Xa (w) and sketch it. Find an analytical expression for X, () the Fourier transform of the naturally- sampled signal T, (t). a. c. Sketch the transform X, (w). 613. Repeat...
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 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
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)...
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....
5.1-7 Consider a bandlimited signal g1(C) whose Fourier transform is (a) If g1(t) is uniformly sampled at the rate of fs400 Hz, show the resulting spectrum of the ideally sampled signal. (b) If we attempt to reconstruct gi (t) from the samples in Part (a), what will be the recovered analog signal in both time and frequency domains? (c) Determine another analog signal G2(f) in frequency domain such that its samples at = 400 Hz will lead to the same...
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...
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