Consider signal ?(?)=cos(2??)cos(20??) a.(10 Points) Calculate the Fourier transform of ℎ(?)=?(?)cos(20??) using impulse functions. b.(10 Points)...
Consider signal ?(?)=cos(2??)cos(20??)
a.(10 Points) Calculate the Fourier transform of ℎ(?)=?(?)cos(20??)
using impulse functions.
b.(10 Points) Specify the frequency response of a filter that
returns an output signal proportional to the cos(2??)
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Consider signal ?(?)=cos(2??)cos(20??)
a.(10 Points) Calculate the Fourier transform of ℎ(?)=?(?)cos(20??)
using impulse functions.
b.(10 Points)...
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...
PROBLEM III (25 points) The signal v,(t) circuit 2 cos(20rt) cos(10rt) is placed at the input...
PROBLEM III (25 points) The signal v,(t) circuit 2 cos(20rt) cos(10rt) is placed at the input of a linear and time invariant Ideal #1 low-pass filter with frequency response H(o) al where de 20π. Find the output signal v2(t) using Fourier transform.
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first sampled at the rate of 80 samples per second and the result was processed with an ideal reconstruction filter, again assuming that sampling rate was 80 samples per second. What is the signal that results after the reconstruction? Show enough details in your answer to demonstrate that you understand the theory of sampling and reconstruction from samples. Hint: Write (t) as a sum of...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
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...
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...
Using parsevals theorem and FT to find y(t) and its power (b) (4 pts) Fourier Series The input signal r(t) and impulse...
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communicat...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
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...
PROBLEM III (25 points) The signal v,(t) circuit 2 cos(20rt) cos(10rt) is placed at the input of a linear and time invariant Ideal #1 low-pass filter with frequency response H(o) al where de 20π. Find the output signal v2(t) using Fourier transform.
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first sampled at the rate of 80 samples per second and the result was processed with an ideal reconstruction filter, again assuming that sampling rate was 80 samples per second. What is the signal that results after the reconstruction? Show enough details in your answer to demonstrate that you understand the theory of sampling and reconstruction from samples. Hint: Write (t) as a sum of...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
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...
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...
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
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