GATE Exam > GATE Questions > A discrete-time signal x[n]is obtained by sam...
Start Learning for Free
A discrete-time signal x[n] is obtained by sampling an analog signal at 10 kHz. The signal x[n] is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutoff frequency of the filter is:
- a)1.25 kHz
- b)2.50 kHz
- c)4 .00 kHz
- d)5.00 kHz
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A discrete-time signal x[n]is obtained by sampling an analog signal at...
Most Upvoted Answer
A discrete-time signal x[n]is obtained by sampling an analog signal at...
Assuming that the rest of the impulse response is not given, it is not possible to fully determine the system's characteristics. However, some information can be deduced based on the given portion of the impulse response.
Firstly, we can see that the system is a low-pass filter, since it attenuates higher frequencies more strongly than lower frequencies. This is because the cosine term in the expression for h[n] oscillates more rapidly at higher frequencies, causing cancellations.
Secondly, we can determine the cutoff frequency of the filter. The cutoff frequency is the frequency at which the filter's attenuation is -3 dB, or 50% in magnitude. From the given expression for h[n], we can see that the cosine term is equal to 1 when w = 0, and it becomes 0 at w = pi/2. Therefore, the cutoff frequency is pi/2, or approximately 1.57 radians/sample. In Hz, this corresponds to a frequency of 1.57/(2*pi) * 10000 = 250 Hz.
Finally, we can calculate the frequency response of the filter by taking the Fourier transform of h[n]. This gives:
H(w) = 0.5{1 + cos(w)} e^(-j*w*(N-1)/2)
where N is the length of the impulse response (which is not given). The frequency response is a complex function that describes how the filter modifies each frequency component of the input signal.
Firstly, we can see that the system is a low-pass filter, since it attenuates higher frequencies more strongly than lower frequencies. This is because the cosine term in the expression for h[n] oscillates more rapidly at higher frequencies, causing cancellations.
Secondly, we can determine the cutoff frequency of the filter. The cutoff frequency is the frequency at which the filter's attenuation is -3 dB, or 50% in magnitude. From the given expression for h[n], we can see that the cosine term is equal to 1 when w = 0, and it becomes 0 at w = pi/2. Therefore, the cutoff frequency is pi/2, or approximately 1.57 radians/sample. In Hz, this corresponds to a frequency of 1.57/(2*pi) * 10000 = 250 Hz.
Finally, we can calculate the frequency response of the filter by taking the Fourier transform of h[n]. This gives:
H(w) = 0.5{1 + cos(w)} e^(-j*w*(N-1)/2)
where N is the length of the impulse response (which is not given). The frequency response is a complex function that describes how the filter modifies each frequency component of the input signal.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer?
Question Description
A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer?.
A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A discrete-time signal x[n]is obtained by sampling an analog signal at 10 kHz. The signalx[n]is filtered by a system with impulse response h[n] = 0.5{ δ[n] + δ[n - 1]}. The 3dB cutofffrequency of the filter is:a)1.25 kHzb)2.50 kHzc)4 .00 kHzd)5.00 kHzCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup