Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Questions  >  A discrete-time x[n] is obtained by sampling ... Start Learning for Free
A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.
  • a)
    1.25 KHZ
  • b)
    2.50 KHZ
  • c)
    4 KHZ
  • d)
    5 KHZ
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A discrete-time x[n] is obtained by sampling an analog signal at 10 kH...

View all questions of this test
Most Upvoted Answer
A discrete-time x[n] is obtained by sampling an analog signal at 10 kH...
- **Given Information**
A discrete-time signal x[n] is sampled at 10 kHz. The signal x[n] is filtered by a system with impulse response h(n) = 0.5 { d [n] +d (n – 1]}
- **Impulse Response**
The impulse response of the filter is given by h(n) = 0.5 { d [n] +d (n – 1]} where d[n] represents the unit impulse function.
- **3 dB Cut-off Frequency**
The 3 dB cut-off frequency of a filter is the frequency at which the power is halved or the amplitude is reduced to 0.707 of its original value.
- **Calculation**
For a discrete-time system, the 3 dB cut-off frequency can be calculated using the formula:
f_c = f_s / (2 * π) * arccos(1 - sqrt(2)/2)
where f_c is the cut-off frequency, f_s is the sampling frequency (10 kHz in this case), and arccos is the inverse cosine function.
- **Solution**
Substitute the values into the formula:
f_c = 10 kHz / (2 * π) * arccos(1 - sqrt(2)/2)
f_c = 10 kHz / (2 * π) * arccos(1 - 0.707)
f_c = 10 kHz / (2 * π) * arccos(0.293)
f_c = 10 kHz / (2 * π) * 1.26 kHz
f_c ≈ 2.50 kHz
Therefore, the 3 dB cut-off frequency of the filter is approximately 2.50 kHz, which corresponds to option 'B'.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
Explore Courses for Electronics and Communication Engineering (ECE) exam

Top Courses for Electronics and Communication Engineering (ECE)

A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer?
Question Description
A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE). Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 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 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A discrete-time 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 { d [n] +d (n – 1]}. The 3 dB cut off frequency of the filter is.a)1.25 KHZb)2.50 KHZc)4 KHZd)5 KHZCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
Explore Courses for Electronics and Communication Engineering (ECE) exam

Top Courses for Electronics and Communication Engineering (ECE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev