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A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.
x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt)
cos(0.125πt)
sin(0.125πt)
sin(0.5πt)
- a)1, 2
- b)1
- c)2, 3
- d)1, 2, 3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A filter has filter response given by h(t) = (sin(0.25πt))/πt. An inp...
Filter Response:
The given filter has a filter response given by h(t) = (sin(0.25πt))/πt.
Input Signal:
The input signal x(t) is given as x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt).
Analysis:
To determine which signal components would be visible at the output, we need to convolve the input signal with the filter response.
Convolution:
The convolution of two signals x(t) and h(t) is given by the integral of their product over all time:
y(t) = ∫[x(τ)h(t-τ)]dτ
Let's calculate the convolution of the input signal x(t) and the filter response h(t).
y(t) = ∫[(cos(0.125πτ) – 2sin(0.125πτ) + 0.125sin(0.5πτ))(sin(0.25π(t-τ)))/π(t-τ)]dτ
Simplifying the above expression, we get:
y(t) = (1/π)∫[cos(0.125πτ)sin(0.25π(t-τ)) - 2sin(0.125πτ)sin(0.25π(t-τ)) + 0.125sin(0.5πτ)sin(0.25π(t-τ))]dτ
Expanding the trigonometric functions using the sine double-angle formula and simplifying further, we get:
y(t) = (1/π)∫[0.5sin(0.375π(t-τ)) + 0.5sin(0.125π(t-τ)) - 0.25cos(0.125π(t-τ)) + 0.125sin(0.375π(t-τ))]dτ
Now, we can evaluate the integral term by term:
y(t) = (1/π)[0.5∫sin(0.375π(t-τ))dτ + 0.5∫sin(0.125π(t-τ))dτ - 0.25∫cos(0.125π(t-τ))dτ + 0.125∫sin(0.375π(t-τ))dτ]
Integrating each term, we get:
y(t) = (1/π)[(-2/3)cos(0.375π(t-τ)) + (-2)cos(0.125π(t-τ)) - (0.5/π)sin(0.125π(t-τ)) - (1/3)cos(0.375π(t-τ))]
Simplifying further, we get:
y(t) = (-1/π)[(1/3)cos(0.375π(t-τ)) + (0.5/π)sin(0.125π(t-τ))]
Visible Signal Components:
Comparing the above expression with the input signal x(t), we can see that the visible signal components at the output are:
1. cos(0.
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Community Answer
A filter has filter response given by h(t) = (sin(0.25πt))/πt. An inp...
Here, h(t) is a sinc() function whose transform would give a rect function ranging from [-0.25π, 0.25π].
Transform of x(t) would give impulses centered at -0.125π, 0.125π, -0.5π and 0.5π.
Since the filter window is from -0.25π to 0.25π, it would allow frequencies lying between these two extremes. i.e. only -0.125π and 0.125π components would pass whereas -0.5π and 0.5π would be blocked.
Thus we will get sin(0.125πt) and cos(0.125πt) components at the output.
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A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer?
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A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 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 filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer?.
A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 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 filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer?.
Solutions for A filter has filter response given by h(t) = (sin(0.25πt))/πt. An input signal x(t) is applied at the input. Determine which of the signal component would be visible at the output.x(t) = cos(0.125πt) – 2sin(0.125πt) + 0.125sin(0.5πt) cos(0.125πt) sin(0.125πt) sin(0.5πt) a)1, 2b)1c)2, 3d)1, 2, 3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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