Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Consider two signals x [n] = {1, 2, - 1} and...
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Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] is
- a){1, 4, 1}
- b){1, 4, 2, - 4, 1}
- c){1, 2, - 1}
- d){2, 4, - 2}
Correct answer is option 'B'. Can you explain this answer?
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Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convo...
Convolution of Signals
The convolution of two signals, denoted as y[n] = x[n] * h[n], is a mathematical operation that combines the two signals to produce a third signal. It is often used in signal processing to analyze and manipulate signals.
Given Signals:
x[n] = {1, 2, -1}
h[n] = x[n]
Calculating Convolution:
The convolution y[n] = x[n] * h[n] can be computed using the formula:
y[n] = ∑(k=-∞ to ∞) x[k] * h[n-k]
To calculate the convolution, we need to shift the signal h[n] and multiply it element-wise with x[n]. Let's calculate the convolution step-by-step.
For n = 0:
y[0] = x[0] * h[0] = 1 * 1 = 1
For n = 1:
y[1] = x[0] * h[1] + x[1] * h[0] = 1 * 2 + 2 * 1 = 4
For n = 2:
y[2] = x[0] * h[2] + x[1] * h[1] + x[2] * h[0] = 1 * (-1) + 2 * 2 + (-1) * 1 = 2
For n = 3:
y[3] = x[1] * h[2] + x[2] * h[1] = 2 * (-1) + (-1) * 2 = -4
For n > 3:
Since both x[n] and h[n] have only 3 elements, the convolution y[n] will be zero for n > 3.
Resultant Convolution Signal:
The resultant convolution signal y[n] is given by {1, 4, 2, -4, 0, 0, ...}.
Correct Answer:
The correct answer is option 'B' which represents the convolution signal {1, 4, 2, -4, 1}.
The convolution of two signals, denoted as y[n] = x[n] * h[n], is a mathematical operation that combines the two signals to produce a third signal. It is often used in signal processing to analyze and manipulate signals.
Given Signals:
x[n] = {1, 2, -1}
h[n] = x[n]
Calculating Convolution:
The convolution y[n] = x[n] * h[n] can be computed using the formula:
y[n] = ∑(k=-∞ to ∞) x[k] * h[n-k]
To calculate the convolution, we need to shift the signal h[n] and multiply it element-wise with x[n]. Let's calculate the convolution step-by-step.
For n = 0:
y[0] = x[0] * h[0] = 1 * 1 = 1
For n = 1:
y[1] = x[0] * h[1] + x[1] * h[0] = 1 * 2 + 2 * 1 = 4
For n = 2:
y[2] = x[0] * h[2] + x[1] * h[1] + x[2] * h[0] = 1 * (-1) + 2 * 2 + (-1) * 1 = 2
For n = 3:
y[3] = x[1] * h[2] + x[2] * h[1] = 2 * (-1) + (-1) * 2 = -4
For n > 3:
Since both x[n] and h[n] have only 3 elements, the convolution y[n] will be zero for n > 3.
Resultant Convolution Signal:
The resultant convolution signal y[n] is given by {1, 4, 2, -4, 0, 0, ...}.
Correct Answer:
The correct answer is option 'B' which represents the convolution signal {1, 4, 2, -4, 1}.
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Community Answer
Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convo...
Y[n] = {1, 4, 2, -4, 1}
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Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct answer is option 'B'. Can you explain this answer?
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Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct 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 Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct 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 Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct answer is option 'B'. Can you explain this answer?.
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Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider two signals x [n] = {1, 2, - 1} and h [n] = x [n]. The convolution y [n] = x [n] x h [n] isa){1, 4, 1}b){1, 4, 2, - 4, 1}c){1, 2, - 1}d){2, 4, - 2}Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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