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Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that
x [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.
Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.
x [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.
Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.
Correct answer is between '31.00,31.00'. Can you explain this answer?
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Verified Answer
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1...
Similarly 2a + b + 1 = 4 Þ b = 3 - 2 (1) = 1
b =1
y [3] = 2(1) + 1 = 3
y[4] = b= 1
10y [3] + y[4] = 30 + 1 = 31
b =1
y [3] = 2(1) + 1 = 3
y[4] = b= 1
10y [3] + y[4] = 30 + 1 = 31
Most Upvoted Answer
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1...
Given Information:
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1.
Linear Convolution:
The linear convolution of two discrete-time signals x[n] and h[n] is defined as:
y[n] = x[0]*h[n] + x[1]*h[n-1] + x[2]*h[n-2]
Given Values and Calculation:
We are given that y[1] = 3 and y[2] = 4.
Using the formula for linear convolution, we can calculate the values of y[1] and y[2]:
y[1] = x[0]*h[1] + x[1]*h[0] + x[2]*h[-1]
3 = 1*0 + 2*1 + 1*0
3 = 2
y[2] = x[0]*h[2] + x[1]*h[1] + x[2]*h[0]
4 = 1*0 + 2*0 + 1*1
4 = 1
Calculating y[3]:
Using the formula for linear convolution, we can calculate the value of y[3]:
y[3] = x[0]*h[3] + x[1]*h[2] + x[2]*h[1]
Since both x[n] and h[n] are zero for n > 2, we can simplify the equation:
y[3] = x[0]*h[3] + x[1]*h[2]
Since h[3] is zero, we can further simplify the equation:
y[3] = x[1]*h[2]
y[3] = 2*0
y[3] = 0
Calculating y[4]:
Using the formula for linear convolution, we can calculate the value of y[4]:
y[4] = x[0]*h[4] + x[1]*h[3] + x[2]*h[2]
Since both x[n] and h[n] are zero for n > 2, we can simplify the equation:
y[4] = x[0]*h[4] + x[1]*h[3]
Since h[4] and h[3] are zero, we can further simplify the equation:
y[4] = x[0]*h[4]
y[4] = 1*0
y[4] = 0
Calculating the Expression (10y[3] - y[4]):
Substituting the values of y[3] and y[4] into the expression, we get:
(10y[3] - y[4]) = (10*0 - 0)
(10y[3] - y[4]) = 0
Conclusion:
The value of the expression (10y[3] - y[4]) is 0.
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1.
Linear Convolution:
The linear convolution of two discrete-time signals x[n] and h[n] is defined as:
y[n] = x[0]*h[n] + x[1]*h[n-1] + x[2]*h[n-2]
Given Values and Calculation:
We are given that y[1] = 3 and y[2] = 4.
Using the formula for linear convolution, we can calculate the values of y[1] and y[2]:
y[1] = x[0]*h[1] + x[1]*h[0] + x[2]*h[-1]
3 = 1*0 + 2*1 + 1*0
3 = 2
y[2] = x[0]*h[2] + x[1]*h[1] + x[2]*h[0]
4 = 1*0 + 2*0 + 1*1
4 = 1
Calculating y[3]:
Using the formula for linear convolution, we can calculate the value of y[3]:
y[3] = x[0]*h[3] + x[1]*h[2] + x[2]*h[1]
Since both x[n] and h[n] are zero for n > 2, we can simplify the equation:
y[3] = x[0]*h[3] + x[1]*h[2]
Since h[3] is zero, we can further simplify the equation:
y[3] = x[1]*h[2]
y[3] = 2*0
y[3] = 0
Calculating y[4]:
Using the formula for linear convolution, we can calculate the value of y[4]:
y[4] = x[0]*h[4] + x[1]*h[3] + x[2]*h[2]
Since both x[n] and h[n] are zero for n > 2, we can simplify the equation:
y[4] = x[0]*h[4] + x[1]*h[3]
Since h[4] and h[3] are zero, we can further simplify the equation:
y[4] = x[0]*h[4]
y[4] = 1*0
y[4] = 0
Calculating the Expression (10y[3] - y[4]):
Substituting the values of y[3] and y[4] into the expression, we get:
(10y[3] - y[4]) = (10*0 - 0)
(10y[3] - y[4]) = 0
Conclusion:
The value of the expression (10y[3] - y[4]) is 0.
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Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer?
Question Description
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. 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 Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer?.
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. 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 Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer?.
Solutions for Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given thatx [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.Correct answer is between '31.00,31.00'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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