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Q.100
What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} and
a)
{7,5,7,8}
b)
{1,3,7,8,6,2}
c) {7,8,7,5}
d)
{1,2,6,8,7,3}?
What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} and
a)
{7,5,7,8}
b)
{1,3,7,8,6,2}
c) {7,8,7,5}
d)
{1,2,6,8,7,3}?
Most Upvoted Answer
Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? ...
Understanding Circular Convolution
Circular convolution is a mathematical operation used in signal processing where two sequences are convolved in a circular manner. For sequences of different lengths, the shorter sequence is often padded with zeros.
Given Sequences
- x1(n) = {1, 2, 4, 2}
- x2(n) = {1, 1, 1}
Length Consideration
- The length of x1(n) is 4.
- The length of x2(n) is 3.
- To perform circular convolution, pad x2(n) with zeros to match the length of x1(n): x2(n) = {1, 1, 1, 0}.
Circular Convolution Calculation
1. Shift x2(n): Rotate the sequence x2(n) across all positions.
2. Multiply and Sum: For each shift, multiply overlapping elements and sum them.
Detailed Steps
- 0th Shift: (1*1) + (2*1) + (4*1) + (2*0) = 1 + 2 + 4 + 0 = 7
- 1st Shift: (1*1) + (2*1) + (4*0) + (2*1) = 1 + 2 + 0 + 2 = 5
- 2nd Shift: (1*1) + (2*0) + (4*1) + (2*1) = 1 + 0 + 4 + 2 = 7
- 3rd Shift: (1*0) + (2*1) + (4*1) + (2*1) = 0 + 2 + 4 + 2 = 8
Final Result
- The circular convolution result is: {7, 5, 7, 8}.
Correct Option
- The correct answer is option a) {7, 5, 7, 8}.
Circular convolution is a mathematical operation used in signal processing where two sequences are convolved in a circular manner. For sequences of different lengths, the shorter sequence is often padded with zeros.
Given Sequences
- x1(n) = {1, 2, 4, 2}
- x2(n) = {1, 1, 1}
Length Consideration
- The length of x1(n) is 4.
- The length of x2(n) is 3.
- To perform circular convolution, pad x2(n) with zeros to match the length of x1(n): x2(n) = {1, 1, 1, 0}.
Circular Convolution Calculation
1. Shift x2(n): Rotate the sequence x2(n) across all positions.
2. Multiply and Sum: For each shift, multiply overlapping elements and sum them.
Detailed Steps
- 0th Shift: (1*1) + (2*1) + (4*1) + (2*0) = 1 + 2 + 4 + 0 = 7
- 1st Shift: (1*1) + (2*1) + (4*0) + (2*1) = 1 + 2 + 0 + 2 = 5
- 2nd Shift: (1*1) + (2*0) + (4*1) + (2*1) = 1 + 0 + 4 + 2 = 7
- 3rd Shift: (1*0) + (2*1) + (4*1) + (2*1) = 0 + 2 + 4 + 2 = 8
Final Result
- The circular convolution result is: {7, 5, 7, 8}.
Correct Option
- The correct answer is option a) {7, 5, 7, 8}.
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Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}?
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Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}?.
Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}?.
Solutions for Q.100What is the circular convolution of the x * 2(n) = \{1, 1, 1\} ? sequences xl(n) = \{1, 2, 4, 2\} anda){7,5,7,8}b){1,3,7,8,6,2}c) {7,8,7,5}d){1,2,6,8,7,3}? in English & in Hindi are available as part of our courses for UPSC.
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