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F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
F(t) is a periodic square wave function as shown. It takes only two va...
Explanation:
The constant term in the Fourier series expansion of a periodic function represents the average value of the function over one period. In this case, the periodic function is a square wave that takes only two values, 4 and 0, and stays at each value for 1 second before changing.
Step 1: Understanding the Period
The period of the square wave function is the time it takes for the function to repeat itself. In this case, the period is 2 seconds because the function stays at each value for 1 second before changing.
Step 2: Calculating the Average Value
To find the constant term in the Fourier series expansion, we need to calculate the average value of the function over one period. Since the function takes only two values, 4 and 0, and stays at each value for 1 second before changing, the average value can be calculated as follows:
Average value = (4 * time at 4 + 0 * time at 0) / period
The time at 4 is the time the function stays at 4 before changing to 0, which is 1 second. The time at 0 is the time the function stays at 0 before changing to 4, which is also 1 second. Therefore, the average value is:
Average value = (4 * 1 + 0 * 1) / 2 = 4 / 2 = 2
Step 3: Conclusion
The constant term in the Fourier series expansion of the square wave function is 2.
Therefore, the correct answer is option B) 2.
The constant term in the Fourier series expansion of a periodic function represents the average value of the function over one period. In this case, the periodic function is a square wave that takes only two values, 4 and 0, and stays at each value for 1 second before changing.
Step 1: Understanding the Period
The period of the square wave function is the time it takes for the function to repeat itself. In this case, the period is 2 seconds because the function stays at each value for 1 second before changing.
Step 2: Calculating the Average Value
To find the constant term in the Fourier series expansion, we need to calculate the average value of the function over one period. Since the function takes only two values, 4 and 0, and stays at each value for 1 second before changing, the average value can be calculated as follows:
Average value = (4 * time at 4 + 0 * time at 0) / period
The time at 4 is the time the function stays at 4 before changing to 0, which is 1 second. The time at 0 is the time the function stays at 0 before changing to 4, which is also 1 second. Therefore, the average value is:
Average value = (4 * 1 + 0 * 1) / 2 = 4 / 2 = 2
Step 3: Conclusion
The constant term in the Fourier series expansion of the square wave function is 2.
Therefore, the correct answer is option B) 2.
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Community Answer
F(t) is a periodic square wave function as shown. It takes only two va...
Given : F (t) is a periodic square wave function with time period T = 2 second.
Complete Fourier series is given by,
Constant term in Fourier is given by a0/2
a0 = 4
Thus, constant term,
= 2
Hence, the correct option is (B).
Complete Fourier series is given by,
Constant term in Fourier is given by a0/2
a0 = 4
Thus, constant term,
= 2
Hence, the correct option is (B).
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