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Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF is
- a)sin200πt
- b)1/2 sin200πt
- c)2sin 200πt
- d)0
Correct answer is option 'A'. Can you explain this answer?
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Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 4...
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Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 4...
Given:
Signal x(t) = sin 200t + 2 sin 400t
Signal g(t) = x(t) sin 400t
To Find:
The signal obtained at the output of the LPF.
Solution:
Step 1: Modulation of x(t) with sin 400t
The given signal x(t) is modulated with sin 400t to obtain the signal g(t).
g(t) = x(t) sin 400t
Step 2: Applying the modulation
Let's apply the modulation to the given signal x(t).
g(t) = (sin 200t + 2 sin 400t) sin 400t
Simplifying the above expression,
g(t) = sin 200t sin 400t + 2 sin 400t sin 400t
g(t) = 1/2 (cos (200t - 400t) - cos (200t + 400t)) + 1/2 (cos (400t - 400t) - cos (400t + 400t))
g(t) = 1/2 (cos (-200t) - cos (600t)) + 1/2 (cos (0) - cos (800t))
g(t) = 1/2 (-cos (200t) - cos (600t) + 1 - cos (800t))
g(t) = 1/2 (-cos (200t) - cos (600t) + 1 - cos (800t))
Step 3: Pass through an ideal LPF
The product of g(t) sin 400t is passed through an ideal LPF with a cutoff frequency of 400 and a passband gain of 2.
Step 4: Output of the LPF
The output of the LPF will contain the signal components within the passband, which is 0 to 400 Hz in this case. The LPF will remove the high-frequency components beyond the cutoff frequency.
Step 5: Analyzing the output
Analyzing the expression for g(t), we can see that it contains sine and cosine terms with frequencies of 200t, 600t, and 800t. The LPF with a cutoff frequency of 400 will remove the cosine terms with frequencies 600t and 800t, as they are beyond the cutoff frequency.
The output of the LPF will contain only the sine term with a frequency of 200t, which is the original signal x(t) = sin 200t.
Therefore, the signal obtained at the output of the LPF is sin 200t.
Answer:
The correct answer is option 'A', sin 200t.
Signal x(t) = sin 200t + 2 sin 400t
Signal g(t) = x(t) sin 400t
To Find:
The signal obtained at the output of the LPF.
Solution:
Step 1: Modulation of x(t) with sin 400t
The given signal x(t) is modulated with sin 400t to obtain the signal g(t).
g(t) = x(t) sin 400t
Step 2: Applying the modulation
Let's apply the modulation to the given signal x(t).
g(t) = (sin 200t + 2 sin 400t) sin 400t
Simplifying the above expression,
g(t) = sin 200t sin 400t + 2 sin 400t sin 400t
g(t) = 1/2 (cos (200t - 400t) - cos (200t + 400t)) + 1/2 (cos (400t - 400t) - cos (400t + 400t))
g(t) = 1/2 (cos (-200t) - cos (600t)) + 1/2 (cos (0) - cos (800t))
g(t) = 1/2 (-cos (200t) - cos (600t) + 1 - cos (800t))
g(t) = 1/2 (-cos (200t) - cos (600t) + 1 - cos (800t))
Step 3: Pass through an ideal LPF
The product of g(t) sin 400t is passed through an ideal LPF with a cutoff frequency of 400 and a passband gain of 2.
Step 4: Output of the LPF
The output of the LPF will contain the signal components within the passband, which is 0 to 400 Hz in this case. The LPF will remove the high-frequency components beyond the cutoff frequency.
Step 5: Analyzing the output
Analyzing the expression for g(t), we can see that it contains sine and cosine terms with frequencies of 200t, 600t, and 800t. The LPF with a cutoff frequency of 400 will remove the cosine terms with frequencies 600t and 800t, as they are beyond the cutoff frequency.
The output of the LPF will contain only the sine term with a frequency of 200t, which is the original signal x(t) = sin 200t.
Therefore, the signal obtained at the output of the LPF is sin 200t.
Answer:
The correct answer is option 'A', sin 200t.
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Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. Can you explain this answer?
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Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. 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 Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. 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 Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. Can you explain this answer?.
Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. 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 Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. 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 Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. Can you explain this answer?.
Solutions for Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct 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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ample number of questions to practice Suppose we wish to transmit the signal x(t) = sin 200πt + 2 sin 400πt using a modulation that create the signal g(t) = x(t) sin 400πt. If the product g(t) sin 400πt is passed through an ideal LPF with cutoff frequency 400π and pass band gain of 2, the signal obtained at the output of the LPF isa)sin200πtb)1/2 sin200πtc)2sin 200πtd)0Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
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