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2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system is
- a)δ[n - 1] + δ[n - 2]
- b)δ[n - 4]
- c)δ[n - 3]
- d)δ[n - 1] δ[n - 2]
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h...
Problem Statement:
Two discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. We need to find the overall impulse response of the cascaded system.
Solution:
To find the overall impulse response of the cascaded system, we can use the property of convolution. The convolution of two signals in the time domain is equivalent to the multiplication of their Fourier transforms in the frequency domain.
Cascade Connection:
When two systems are connected in cascade, the output of the first system becomes the input to the second system.
Impulse Response of h1[n]:
The impulse response of h1[n] is given by h1[n] = δ[n - 1]. This means that the system h1[n] produces an output of δ[n - 1] when the input is an impulse at n = 0.
Impulse Response of h2[n]:
The impulse response of h2[n] is given by h2[n] = δ[n - 2]. This means that the system h2[n] produces an output of δ[n - 2] when the input is an impulse at n = 0.
Overall Impulse Response:
To find the overall impulse response of the cascaded system, we need to convolve the impulse responses of h1[n] and h2[n].
h1[n] * h2[n] = (δ[n - 1] * δ[n - 2])
Since the convolution of two impulses is a shifted impulse, we can simplify the expression as:
h1[n] * h2[n] = δ[n - 3]
Therefore, the overall impulse response of the cascaded system is given by h[n] = δ[n - 3], which is equivalent to option 'C' (δ[n - 3]).
Two discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. We need to find the overall impulse response of the cascaded system.
Solution:
To find the overall impulse response of the cascaded system, we can use the property of convolution. The convolution of two signals in the time domain is equivalent to the multiplication of their Fourier transforms in the frequency domain.
Cascade Connection:
When two systems are connected in cascade, the output of the first system becomes the input to the second system.
Impulse Response of h1[n]:
The impulse response of h1[n] is given by h1[n] = δ[n - 1]. This means that the system h1[n] produces an output of δ[n - 1] when the input is an impulse at n = 0.
Impulse Response of h2[n]:
The impulse response of h2[n] is given by h2[n] = δ[n - 2]. This means that the system h2[n] produces an output of δ[n - 2] when the input is an impulse at n = 0.
Overall Impulse Response:
To find the overall impulse response of the cascaded system, we need to convolve the impulse responses of h1[n] and h2[n].
h1[n] * h2[n] = (δ[n - 1] * δ[n - 2])
Since the convolution of two impulses is a shifted impulse, we can simplify the expression as:
h1[n] * h2[n] = δ[n - 3]
Therefore, the overall impulse response of the cascaded system is given by h[n] = δ[n - 3], which is equivalent to option 'C' (δ[n - 3]).
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Community Answer
2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h...
We have h1[n] = δ[n - 1] or H1 [Z] = Z-1
and h2[n] = δ[n - 2] or H2(Z) = Z-2
Response of cascaded system
H(z) = H1(z) · H2(z) = z-1 · z-2 = z-3
or, h[n] = δ[n - 3]
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2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. Can you explain this answer?
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2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. 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 2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. 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 2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. Can you explain this answer?.
2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. 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 2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. 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 2 discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system isa)δ[n - 1] + δ[n - 2]b)δ[n - 4]c)δ[n - 3]d)δ[n - 1] δ[n - 2]Correct answer is option 'C'. Can you explain this answer?.
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