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Express the following finite discrete-time signal as the difference of two unit step sequences: x[n] = 1, for 0 ≤ n ≤ 5; and 0 otherwise.
- a)u[n] – u[n - 6]
- b)u[n - 5] – u[n - 6]
- c)u[n - 6] – u[n - 5]
- d)u[n] – u[n - 5]
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Express the following finite discrete-time signal as the difference of...
To express the given finite discrete-time signal as the difference of two unit step sequences, we need to find two unit step sequences that sum up to the given signal.
The unit step sequence u[n] is defined as follows:
u[n] = 1, for n >= 0
u[n] = 0, for n < />
Let's denote the two unit step sequences as u1[n] and u2[n].
u1[n] will represent the step at n = 0, and u2[n] will represent the step at n = N (where N is the last sample of the given signal).
So, u1[n] = u[n] and u2[n] = u[n - N].
Now, let's express the given signal x[n] in terms of the unit step sequences:
x[n] = 1, for 0 <= n=""><=>
0, otherwise
To express x[n] as the difference of two unit step sequences, we can use the following equation:
x[n] = u1[n] - u2[n]
Substituting the expressions for u1[n] and u2[n], we have:
x[n] = u[n] - u[n - N]
Therefore, the given finite discrete-time signal x[n] can be expressed as the difference of two unit step sequences: x[n] = u[n] - u[n - N].
The unit step sequence u[n] is defined as follows:
u[n] = 1, for n >= 0
u[n] = 0, for n < />
Let's denote the two unit step sequences as u1[n] and u2[n].
u1[n] will represent the step at n = 0, and u2[n] will represent the step at n = N (where N is the last sample of the given signal).
So, u1[n] = u[n] and u2[n] = u[n - N].
Now, let's express the given signal x[n] in terms of the unit step sequences:
x[n] = 1, for 0 <= n=""><=>
0, otherwise
To express x[n] as the difference of two unit step sequences, we can use the following equation:
x[n] = u1[n] - u2[n]
Substituting the expressions for u1[n] and u2[n], we have:
x[n] = u[n] - u[n - N]
Therefore, the given finite discrete-time signal x[n] can be expressed as the difference of two unit step sequences: x[n] = u[n] - u[n - N].
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Community Answer
Express the following finite discrete-time signal as the difference of...
Concept:
The signal u[n] is defined as:
u[n] = 1 for n ≥ 0
u[n] = 0 for n < 0
Also, the shifted version of u[n] is defined as:
u[n - n0] = 1 for n ≥ n0
u[n - n0] = 0 for n < n0
Now the combination of two discrete time signals can be analysed as:
u[n] - u[n - n0] = 1 for 0 ≤ n ≤ n0 - 1
u[n] - u[n - n0] = 0, otherwise
Application:
Since the given signal is defined as:
x[n] = 1, for 0 ≤ n ≤ 5
We can write:
x[n] = u[n] - u[n - 6]
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Express the following finite discrete-time signal as the difference of two unit step sequences: x[n] = 1, for 0 ≤ n ≤ 5; and 0 otherwise.a)u[n] – u[n - 6]b)u[n - 5] – u[n - 6]c)u[n - 6] – u[n - 5]d)u[n] – u[n - 5]Correct answer is option 'A'. Can you explain this answer?
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