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Comment on the causality of y[n] = x[-n].
- a)Time invariant
- b)Causal
- c)Non causal
- d)Time varying
Correct answer is option 'C'. Can you explain this answer?
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Comment on the causality of y[n] = x[-n].a)Time invariantb)Causalc)Non...
For positive time, the system may seem to be causal. However, for negative time, the output depends on time at a positive sign, thus being in the future, enforcing non causality.
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Comment on the causality of y[n] = x[-n].a)Time invariantb)Causalc)Non...
Explanation:
The given system is y[n] = x[-n]. Let's see how it works.
1. Time-reversal of input signal:
The given system involves time-reversal of the input signal. This means that for any given input x[n], the output y[n] is obtained by reversing the time index of x[n]. For instance, if x[0] = 1, x[1] = 2, x[2] = 3, then x[-1] = 3, x[-2] = 2, x[-3] = 1. So, y[0] = x[0] = 1, y[1] = x[-1] = 3, y[2] = x[-2] = 2, y[3] = x[-3] = 1.
2. Non-causal system:
A system is said to be causal if its output depends only on the present and past values of the input, not on the future values. In other words, a causal system cannot predict the future values of the input. However, in the given system, the output y[n] depends on the future values of the input x[n] (which are obtained by time-reversal). Hence, the given system is non-causal.
Therefore, the correct option is (c) Non-causal.
The given system is y[n] = x[-n]. Let's see how it works.
1. Time-reversal of input signal:
The given system involves time-reversal of the input signal. This means that for any given input x[n], the output y[n] is obtained by reversing the time index of x[n]. For instance, if x[0] = 1, x[1] = 2, x[2] = 3, then x[-1] = 3, x[-2] = 2, x[-3] = 1. So, y[0] = x[0] = 1, y[1] = x[-1] = 3, y[2] = x[-2] = 2, y[3] = x[-3] = 1.
2. Non-causal system:
A system is said to be causal if its output depends only on the present and past values of the input, not on the future values. In other words, a causal system cannot predict the future values of the input. However, in the given system, the output y[n] depends on the future values of the input x[n] (which are obtained by time-reversal). Hence, the given system is non-causal.
Therefore, the correct option is (c) Non-causal.
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