1. Does the following discrete system have the parameter of memory, y[n] = x[n-1] + x[n] ?
a) Yes
b) No
Explanation: y[n] depends upon x[n-1], i.e at the earlier time instant, thus forcing the system to have memory.
2. y[t]= ∫x[t],t ranges from 0 to t. Is the system a memoryless one?
a) Yes
b) No
c) Both memoryless and having memory
d) None of the Mentioned
Explanation: While evaluating the integral, it becomes imperative to know the values of x[t] from 0 to t, thus making the system requiring memory.
3. y(t) = sin(x(t-1)) : Comment on its memory aspects.
a) Having memory
b) Needn’t have memory
c) Memoryless system
d) Time invariant system
Explanation: The output at any time t = A, requires knowing the input at an earlier time, t = A – 1, hence making the system require memory aspects.
4. Construct the inverse system of y(t) = 2x(t)
a) y(t) = 0.5x(t)
b) y(t) = 2x(t)
c) y(2t) = x(t)
d) y(t) = x(2t)
Explanation: Now, y(t) = 2x(t) => x(t) = 0.5*y(t)
Thus, reversing x(t) <-> y(t), we obtain the inverse system: y(t) = 0.5x(t)
5. y(t) = x2(t). Is y(t) = sqrt(x(t)) the inverse of the first system?
a) Yes
b) No
c) Inverse doesn’t exist
d) Inverse exist
Explanation: We cannot determine the sign of the input from the second function, thus, the output doesn’t replicate the input. Thus, the second function is not an inverse of the first one.
6. Comment on the causality of y[n] = x[-n].
a) Time invariant
b) Causal
c) Non causal
d) Time varying
Explanation: 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.
7. y(t) = x(t-2) + x(2-t). Comment on its causality:
a) Causal
b) Time variant
c) Non causal
d) All of the mentioned
Explanation: For a time instant existing between 0 and 1, it would depend on the input at a time in the future as well, hence being non causal.
8. Comment on the causality of y[n] = n*x[n].
a) Time invariant
b) Time varying
c) Non causal
d) Causal
Explanation: For positive time, the system may seem to be causal. For negative time, the output depends on the same time instant, thus making it causal.
9. Comment on the linearity of y[n] = n*x[n].
a) Linear
b) Only additive
c) Not scalable
d) Non linear
Explanation: The function obeys the scaling/homogeneity property, but doesn’t obey the additivity property, thus not being linear.
10. Which one of the following is an example of a system with memory?
a) Identity System
b) Resistor
c) y(n)=x(n)-2x(n)
d) Accumulator
Explanation: An identity system gives the output same as input hence it totally depends on the present state of the input. Therefore, it is memory less. Similarly, a resistor and the expression in option c are memory less systems as they depend upon the present state of the input. An accumulator sums up the values of all past and present states of input. Therefore, it is a system with memory.