Signals & Systems Questions and Answers Part-7

1. Which among the following is a memory less system?
a) Delay
b) Summer
c) Resistor
d) Capacitor

Answer: c
Explanation: Options Delay, Summer and Capacitor are all systems with memory as they depend upon past, past and present, past and present values of input respectively. Whereas, a resistor is a memory less system as its relationship with output always depends upon the current or present state of the input.

2. In a continuous-time physical system, memory is directly associated with _____________
a) Storage registers
b) Time
c) Storage of energy
d) Number of components in the system

Answer: c
Explanation: Memory is directly associated with storage of energy such as electric charge in the capacitor or kinetic energy in an automobile. Storage registers are for discrete time systems such as microprocessor etc. Time and number of components of a system have got nothing to do with memory.

3. A system with memory which anticipates future values of input is called _________
a) Non-causal System
b) Non-anticipative System
c) Causal System
d) Static System

Answer: a
Explanation: A system which anticipates the future values of input is called a non-causal system. A causal depends only on the past and present values of input. Non-anticipative is another name for the causal system. A static system is memory less system.

4. Determine the nature of the system: y(n)=x(-n).
a) Causal
b) Non-causal
c) Causal for all positive values of n
d) Non-causal for negative values of n

Answer: b
Explanation: The given system gives negative values of input i.e., past values of input when we feed positive integers to LHS. However, it gives positive values for negative values of n i.e., future values. Therefore, the system depends upon past values for some integers and future values for some other. A system cannot be called partially causal or non-causal, therefore, the system is non-causal.

5. Which among the following is an application of non-causal system?
a) Image processing
b) RC circuit
c) Stock market Analysis
d) Automobile

Answer: c
Explanation: Image processing, RC circuit, and an automobile are all causal systems as they do not anticipate the future values of an image, RC circuit and future actions of a driver respectively. Instead, they function upon either the stored information or on the current values of the input. Whereas, in the stock market, analysts try to figure out a trend in the future based upon the stored information. Therefore, it is non-causal.

6. Determine the nature of the given system: y(t)=x(sint)
a) Causal, Non-linear
b) Causal, Linear
c) Non-Causal, Non-linear
d) Non-causal, Linear

Answer: d
Explanation: The system is non-causal as it gives future values for some inputs.
E.g. y (- π) = x (sin (-π)) = x (0)
For linearity, it needs to satisfy superposition principle,
⇒ y1 (t) = x1 (sint)
⇒ y2 (t) = x2 (sint)
⇒ ay1 (t) + by2 (t) = ax1 (sint) + bx1 (sint) Equation 1
Now, y3 (t) = x3 (sint) = (ax1 + bx2)(sint) = ax1 (sint) + bx1 (sint) Equation 2
Clearly, Equation 1 and 2 are equal, hence the system is linear.

7. Is the system y[n]=2x[n]+2 linear?
a) Yes
b) No

Answer: b
Explanation: The system needs to satisfy superposition principle for linearity:
For input x1[n], y1 [n] = 2x1 [n] + 2
For input x2[n], y2 [n] = 2x2 [n] + 2
⇒ ay1 [n]+ by2 [n] = 2(ax1 [n]+ bx2 [n]) + 2(a+b) Equation 1
For, x3[n], y3 [n]=2x3 [n]+2 = 2(ax1 [n]+ bx2 [n]) + 2 Equation 2
Clearly, Equation 1 is not equal to equation
The system does not satisfy superposition principle ⇒ The system is not linear.

8. An inverse system with the original system gives an output equal to the input. How is the inverse system connected to the original system?
a) Series
b) Cascaded
c) parallel
d) No connection

Answer: c
Explanation: An inverse system when cascaded with the original system gives an output equal to the input.

9. Which among the following is an invertible system?
a) y[n] = 0
b) y[n] = 2x[n]
c) y(t) = x2(t)
d) y(t) = dx(t)/dt

Answer: b
Explanation: A system is said to be invertible if it’s input can be found out from its output. Implying, if a system has same outputs for several inputs then it is impossible to find the correct input as output is same for many. Therefore, a system is invertible if it gives distinct outputs to distinct inputs. It is non-invertible if it gives same outputs for many inputs.
Option a produces 0 output for any input → Non-invertible
Option b produces different outputs for different inputs and also it’s inverse system is (1/2)y[n] → Invertible
Option c, we get same output for both positive and negative values → Non-invertible
Option d, we get 0 for all constant input values → Non-invertible.

10. Is the system time invariant: y(t) = x(4t)?
a) Yes
b) No

Answer: b
Explanation: A system is said to be time invariant if a change input causes the same change in output.
For change in input by T
⇒ y(t, T) = x(4(t – T)) = x(4t – 4T) Equation 1
For the same change in output
⇒ y(t – T) = x(4t – T) Equation 2
Equation 1 is not equal to equation 2.
The system is not time invariant or is time variant.