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# Digital Signal Processing Important questions IT6502

## Sample Digital Signal Processing Important questions

1. State the sampling theorem
The sampling frequency must be at least the highest frequency present in the signal
F≥2fm

2. Define a signal
A signal is defined as any physical quantity that varies with time, space or any other independent variable.

3. define a system
A system is defined as an entity that manipulates one or more signals to accomplish a function, therefore producing new signal.
x(t) input signal

4. What is the condition for stability?
A system is said to be stable if it produces a bounded output for every bounded input (BIBO).
The system which does not satisfy this condition is an unstable system.
Condition for Stability:
∫∣ℎ(?)∣??< ∞∞−∞

5. State the superposition theorem
The response to a weighted sum of a signal be equal to the corresponding weighted sum of the outputs of the system to each of the individual input signal,
A system is said to be linear if and only if
T [a1 x1(n) + a2x2 (n)] = a1T [x1(n)] + a2T [x2(n)]

A system is said to be non-linear if it doesn’t obey superposition principle.

6. Define Z transform.
Z transform converts difference equations into algebraic equations thereby simplifying the analysis of discrete time systems
Definition
The Z transform of a discrete time sequence x (n) is defined as
X (Z) =Σ? (?) ?−?∞
?=−∞

7. What is bilateral Z transform?
The Z transform of a discrete time sequence x (n) is defined as
X (Z) =Σ? (?) ?−?∞
?=−∞
If the sequence x (n) exists for n in the range -∞ to ∞ the above equation represents two sided or bilateral Z transform

8. What is unilateral Z transform?
If the sequence exists only for n≥0 then the equation changes to
X (Z) =Σ? (?) ?−?∞
?=0
Which is called one sided Z transform or unilateral Z transform

9. Define inverse Z transform.
Inverse Z transform of X (z) is
X (n) =12??∮? (?) ??−1??

 Subject Name Digital Signal Processing Subject code IT6502 Regulation 2013