Q.1 Define a signal?
Ans.
A signal is a function that conveys information about the behavior or attributes of some phenomenon. It typically varies with time or space.
Q.2 Distinguish between continuous time and discrete time signals. Give an example?
Ans.
Difference
between Continuous-Time and Discrete-Time Signals:
- Continuous-Time Signal:
Defined for every value of time. It is continuous and smooth.
- Example: x(t) = sin(t)
- Discrete-Time Signal:
Defined only at specific time intervals. It is a sequence of values.
- Example: x[n] = sin(n)
Q.3 Define discrete time unit impulse signal?
Ans.
Discrete-Time
Unit Impulse Signal:
It is a signal defined as
It
acts like an identity element in convolution and is used to analyse and
represent discrete-time systems.
Q.4 Define periodic signal and non-periodic signal?
Ans.
Periodic Signal:
A signal is periodic if it repeats itself after a fixed interval of
time.
Mathematically,
where
T (for continuous-time) or N (for discrete-time) is the period.
Non-Periodic
Signal:
A signal is non-periodic if it does not repeat itself at regular
intervals.
It has no fixed period.
Q.5 Define a system. Elaborate with an example?
Ans.
A system
is a process or device that takes an input signal, performs some operation on
it, and produces an output signal.
It
can be represented as:
Input
→ [System] → Output
Example:
Let’s
say the input signal is a voltage signal:
x(t) = 5 sin(t)
And
the system doubles the input signal.
Then the output will be:
y(t) = 2 × x(t) = 10 sin(t)
So, the system here is a "Multiplier by 2".
Q.6 Distinguish causal and non-causal system. Give an example.
Ans.
Causal
System:
A system is causal if its output at any time depends only on present
and past inputs, not future inputs.
Real-time systems are always causal.
Example:
If output is:
y(t) = x(t) + x(t−1)
→ Depends on present and past → Causal
Non-Causal
System:
A system is non-causal if its output depends on future inputs.
Non-causal systems are not physically realizable in real-time.
Example:
If output is:
y(t) = x(t+1)
→ Depends on future → Non-Causal.
Q.7 Explain time shifting on signals with the help of an example.
Ans.
Time
shifting means moving a signal forward or backward in time.
- If the signal is x(t),
then:
- x(t − T)
→ Shifted right by T units (delay)
- x(t + T)
→ Shifted left by T units (advance)
Example:
Let’s
say the original signal is:
x(t) = sin(t)
- x(t − 2)
→ Delayed by 2 units → The signal starts 2 units later.
- x(t + 2)
→ Advanced by 2 units → The signal starts 2 units earlier.
Q. 8 Explain time scaling on signals with the help of an example.
Ans.
Time
Scaling in Signals
Time
scaling means compressing or stretching a signal in time.
- If the signal is x(t),
then:
- x(at)
→ Time-scaled signal
- If a > 1
→ Signal is compressed (faster)
- If 0 < a
< 1 → Signal is stretched (slower)
Example:
Let’s
say the original signal is:
x(t) = sin(t)
- x(2t)
→ Compressed → Oscillates twice as fast
x(0.5t) → Stretched → Oscillates half as fast.
Q. 9 Explain amplitude scaling on signals with the help of an example?
Ans.
Amplitude
Scaling in Signals
Amplitude
scaling means changing the height (amplitude) of a signal
by multiplying it with a constant.
- If the signal is x(t),
then:
- A × x(t)
→ Amplitude-scaled signal
- If A > 1
→ Signal becomes taller (amplified)
- If 0 < A
< 1 → Signal becomes shorter (attenuated)
Example:
Let’s
say the original signal is:
x(t) = sin(t)
- 2 × x(t) = 2 sin(t)
→ Amplitude is doubled
- 0.5 × x(t) = 0.5 sin(t)
→ Amplitude is halved.
Q.10 Explain time reversal on signals with the help of an example?
Ans.
Time
Reversal in Signals
Time
reversal means flipping the signal around the vertical axis
(mirror image in time).
- If the signal is x(t),
then:
- x(−t)
→ Time-reversed signal
Example:
Let’s
say the original signal is:
x(t) = t²
Then
the time-reversed signal is:
x(−t) = (−t)² = t² → Looks the same (even function)
But
for x(t) = t,
x(−t) = −t → Signal is flipped horizontally.