Basics of Control System(PART A — SIGNAL)
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Q1. What is a Signal?
Answer:
A signal is a physical quantity that contains information and varies with time, space, or another independent variable.
Mathematically, a signal can be represented as:
where � represents time.
Visual
Amplitude
↑
│ /\
│ / \ /\
│ / \ / \
│____/______\__/____\____→ Time
Examples:
Speech signal
Temperature signal
Voltage signal
ECG signal
Audio signal
Sensor output
Q2. What is an Analog Signal?
Answer:
An analog signal is a continuous-time signal whose amplitude can take any value within a given range.
Visual
Amplitude
↑
│ /‾\ /‾\
│ / \ / \
│___/ \___/ \___ → t
Examples:
Microphone output
Room temperature
Analog voltage
Human voice
Important point
Analog signal → continuous in amplitude and time.
Q3. What is a Digital Signal?
Answer:
A digital signal represents information using discrete levels, commonly 0 and 1.
Visual
1 ────┐ ┌──────┐
│ │ │
0 ────┴──────┘ └──────→ t
Examples:
Computer data
Digital communication
Logic circuits
Microprocessor signals
Difference
Analog
Digital
Continuous
Discrete levels
Can have infinite amplitude values
Usually finite levels
More affected by noise
Better noise immunity
Example: microphone voltage
Example: binary data
Q4. What is a Deterministic Signal?
Answer:
A signal whose value can be predicted exactly at every instant of time is called a deterministic signal.
Visual
x(t)
↑
│ /\
│ / \
│___/ \___
└────────────→ t
Predictable
Example:
We can calculate its value at any time.
Key point:
Deterministic = predictable.
Q5. What is a Random Signal?
Answer:
A signal whose instantaneous value cannot be predicted exactly is called a random signal.
Visual
Amplitude
↑
│ /\ /\/\ /\
│ / \_/ \_/\/ \__
│/ \
└──────────────────────→ t
Unpredictable
Examples:
Noise
Atmospheric interference
Random electronic noise
Key point:
Random = unpredictable.
Q6. What is an Energy Signal?
Answer:
A signal having finite energy and zero average power is called an energy signal.
The energy of a continuous-time signal is:
For an energy signal:
and average power is zero.
Visual
Signal
↑
│ /\
│ / \
│____/ \____
└──────────────→ t
Finite
energy
Example: A finite-duration pulse.
Q7. What is a Power Signal?
Answer:
A signal having finite, non-zero average power but generally infinite energy is called a power signal.
Average power:
For a power signal:
Visual
Amplitude
↑
│ /‾\ /‾\ /‾\ /‾\
│ / V V V \
└──────────────────→ t
Continues
Example: Sinusoidal signal.
Q8. What is an Odd Signal?
Answer:
A signal is called odd if:
Visual
x(t)
↑
/\ │
/ \ │
────/────\─┼────\────→ t
│ \ /
│ \/
Mirror image with
opposite amplitude
Example
because:
Q9. What is an Even Signal?
Answer:
A signal is called even if:
It is symmetrical about the vertical axis.
Visual
│
/\ │ /\
/ \ │ / \
──────/────\─┼─/────\────→ t
│
Symmetrical
Example
because:
Q10. What is a Periodic Signal?
Answer:
A signal that repeats itself after a fixed interval is called a periodic signal.
Mathematically:
where � is called the fundamental period.
Visual
/\ /\ /\
/ \ / \ / \
_/ \__/ \__/ \__
← T → ← T →
Examples:
Sine wave
Cosine wave
AC voltage
For:
the period is:
Q11. What is an Aperiodic Signal?
Answer:
A signal that does not repeat itself periodically is called an aperiodic signal.
Visual
Amplitude
↑
│ /\ /\
│____/ \__/\_/ \____
│ \__
└────────────────────→ t
No fixed repetition
Basics of Control SystemExample: A single pulse or a speech signal over a finite interval
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