1. UNIT I CLASSIFICATION OF SIGNALS AND SYSTEMS
• Standard signals- Step, Ramp, Pulse, Impulse, Real and
complex exponentials and Sinusoids
• Classification of signals – Continuous time (CT) and Discrete
Time (DT) signals, Periodic & Aperiodic signals,
Deterministic & Random signals, Energy & Power signals -
Classification of systems- CT
• systems and DT systems- – Linear & Nonlinear, Time-variant
& Time-invariant, Causal & Non-causal, Stable & Unstable.
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2. SIGNALS
CONTENT
– Definition of Signals
– Examples of signals
– Classification of Signals
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3. Definition
According to ALLEN.V.OPPENHEIM,” Signal is a physical
quantity that varies time, space or any other independent variables”.
OR
Signal: A function of one or more variables that convey information
on the nature of a physical phenomenon
• Examples:
– TV signal, radio signal, mp3
– Heartbeat, blood pressure, temperature, vibration
– Electrical signals (voltages and currents)
– Acoustic signals (both analog and digital)
– Video signals
• Variation in the intensity of a color
– Biological signals
• DNA sequence
– Economic signals – stock prices, DJIA
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4. Types of dimensional
One-dimensional signals: function depends on a
single variable, e.g., speech signal ,ECG
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5. 2D
Two -dimensional signals: function depends
on a two variable, e.g., image
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6. Multi-dimensional signals: function depends on
two or more variables, e.g., video.
CLASSIFICATION OF SIGNALS
Signals can be classified in to two types
1. Continuous Time Signal(CTS)
2. Discrete Time Signal(DTS)
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7. Continuous & Discrete-Time
Signals
Continuous-Time Signals
• Most signals in the real world are continuous
time, as the scale is infinitesimally fine.
• Eg voltage, velocity,
• Denote by x(t), where the time interval may
be bounded (finite) or infinite
SREE SAKTHI ENGINEERING COLLEGE, KARAMADAI, COIMBATORE
x(t)
t
8. Discrete-Time Signals
• Some real world and many digital signals are
discrete time, as they are sampled
• E.g. pixels, daily stock price (anything that a
digital computer processes)
• Denote by x[n], where n is an integer value that
varies discretely
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x[n]
n
9. Both CTS AND DTS further classified as
• Periodic and non-periodic signals
• Even and odd signals
• Deterministic and random signals
• Energy and power
• Casual and Non-casual signals
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10. Periodic & Non-periodic Signals
• Periodic signals have the property that x(t + T) = x(t) for all t.
• The smallest value of T that satisfies the definition is called the
period.
• Shown below are an non-periodic signal (left) and a periodic
signal (right).
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11. Even & Odd signal
Even signal: A signal that exhibits symmetry with
respect to t=0 is called even signal
• Even signal satisfies the condition 𝑥(𝑡) = 𝑥(−𝑡)
Odd signal: A signal that exhibits anti-symmetry with
respect to t=0 is called odd signal
Odd signal satisfies the condition 𝑥(𝑡) = −𝑥(−𝑡)
Even part 𝒙𝒆(𝒕) and Odd part 𝒙𝟎(𝒕) of continuous time
signal 𝒙 𝒕 :
Even part 𝑥𝑒( 𝑡) = 1/2 [𝑥 (𝑡 )+ 𝑥 (−𝑡) ]
Odd part 𝑥𝑜 (𝑡) = 1 /2 [𝑥 (𝑡) − 𝑥 (−𝑡) ]
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12. Energy and Power signal
• Energy signal: The signal which has finite energy and zero
average power is called energy signal.
• The non periodic signals like exponential signals will have
constant energy and so non periodic signals are energy signals.
i.e., For energy signal, 0 < 𝐸 < ∞ 𝑎𝑛𝑑 𝑃 = 0
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13. • Power signal: The signal which has finite average power and
infinite energy is called power signal.
• The periodic signals like sinusoidal complex exponential signals
will have constant power and so periodic signals are power signals.
i.e., For power signal, 0 < 𝑃 < ∞ 𝑎𝑛𝑑 𝐸 = ∞
For Continuous time signals
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15. Deterministic and Random signals
• Deterministic signal: A signal is said to be deterministic if
there is no uncertainity over the signal at any instant of
time i.e., its instantaneous value can be predicted.
• It can be represented by mathematical equation.
• Example: sinusoidal signal
• Random signal (Non-Deterministic signal): A signal is
said to be random if there is uncertainity over the signal at
any instant of time i.e., its instantaneous value cannot be
predicted.
• It cannot be represented by mathematical equation.
• Example :Noise
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16. CAUSAL AND NON CAUSAL SIGNAL
• Causal signal: A signal is said to be causal if it
is defined for t≥0. 𝑖. 𝑒., 𝑥 𝑡 = 0 𝑓𝑜𝑟 𝑡 < 0
• Non-causal signal: A signal is said to be non-
causal, if it is defined for t< 0 or for both 𝑡 < 0
and 𝑡 ≥ 0
𝑖. 𝑒., 𝑥 𝑡 ≠ 0 𝑓𝑜𝑟 𝑡 < 0
• When a non-causal signal is defined only for
t< 0 it is called anti causal signal
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