Digital Signal Processing

1. BANKURA UNNAYANI INSTITUTE OF
ENGINEERING
NAME : Arun Gorai
DEPT. : AEIE
ROLL : 22
UNIVERSITY ROLL NO. : 10505522030
REGISTRATION NO. : 221050120098
SUBJECT : Digital Signal Processing
SUBJECT CODE : OE EI 603

2. Signal is a time varying physical phenomenon which is intended to convey
information.
OR
Signal is a function of one or more independent variables, which contain some
information.
Example: voice signal, video signal, signals on telephone wires etc.
Note: Noise is also a signal, but the information conveyed by noise is unwanted
hence it is considered as undesirable.
What is Signal?

3.  Continuous-time signals are defined for all values of time within a given interval.
They are represented by continuous functions.
 Discrete-time signals are defined only at specific time instances or intervals. They
are represented by sequences of values.
 Signals can be classified based on various
criteria. Here are some common classifications
of signals:
 Analog signals are continuous-time signals that can take on any value within a
certain range. They are typically represented by continuous voltage or current
signals.
 Digital signals are discrete-time signals that can only take on a finite number of
values. They are typically represented by binary values (0s and 1s) and are
used in digital communication and computing systems.
 Continuous-time vs. Discrete-time Signals:
 Analog vs. Digital Signals:

4.  Deterministic signals have a known relationship between input and output and can be
completely described by mathematical equations.
 Non-deterministic signals have an element of randomness or uncertainty and cannot
be completely described by equations.
 Periodic signals repeat their pattern over a fixed period of time. They have a
fundamental period and can be represented by a Fourier series.
 Aperiodic signals do not repeat their pattern over any fixed period of time. They
cannot be represented by a Fourier series.
 Deterministic vs. Non-deterministic Signals:
 Periodic vs. Aperiodic Signals:
 Energy vs. Power Signals:
 Energy signals have finite energy over a given time interval. They are typically of
finite duration.
 Power signals have finite power over a given time interval. They are typically of
infinite duration.

5.  Deterministic signals have a predictable pattern and can be completely described by
mathematical equations.
 Random signals have an element of randomness and cannot be completely
described by equations. They exhibit statistical properties.
 Deterministic vs. Random Signals:

6.  A deterministic signal is a signal that can be completely described by a
mathematical equation or a set of equations. It is predictable and has a
known relationship between its input and output. The output of a
deterministic signal can be determined with certainty based on its input.
Define Some Signal:
 Deterministic Signal:
Examples of deterministic signals include sinusoidal signals, square
waves, and triangular waves. These signals can be expressed as
mathematical functions and their behavior can be precisely predicted.

7.  A non-deterministic signal, also known as a random signal or a stochastic
signal, is a signal that cannot be completely described by a mathematical
equation. It is unpredictable and has an element of randomness or
uncertainty associated with it. The output of a non-deterministic signal cannot
be determined with certainty based on its input.
 Non-Deterministic Signal:
Examples of non-deterministic signals include noise signals, such as white
noise or Gaussian noise, and random processes, such as random walks or
Markov processes. These signals do not have a predictable pattern and
their behavior cannot be precisely predicted.

8.  A periodic signal is a signal that repeats its pattern over a fixed period of time. This
means that the signal waveform will repeat itself exactly after a certain time
interval, known as the period. The period is denoted by T, and the frequency of the
signal is the reciprocal of the period, f = 1/T.
 Periodic Signal:
Examples of periodic signals include sinusoidal signals (sine wave, cosine
wave), square waves, triangular waves, and sawtooth waves. These
signals have a repetitive pattern that can be described by mathematical
equations.
Mathematically, a periodic signal can be represented as: x(t) = x(t + nT)
where x(t) is the signal at time t, T is the period, and n is an integer
representing the number of periods.

9.  An aperiodic signal is a signal that does not repeat its pattern over any fixed
period of time. This means that the signal waveform does not exhibit any
regular or predictable repetition. Aperiodic signals can have various shapes
and patterns, and they do not have a fundamental period or frequency.
 Aperiodic Signal:
Examples of aperiodic signals include random noise signals, impulse
signals, and transient signals. These signals do not exhibit any repetitive
pattern and cannot be described by a periodic function.
Mathematically, an aperiodic signal cannot be represented by a simple
equation with a fixed period.

10.  Deterministic signals have a known relationship between input and output
and can be described by mathematical equations, while non-deterministic
signals have an element of randomness or uncertainty and cannot be
completely described by equations.
Summary:
 periodic signals repeat their pattern over a fixed period of time, while
aperiodic signals do not exhibit any regular or predictable repetition.