UNIT 1 – SIGNAL PROCESSING BASICS
Time Domain and Frequency domain representation of a signal
To analyze a signal, it has to be represented. This representation in communication systems is of two types
−
Frequency domain representation, and
Time domain representation.
Consider two signals with 1 kHz and 2 kHz frequencies. Both of them are represented in time and frequency
domain as shown in the following figure.
Time domain analysis, gives the signal behavior over a certain time period. In the frequency domain, the
signal is analyzed as a mathematical function with respect to the frequency.
Frequency domain representation is needed where the signal processing such as filtering, amplifying and
mixing are done.
For instance, if a signal such as the following is considered, it is understood that noise is present in it.
,The frequency of the original signal may be 1 kHz, but the noise of certain frequency, which corrupts this
signal is unknown. However, when the same signal is represented in the frequency domain, using a
spectrum analyzer, it is plotted as shown in the following figure.
Here, we can observe few harmonics, which represent the noise introduced into the original signal. Hence,
the signal representation helps in analyzing the signals.
Frequency domain analysis helps in creating the desired wave patterns. For example, the binary bit patterns
in a computer, the Lissajous patterns in a CRO, etc. Time domain analysis helps to understand such bit
patterns.
Classification of signals
Signals are classified into the following categories:
Continuous Time and Discrete Time Signals
Deterministic and Non-deterministic Signals
Even and Odd Signals
Periodic and Aperiodic Signals
Energy and Power Signals
Real and Imaginary Signals
Continuous Time and Discrete Time Signals
A signal is said to be continuous when it is defined for all instants of time.
, A signal is said to be discrete when it is defined at only discrete instants of time/
Deterministic and Non-deterministic Signals
A signal is said to be deterministic if there is no uncertainty with respect to its value at any instant of time.
Or, signals which can be defined exactly by a mathematical formula are known as deterministic signals.
A signal is said to be non-deterministic if there is uncertainty with respect to its value at some instant of
time. Non-deterministic signals are random in nature hence they are called random signals. Random signals
cannot be described by a mathematical equation. They are modelled in probabilistic terms.
Time Domain and Frequency domain representation of a signal
To analyze a signal, it has to be represented. This representation in communication systems is of two types
−
Frequency domain representation, and
Time domain representation.
Consider two signals with 1 kHz and 2 kHz frequencies. Both of them are represented in time and frequency
domain as shown in the following figure.
Time domain analysis, gives the signal behavior over a certain time period. In the frequency domain, the
signal is analyzed as a mathematical function with respect to the frequency.
Frequency domain representation is needed where the signal processing such as filtering, amplifying and
mixing are done.
For instance, if a signal such as the following is considered, it is understood that noise is present in it.
,The frequency of the original signal may be 1 kHz, but the noise of certain frequency, which corrupts this
signal is unknown. However, when the same signal is represented in the frequency domain, using a
spectrum analyzer, it is plotted as shown in the following figure.
Here, we can observe few harmonics, which represent the noise introduced into the original signal. Hence,
the signal representation helps in analyzing the signals.
Frequency domain analysis helps in creating the desired wave patterns. For example, the binary bit patterns
in a computer, the Lissajous patterns in a CRO, etc. Time domain analysis helps to understand such bit
patterns.
Classification of signals
Signals are classified into the following categories:
Continuous Time and Discrete Time Signals
Deterministic and Non-deterministic Signals
Even and Odd Signals
Periodic and Aperiodic Signals
Energy and Power Signals
Real and Imaginary Signals
Continuous Time and Discrete Time Signals
A signal is said to be continuous when it is defined for all instants of time.
, A signal is said to be discrete when it is defined at only discrete instants of time/
Deterministic and Non-deterministic Signals
A signal is said to be deterministic if there is no uncertainty with respect to its value at any instant of time.
Or, signals which can be defined exactly by a mathematical formula are known as deterministic signals.
A signal is said to be non-deterministic if there is uncertainty with respect to its value at some instant of
time. Non-deterministic signals are random in nature hence they are called random signals. Random signals
cannot be described by a mathematical equation. They are modelled in probabilistic terms.
