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Introduction :
A very basic
concept in Signal and System analysis is Transformation
of signals. It involves a whole new paradigm of viewing signals in a context different from the natural domain
of their occurence. For example, the transformation
of a signal from the time domain into a representation
of the frequency components and phases is known as Fourier
analysis.
Why do we
need transformations?
We can't analyse all the signals that we want to, in
their existing domain. Transforming a signal means looking
at a signal from a different angle so as to gain new
insight into many properties of the signal that may
not be very evident in their natural domain. Transformation
is usually implemented on an independent variable.
Examples:
1. A doctor
examines a patient's heart beat, which is a function
of time in real world but is represented as a function
of space for easier diagnosis of the problem. The job is done
by ECG ( Electro-Cardio-Gram ) which shows the variations
in the pulse rate in spatial coordinates.
2. For a musician,
all the ragas played are actually in time domain but
frequency is more important for him than time. Why frequency
has more value must be somewhat intuitive as the variations
in sound are due to change in frequency.
3.
For a circuit, the input and output signals are functions
of time. If we need to study or monitor these signals,
we use an Oscilloscope to
display these signals using spatial coordinates.
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