1. Introduction
The use of frequency domain concepts is extremely useful when it comes to the analysis of
systems. The advantage of the frequency domain is that it can more easily incorporate
uncertainty than time domain analysis. Frequency is nothing but the number of times each event
has occurred during total period of observation.
Time Domain vs. Frequency Domain
In time domain analysis, we analyze the data with respect to time only. But in frequency domain
we don’t analyze the data with respect to time, but with respect to frequency.
Frequency domain analysis is used in situations where process requires filtering, amplifying or
mixing whereas time domain analysis gives the behavior of the data over time. This allows
predictions and regression models for the data.
Frequency domain analysis is very useful in creating desired wave patterns such as bit patterns
of a radio signal whereas Time domain analysis is used to understand data sent in such bit
patterns over time.
Uses
Frequency domain analysis is widely used in fields such as control systems engineering,
electronics and statistics. Frequency domain analysis is mostly used to signals or functions that
are periodic over time.
The most important concept in the frequency domain analysis is the transformation.
Transformation is used to convert a time domain function to a frequency domain function and
vice versa. The most common transformation used in the frequency domain is the Fourier
transformations. Fourier transformation is used to convert a signal of any shape into a sum of
infinite number of sinusoidal waves. Since analyzing sinusoidal functions is easier than
analyzing general shaped functions, this method is very useful and widely used.

2. An Example
Consider sales of umbrella over a period of say 15 years for a particular shop. If the manager
maps the sales with time say monthly or quarterly over the 15 year time span, we call it a time
domain analysis.
However, a number of peaks are expected to appear at the second and third quarter of the year
as demand of umbrella goes up during summer and monsoon. Let us, for a crude sense, say in
one year 4 types of peaks or variations in sale occur. So in frequency domain, over the entire
time period of recording, how many times each peak comes is recorded.
Frequency domain analysis is much simple as you can figure out the key points in the total
interval rather than putting your eye on every variation which occurs in time domain analysis.
Questions on my mind
 What if the data doesn’t exhibits a regular pattern over time
 What are the assumptions that we are making on the data while caring out a Frequency
domain analysis
 What if we have count ably infinite number of peaks in one cyclical period
 Can we predict the type of wave length is repeating for the future time points with the
underlying trend pattern?
Subhankar, 17-05-2015