## Course Wiki

Last modified: May 01, 2012, 11:29 AM

# Time Domain Versus Frequency Domain Analysis

## Time Domain vs Frequency Domain

Time domain and frequency domain are two modes used to analyze data. Both time domain analysis and frequency domain analysis are widely used in fields such as electronics, acoustics, telecommunications, and many other fields.

- Frequency domain analysis is used in conditions where processes such as filtering, amplifying and mixing are required.
- Time domain analysis gives the behavior of the signal over time. This allows predictions and regression models for the signal.
- Frequency domain analysis is very useful in creating desired wave patterns such as binary bit patterns of a computer.
- Time domain analysis is used to understand data sent in such bit patterns over time.

** Time Domain: **

Time domain analysis is analyzing the data over a time period. Functions such as electronic signals, market behaviors, and biological systems are some of the functions that are analyzed using time domain analysis. For an electronic signal, the time domain analysis is mainly based on the voltage – time plot or the current – time plot. In a time domain analysis, the variable is always measured against time. There are several devices used to analyze data on a time domain basis. The cathode ray oscilloscope (CRO) is the most common device when analyzing electrical signals on a time domain.

** Frequency Domain: **

Frequency domain is a method used to analyze data. This refers to analyzing a mathematical function or a signal with respect to the frequency. 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. This does not mean that frequency domain analysis cannot be used in signals that are not periodic.

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.

All signals have a frequency domain representation and Fourier detailed the theory that any real world waveform can be generated by the addition of sinusoidal waves. The following diagram shows an example of this process:

There are a number of different mathematical transforms which are used to analyze time functions and are referred to as frequency domain methods. The following are some most common transforms, and the fields in which they are used:

- Fourier series – repetitive signals, oscillating systems Link
- Fourier transform – nonrepetitive signals, transients Link
- Laplace transform – electronic circuits and control systems Link
- Z transform – discrete signals, digital signal processing Link

Signals can be transformed between the time and the frequency domain through various transforms. The signals can be processed within these domains and each process in one domain has a corollary in the other, as shown :