Frequency Domain: Definition

Frequency domain analysis refers to analysis where a signal is studied with respect to frequency, rather than with respect to time. The data being studied is plotted with the frequency on the x axis and the amplitude on the y axis; this shows how the signal’s energy is distributed as a function of frequency.

A function can be represented by either a time domain or a frequency domain; each is useful for different purposes. A time domain representation of a signal can be converted into a frequency representation using a Fourier transform or similar manipulation.

The Fourier transform converts time domain representation (red), to frequency domain (blue). Peaks in the frequency domain represent component frequencies.

Importance and Use of Frequency Domain Analyses

The term ‘frequency domain’ first made its appearance in 1953, in communications engineering. Today, though, this analysis is used in many different fields, including geology, chemistry, remote sensing, image processing, electrical engineering and communications. It has been called a cornerstone of systems engineering, and is an important part of the toolbox of almost any scientist, engineer or statistician.

The frequency domain representation often allows us to characterize a signal or series of signals using simple algebra, as opposed to the complicated differential equations that go with a time-domain representation of a signal. The easy calculations involved with manipulating these signals make it especially useful for engineers. Perhaps more importantly, a frequency based analysis allows you to see cyclic behavior that might not have been immediately obvious in a time domain representation.

References

1. MathWorks Documentation. Practical Introduction to Freq. Domain Analysis. Retrieved from https://www.mathworks.com/help/signal/examples/practical-introduction-to-frequency-domain-analysis.html on June 15, 2018.
2. Cassidy, Steve. COMP449 Course Notes. Speech Recognition: Chapter 6. Frequency Dom. Analysis. Retrieved from http://web.science.mq.edu.au/~cassidy/comp449/html/ch06.html on June 15, 2018
3. Kulkarni. Frequency Domain and Fourier Transforms. Retrieved from https://www.princeton.edu/~cuff/ele201/kulkarni_text/frequency.pdf on June 16, 2018.
4. MIT Department of Mechanical Enginering. 2.14 Handout; Introduction to Freq. Domain Processing. Retrieved from http://web.mit.edu/2.14/www/Handouts/FreqDom.pdf on June 16, 2018.
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