Frequency domain

The time domain is the analysis of mathematical functions, physical signals with respect to time . In the time domain, the signal or function’s value is known for all real numbers, for the case of continuous-time, or at various separate instants in the case of discrete-time.

The period T is the reciprocal of a frequency, T = 1 / f . The period of a waveform is the time required for one complete cycle of the wave to occur. The relationship between period, frequency, and amplitude for a sine wave is illustrated in the graphic.

The Frequency Domain refers to the analytic space in which mathematical functions or signals are conveyed in terms of frequency, rather than time . For example, where a time-domain graph may display changes over time, a frequency-domain graph displays how much of the signal is present among each given frequency band.

In this case, the frequency-domain analysis gives a better understanding than time domain analysis because music is tacitly based on the breaking down of intricate sounds into their separate component frequencies. An oscilloscope is an invaluable tool for detecting signals.17 Mar 2022

Frequency-domain analysis is widely used in such areas as communications, geology, remote sensing, and image processing. While time-domain analysis shows how a signal changes over time , frequency-domain analysis shows how the signal’s energy is distributed over a range of frequencies.

To convert a time domain signal into frequency domain, one must use the Fourier transform to do so. MATLAB has a function fft which is a Fast Fourier Transform algorithm designed to implement the Fourier Transform on digital signals.

The time-shifting property identifies the fact that a linear displacement in time corresponds to a linear phase factor in the frequency domain . This becomes useful and important when we discuss filtering and the effects of the phase characteristics of a filter in the time domain.