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# Time and Frequency Domain Analysis

## INTRODUCTION:

• In signals and systems, time and frequency domain are basically two different perspective of looking at the same signal. In time domain we measure change in amplitude of signal with respect to time. In frequency domain we measure how many times a particular amplitude of the signal has been achieved in given time interval.

• At the first instance, frequency domain raises a lot questions in mind as we are only used to see the time domain in our everyday life. But it's just the matter of our view. In fact, there are innumerous examples of frequency domain around us.

• Our ear-brain combination is an excellent frequency domain analyzer. The ear-brain splits the audio spectrum into many narrow bands and determines the power present in each band. It can easily pick small sounds out of loud background noise thanks in part to its frequency domain capability.

• A doctor listens to your heart and breathing for any unusual sounds. He is listening for frequencies that will tell him something is wrong. An experienced mechanic can do the same thing with a machine. Using a screwdriver as a stethoscope, he can hear when a bearing is failing because of the frequencies it produces. So we see that the frequency domain is not at all uncommon. We are just not used to seeing it in graphical form.

• ## TOOLS FOR TRANSFORMATION OF DOMAINS:

• Any signal can be converted from time domain to frequency domain and vice-versa using various mathematical transforming tools. Laplace transform and Fourier transform are tools to convert time domain signal to frequency domain. Inverse Laplace and Inverse Fourier transform can be utilized to transform frequency domain signal to time domain.

•  TIME DOMAIN >> FREQUENCY DOMAIN FREQUENCY DOMAIN >> TIME DOMAIN LAPLACE TRANSFROM INVERSE LAPLACE TRANSFORM FOURIER TRANSFROM INVERSE FOURIER TRANSFORM

• In order to restore the original time domain signal from frequency domain, it is very important to have both the amplitude spectrum and phase spectrum in frequency domain. While the amplitude spectrum specifies the magnitude of signal at different frequencies, the phase spectrum gives information about the change in phase (angle) at various frequencies.

• ## WHICH DOMAIN IS BETTER?

• Time domain and frequency domain each has its own significance. Depending on the signal and its required analysis, we decide the domain which one is better. While oscilloscopes measures signals in time domain, Wave analyzers measures signals in frequency domain and currently, both the instruments are equally important in analysis of signal and systems.

• Yet frequency domain is often considered better as it has far more applications and often analysis is easier than in time domain. For example, in electrical circuits, time domain analysis of components like inductor and capacitor would include differential and integral operators in equations. It makes the analysis very much complicated. However, the same circuit when analyzed in frequency domain (using laplace transform), it is much more simpler.

• Also, frequency domain is used to understand several characteristics of signal which are not observable in time domain like cyclic behavior of signal.

• ## APPLICATIONS:

• Both time domain analysis and frequency domain analysis are widely used in fields such as electronics, acoustics, telecommunications, and many other fields.

• Time domain analysis gives the behavior of the signal over time. This allows predictions and regression models for the signal. It is also used to understand data sent in such bit patterns over time. Functions such as electronic signals, market behaviours, and biological systems are some of the functions that are analyzed using time domain analysis.

• Frequency domain analysis gives the characteristics and the wave pattern of the signal. Hence it is widely used to analysis 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. It is also used in conditions where processes such as filtering, amplifying and mixing of signals is required. Practically, it has a lot of application in image processing, communications, geology and remote sensing.

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