Soumen Mandal · Central Mechanical Engineering Research Institute

I will explain you by a very simple example. Time domain refers to variation of amplitude of signal with time. For example consider a typical Electro cardiogram (ECG). If the doctor maps the heartbeat with time say the recording is done for 20 minutes, we call it a time domain signal.
However, as in ECG a number of peaks are there (of different types). Say in one heartbeat 4 types of peaks or variation in amplitude occurs. So in frequency domain, over the entire time period of recording, how many times each peak comes is recorded. Frequency is nothing but the number of times each event has occured during total period of observation. 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.
In ECG frequency domain analysis is used

Time domain : how the signals change over time
Freq - domain : how much signals lie in the frequency range, theoretically signals are composed of many sinusoidal signals with different frequencies (Fourier series), like triangle signal, its actually composed of infinite sinusoidal signal (fundamental and odd harmonics frequencies)

well, almost everything... in time domain your model/system is evaluated according to the progression of it's state with time. In Frequency domain your model/system is analyzed according to it's response for different frequencies.
In linear system you can find a transformation (usually fourier transform) to "transport" your model into frequency domain from time domain.

Time domain simply mean that all your equations are cast in the form time, for example tau*dp/dt + p = Kp*u. You can convert this equation into the frequency domain, which physically meant how your system would response to a sinusoidal wave of different frequencies. In control, you can easily obtain the frequency domain AR and phase angle by substituting s = j*w in the Laplace domain. I would recommend the book "process dynamics and control" by Seborg.

Time domain : how the signals change over time
Freq - domain : how much signals lie in the frequency range, theoretically signals are composed of many sinusoidal signals with different frequencies (Fourier series), like triangle signal, its actually composed of infinite sinusoidal signal (fundamental and odd harmonics frequencies)

Sep 2, 2012

Adolfo Silva · National Institute for Space Research, Brazil

Time domain usually put the equations at the form of state space, then you're capable of looking "inside" of your system I mean the internal variables that are invisible when you use frequency domain(transfer function).

But when you study the system in frequency domain you stabilish a relationship beetween input and output by laplace transform.

Summarizing the both approaches are useful when you're desing a system.

If one wants to understand the dynamics of a system or in other words he or she intends to know the output of a system for a perticular input before applying such an input to the actual system one needs to model the system and the input using mathematics. If we use differential or difference equation to model the system dynamics (and also the input ) it is said that we are representing the system dynamics in the time domine.If we are obtaining the transfer function then we are performing the analysis in the frequency domine. solving a differential equation is difficult as one needs to assume the solution as a first step. getting a solution in the frequency domine is much easy than in the time domine.

Let us explain a signal x in a time domain, it 's simply a variation of your signal at each time. x(t) is a function of a time t. Any real signal can be represented as a sum of many sine wave with different pulses, amplitudes and phases. The differents sine wave components, also named harmonics represent the frequency representation of your signal, which is in a frequency domain. Look at my website www.azzimalik.com

Nov 18, 2012

Soumen Mandal · Central Mechanical Engineering Research Institute

I will explain you by a very simple example. Time domain refers to variation of amplitude of signal with time. For example consider a typical Electro cardiogram (ECG). If the doctor maps the heartbeat with time say the recording is done for 20 minutes, we call it a time domain signal.
However, as in ECG a number of peaks are there (of different types). Say in one heartbeat 4 types of peaks or variation in amplitude occurs. So in frequency domain, over the entire time period of recording, how many times each peak comes is recorded. Frequency is nothing but the number of times each event has occured during total period of observation. 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.
In ECG frequency domain analysis is used

Simply put, the frequency domain is the dual (complex) coefficient set of the complete sinusoidal basis of the time domain signal.

Jan 9, 2013

Pias Ali Pitafi · Sukkur Institute of Business Administration

The analysis of a system with respect to time is known as time domain analysis and with respect to frequency is frequency domain analysis. we usually change our systems from time to frequency by using (fourier, laplace ) to make it easy to understand the response of the system because time domain is more complex for higher orders.

I have a problem, I have a signal in time domain, actually, acceleration was calculated in time domain and the acceleration changes between [-4,4] m/s2. Then I did an FFT on the signal and converted to frequency domain; but the amplitude of acceleration in frequency domain is between [10e-4,1]. Why this difference? acceleration is normalized during the FFT transform or not?

What does FFT transform affect on the acceleration unit? is it m/s2 in frequency domain?

When a researcher uses the "second" or one of its multiples as a unit of measurement in her research or analysis, then it is in the time domain. e.g. An oscilloscope uses real-world signals in the time domain to visualize input. So we can say that, in Time Domain we analyze with respect to time. Other examples include time series data of economic indicators; or environmental data such as pollutants, heat, temperature, humidity; or sales of products etc.

On the other hand, when she is concerned with the reciprocal units such as Hertz in her research or analysis, then it is in the frequency domain i.e. we are analyzing something with respect to the frequency. The most common and familiar example of frequency content in signals is probably audio signals, and music in particular. Other examples are internet data transfer, television transmission etc.

## Popular Answers

Soumen Mandal· Central Mechanical Engineering Research InstituteHowever, as in ECG a number of peaks are there (of different types). Say in one heartbeat 4 types of peaks or variation in amplitude occurs. So in frequency domain, over the entire time period of recording, how many times each peak comes is recorded. Frequency is nothing but the number of times each event has occured during total period of observation. 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.

In ECG frequency domain analysis is used

Edi Kurniawan· Indonesian Institute of SciencesFreq - domain : how much signals lie in the frequency range, theoretically signals are composed of many sinusoidal signals with different frequencies (Fourier series), like triangle signal, its actually composed of infinite sinusoidal signal (fundamental and odd harmonics frequencies)

## All Answers (12)

Pedro Bittencourt· Federal University of Rio de JaneiroIn linear system you can find a transformation (usually fourier transform) to "transport" your model into frequency domain from time domain.

I suppose the keywords for your search in the topic are: Fourier Transform, System modelling.

I recommend a signals and systems introductory book such as Haykin's : http://books.google.com.br/books?id=QA9LAQAAIAAJ&source=gbs_similarbooks

Yong Kuen Ho· Taylor's UniversityPoom JatunitanonEdi Kurniawan· Indonesian Institute of SciencesFreq - domain : how much signals lie in the frequency range, theoretically signals are composed of many sinusoidal signals with different frequencies (Fourier series), like triangle signal, its actually composed of infinite sinusoidal signal (fundamental and odd harmonics frequencies)

Adolfo Silva· National Institute for Space Research, BrazilBut when you study the system in frequency domain you stabilish a relationship beetween input and output by laplace transform.

Summarizing the both approaches are useful when you're desing a system.

Purushotam Y.R.Azzi Abdelmalek· Université de BéjaïaSoumen Mandal· Central Mechanical Engineering Research InstituteHowever, as in ECG a number of peaks are there (of different types). Say in one heartbeat 4 types of peaks or variation in amplitude occurs. So in frequency domain, over the entire time period of recording, how many times each peak comes is recorded. Frequency is nothing but the number of times each event has occured during total period of observation. 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.

In ECG frequency domain analysis is used

Mark Alan Mendlovitz· Raytheon Company Space and Airborne SystemsPias Ali Pitafi· Sukkur Institute of Business AdministrationThe analysis of a system with respect to time is known as time domain analysis and with respect to frequency is frequency domain analysis. we usually change our systems from time to frequency by using (fourier, laplace ) to make it easy to understand the response of the system because time domain is more complex for higher orders.

Ali Esmaeili· University of LisbonThanks all,

I have a problem, I have a signal in time domain, actually, acceleration was calculated in time domain and the acceleration changes between [-4,4] m/s2. Then I did an FFT on the signal and converted to frequency domain; but the amplitude of acceleration in frequency domain is between [10e-4,1]. Why this difference? acceleration is normalized during the FFT transform or not?

What does FFT transform affect on the acceleration unit? is it m/s2 in frequency domain?

Manoj Kumar· CyientWhen a researcher uses the "second" or one of its multiples as a unit of measurement in her research or analysis, then it is in the time domain. e.g. An oscilloscope uses real-world signals in the time domain to visualize input. So we can say that, in Time Domain we analyze with respect to time. Other examples include time series data of economic indicators; or environmental data such as pollutants, heat, temperature, humidity; or sales of products etc.

On the other hand, when she is concerned with the reciprocal units such as Hertz in her research or analysis, then it is in the frequency domain i.e. we are analyzing something with respect to the frequency. The most common and familiar example of frequency content in signals is probably audio signals, and music in particular. Other examples are internet data transfer, television transmission etc.

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