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.

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

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.

Very thank, Pedro Bittencourt and Yong Kuen HO

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)

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 http://azzimalikcom.ipage.com/

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.

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.

Thanks 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?

Here is a picture explain time domain  vs frequency domain signal.

Red graph is time domain and blue graph is frequency domain.

reference: Wikipedia.org

This question is an interesting basic question in describing the signals.

The signals are are considered as variation with time such as the voltage or the current in an a circuit.

The signals can be either represented in time domain by expressing its dependence on time as x(t) or in frequency domain X(f) where x(t) is analysed to its frequency components. The two descriptions are equivalent if one is known the other can be determined according to Fourier Transformation F or inverse Fourier misinformation F^-1. Then X(f)= F(x(t)).

This is the formal side of the two descriptions.

To complete the picture, the systems are running and operated in time domain with their performance described by differential equation.

The power of the signal description of in frequency domain that the signal is analysed in its basic functional elements of sinusoidal waves. So, in frequency domain the signal is represented by it frequency completion covering specific range of frequencies called the signal bandwidth. So, the concept of the bandwidth is associated with spectral representation in the frequency domain.

So, when characterizing and measuring the system, it is easier to do in the frequency domain.

The time domain signal description is abstract while the frequency domain signal description is detailed. So, frequency domain is more understandable than time domain.

Best wishes

Please look at the book (Linear Time-Invariant Systems)

by

Schetzen

from

Northeastern Universiy

in

Boston, MA

Example Representation of Signals

Electrical signals have both time and frequency domain representations.

Time Domain: In the time domain, voltage or current is expressed as a function of time. Most people are relatively comfortable with time domain representations of signals. Signals measured on an oscilloscope are displayed in the time domain and digital information is often conveyed by a voltage as a function of time.

Frequency Domain: Signals can also be represented by a magnitude and phase as a function of frequency. Signals that repeat periodically in time are represented by a power spectrum.

Signals that are time limited (i.e. are only non-zero for a finite time) are represented by an energy spectrum.

Signal sources and interference are often defined in the time domain.

Frequency domain representations are particularly useful when analyzing linear systems.

However, system behavior and signal transformations are more convenient and intuitive when working in the frequency domain.

EMC and signal integrity engineers must be able to work with signals represented in both the time and frequency domains.

Please look at the class by

Professor Leonard

From

Stanford university

At

YouTube

On

Quantum mechanics

In time domain we need to find the time variations of amplitude but in frequency domain we need to find the response of the system as a function of frequency

Dear Poom Jatunitanon ;

Please read this article:

COMPARISON BETWEEN FREQUENCY DOMAIN AND TIME DOMAIN METHODS FOR PARAMETER RECONSTRUCTION ON NONUNIFORM DISPERSIVE TRANSMISSION LINES by:

J. Lundstedt and M. Norgren

Best regards

In the time domain, a plot of amplitude vs time.

In the frequency domain, a plot of amplitude vs frequency.

Advantages of Frequency domain: 1. complexity is lesser than time domain

2. In the frequency domain, stability is decided.

3. Filtering concept is useful to filter the appropriate part.

4. convolution of two signals is simply in multiplication form.