What is the difference between periodicity in time domain and periodicity in spatial domain when we say that cos and sine function has the period of 2*pi what does it mean whether we are referring to time domain or space domain?
A signal is a periodic signal if it completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods. The completion of a full pattern is called a cycle. A period is defined as the amount of time (expressed in seconds) required to complete one full cycle. The duration of a period represented by T, may be different for each signal but it is constant for any given periodic signal.
http://en.wikibooks.org/wiki/Signals_and_Systems/Periodic_Signals
thank u Ranjeet , you're talking about periodcity in time domain ,how periodicity in spatial domain can be explain and how can we relate both time and spatial domain with each other
In the time domain the signal repeates itself along time. In spatial domain, it repeats itself with position (say in the 'x' direction). In mathematical terms, just replace t with x. The period will not be in seconds but in metres. The frequency will not be in Hz (1/s) but in 'per metre', 1/m. Simple!
Generally, the periodicity in the frequency (spatial) domain is a consequence of the presence of harmonics.
The same concepts apply in time and space. Except we usually talk about the period (T) in the temporal domain and the wavelength (lambda) in the spatial domain. And yes, as Fernando mentioned, units are important. If you are talking about multiples of pi then that probably is referring to phase.
As mentioned before, in the spatial domain you talk of lines/cm. instead of cycles/second, but this similitude allows you to transport all the methods used in electronics to optics (see Fourier Optics, an excellent textbook by Joseph Goodman). Now you can define low pass and high pass filters for optical frequencies (not to be confused with the electromagnetic frequencies).
Dear Michael,
I think, the dominant vibration is accountable for the periodicity and not the harmonics!
Regards Christian
thank you all for your answers!!
Can any one relate both time and spatial domain with each other considering wave motion like we use the equation " v=f*lambda" here both domain are used i-e time and space.
This question reminds me electromagnetic theory. There you see electric and magnetic fields as a function of spatial coordinates, so they are vectors. But they are related to space through the harmonic e^{jwt} function, so any given field changing in time domain could be reconstructed using Fourier Transform analysis. And it of course depend on spatial coordinates too. You could read it in any text about electromagnetics. I suggest advanced electromagnetics by Balanis
In spatial domain it is the periodic repetition of intensity values in image processing or gray scale values in the spatial coordinates.
Periodicity with respect to time domain is the time interval commonality data is repeated,and for space periodicity it is data occurring in the same/common frequency range
Actually if you look at the equation we can see y is time value varying with time.
y=sin(t)
That value can be voltage ,movement of a particle or any physical phenomenon.
But when you consider x to be spatial in nature like varying of pressure parameters over an altitude range them probably you are taking of spatial model.
y=sin(x)
other examples could be population over some area at a given time say t.
Here time remains same but y varies with spatial location of the model.
In spatial domain or frequency domain, the periodic repetition of intensity values in image processing or gray scale values has different scales of measurements.
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