Time-domain to frequency domain

[justwild]

How will the graph of a sine wave (plotted against time axis) of a particular frequency look like if the same is plotted against frequency?

 

[mathman]

Single sine wave frequency domain graph is a delta function at the frequency of the sine wave.

 

[justwild]

... is a delta function at the frequency of the sine wave.

Do you mean that there will be single thin line rising upto 1 corresponding to that frequency only?

 

[davenn]

from a practical point of view, for an example of this your could compare 2 different pieces if test equip used for measuring/displaying a signal
An Oscilloscope gives a time domain view ... the y ( vertical ) axis is amplitude
the x-axis is time ... you will see the signal ( frequency ) displayed as a series of cycles on the screen

A Spectrum Analyser gives a frequency domain view ... again you have y-axis as amplitude, but in the x-axis is frequency, there is only that single vertical line representing that frequency

Dave

 

[PlanckShift]

Single sine wave frequency domain graph is a delta function at the frequency of the sine wave.

There is a second delta function at the negative frequency. In addition, there's a phase shift of \pi/2.