Time-domain to frequency domain

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Discussion Overview

The discussion centers on the representation of a sine wave in the time domain versus the frequency domain, exploring how a sine wave's characteristics translate between these two domains. The conversation includes theoretical aspects and practical implications related to signal measurement and display.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Experimental/applied

Main Points Raised

  • One participant asks how a sine wave plotted against time would appear when plotted against frequency.
  • Another participant asserts that the frequency domain representation of a single sine wave is a delta function at the frequency of the sine wave.
  • A follow-up question seeks clarification on whether this means there will be a single thin line rising to 1 at that frequency.
  • A participant provides a practical comparison between an oscilloscope and a spectrum analyzer, describing how each displays signals in time and frequency domains, respectively.
  • Another participant reiterates the delta function representation and adds that there is also a second delta function at the negative frequency, along with a phase shift of \(\pi/2\).

Areas of Agreement / Disagreement

Participants express differing views on the specifics of the frequency domain representation, particularly regarding the presence of negative frequencies and phase shifts, indicating that multiple competing views remain in the discussion.

Contextual Notes

Some assumptions about the definitions of frequency and amplitude may not be explicitly stated, and the implications of phase shifts are not fully explored.

justwild
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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?
 
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Single sine wave frequency domain graph is a delta function at the frequency of the sine wave.
 
mathman said:
... 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?
 
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
 
mathman said:
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.
 

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