Representing graphically an analog signal?

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Discussion Overview

The discussion revolves around how to graphically represent the components of an analog signal in both time and frequency domains, using a specific equation as an example. Participants explore methods for plotting the signal and understanding its characteristics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to graphically represent the components of the analog signal given by the equation v(t)=3 + 1.414cos(w0t) - 1.414sin(w0t) + 2cos(2w0t + 5pi/2.
  • Another participant suggests calculating v(t) for different values of t and plotting these values against t.
  • A question is raised regarding the identification of amplitude and frequency values in the equation.
  • One participant proposes using the variable x = w0*t to simplify the analysis, noting that the angular frequency is w0 and expressing uncertainty about the amplitude.
  • A later reply indicates that plotting the frequency domain can be achieved by plotting the Fourier transform, which would yield discrete frequency components represented as delta functions with varying heights based on amplitude.

Areas of Agreement / Disagreement

Participants express different approaches to the problem, with no consensus on the best method for representation or the specifics of amplitude and frequency identification.

Contextual Notes

There are unresolved aspects regarding the definitions of amplitude and frequency in the context of the provided equation, as well as the dependence on the variable w0.

esmeco
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I was wondering,how do I represent graphically an analog signal components in time and frequency using an equation for example like this:

v(t)=3 + 1.414cos(w0t) - 1.414sin (w0t) + 2cos(2w0t + 5pi/2)

Thanks in advance for the reply!
 
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esmeco said:
I was wondering,how do I represent graphically an analog signal components in time and frequency using an equation for example like this:

v(t)=3 + 1.414cos(w0t) - 1.414sin (w0t) + 2cos(2w0t + 5pi/2)

Thanks in advance for the reply!
Calculate v(t) for different values of t. Plot the values for v(t) on the vertical axis for values of t on the horizontal axis.

AM
 
But in the equation,what are the values that correspond to the amplitude and frequency?
 
It may be more enlightening to use the variable x = w0*t. x varies from 0 to 2*pi; one needn't know what w0 is. The angular frequency of the equation you wrote is w0; amplitude I'm not sure about. If you have to plot it anyway, might as well do that and find the maximum deviation from 3 (the DC value).
 
Plotting the frequency domain is simple - just plot the Fourier transform. Because the frequency components are discrete, you will get a series of delta functions of varying heights (depending on the amplitude of each component).

Claude.
 

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