Why Calculate the Power Spectrum of a 10MHz Square Wave?

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Discussion Overview

The discussion revolves around the calculation of the power spectrum of a 10MHz square wave, specifically addressing the relationship between power spectrum and power spectral density, the relevance of amplitude in calculations, and the broader context of why power spectrums are calculated in various fields.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the power spectrum is the same as the power spectral density and seeks tips and formulas for solving the problem.
  • Another participant explains that for a periodic signal, the Fourier series can be used to approximate the signal, and the power at each frequency can be derived from the complex amplitudes of the Fourier series coefficients.
  • There is a query about the relevance of amplitude A in the calculation of the power spectrum, with a suggestion that the power can be calculated from specific harmonic terms in the Fourier series.
  • A later reply emphasizes that each term of the Fourier series does depend on the amplitude A, indicating its importance in the calculations.
  • Another participant introduces a question about the rationale behind calculating power spectrums in various contexts, such as MRI signal intensity, seeking insight into its broader applications.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the role of amplitude in the power spectrum calculations and the distinction between power spectrum and power spectral density. There is no consensus on the necessity of calculating power spectrums in different contexts, as the discussion raises varied applications without resolution.

Contextual Notes

Participants have not reached a consensus on the definitions and implications of power spectrum versus power spectral density, nor on the significance of amplitude in the calculations. The discussion also highlights the potential for different interpretations of power spectrum calculations across various fields.

Who May Find This Useful

This discussion may be useful for students and professionals interested in signal processing, Fourier analysis, and applications of power spectrum calculations in physics and engineering contexts.

ACLerok
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Homework Statement


Calculate the power spectrum in dBm of a zero offset, 10MHz square wave with amplitude A from DC to 50MHz.


Homework Equations


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The Attempt at a Solution


I was given this problem but am not sure how to go about solving it. Is the power spectrum the same as the power spectral density? I don't need the solution rather some tips and formulas that can be used to solve it. Thanks
 
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When you have a periodic signal you use the Fourier series to approximate the signal as a sum of sinusoidal signals at frequencies of 0 (the DC component), F (the frequency of the periodic signal), and positive integer multiples of F. The coefficients of the Fourier series are the complex amplitudes of this sinusoidals. Knowing the complex amplitudes at each frequency you can calculate the power at each frequency (considering a load of 1 ohm), and this would be the power spectrum. Ofcourse you can't calculate the whole spectrum because it has an infinity of components. But in this problem you are asked to calculate it from DC (0 Hz) to 50MHz.

If you had a non-periodic signal you would have used the Fourier transform to calculate it's spectral density of complex amplitude from which you would have calculated the power spectral density.

So, when you have a periodic signal you calculate it's power spectrum and when you have a non-periodic signal you calculate it's power spectral density.

This is because the spectrum of a periodic signal is discrete as opposed to that of a non-periodic signal which is continuous (and in the case of a continuous spectrum it's not handy to tell the power at each frequency).
 
so in calculating the power spectrum, the amplitude A is not relevant? Once i have the Fourier series representation of the square wave, I can just take the 3rd term (for the 3rd harmonic) and use the Power equation to calculate the power generated at that harmonic?
 
ACLerok said:
so in calculating the power spectrum, the amplitude A is not relevant? Once i have the Fourier series representation of the square wave, I can just take the 3rd term (for the 3rd harmonic) and use the Power equation to calculate the power generated at that harmonic?

Each term of the Fourier series depends on the amplitude A.
 
I thought I would add to this thread instead of making another one.

My question is this: why do we calculate power spectrums at all?

This makes sense in the context of voltage (power = V2/R), but I've seen this used in numerous other contexts with other units for the signal.

For example, some might calculate the power spectrum for the signal intensity of an MRI image of the brain.

Why?

Thanks in advance for any insight!
 

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