Getting the components of a sum of square waves

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SUMMARY

The discussion centers on the mathematical operations required to decompose a resultant waveform composed of multiple square waves into its individual components. Participants explore the applicability of the Fourier Transform and its inverse, specifically questioning whether the inverse Fourier Transform can effectively retrieve the original square waves from the combined waveform. The consensus leans towards the necessity of understanding the limitations of the Fourier Transform in this context, particularly regarding non-sinusoidal waveforms like square waves.

PREREQUISITES
  • Fourier Transform and Inverse Fourier Transform
  • Understanding of periodic functions and waveforms
  • Mathematical decomposition of signals
  • Knowledge of square wave characteristics
NEXT STEPS
  • Study the properties of the Fourier Transform in relation to non-sinusoidal waveforms
  • Research techniques for signal decomposition, such as wavelet transforms
  • Explore the limitations of Fourier analysis in reconstructing square waves
  • Learn about harmonic analysis and its application to periodic functions
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Mathematicians, electrical engineers, signal processing professionals, and anyone interested in waveform analysis and decomposition techniques.

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If I have a periodic function that is say a sum of a number of sine functions I can use a Fourier Transform to get the component functions.

Now, if I have a bunch of square waves of differing amplitudes and frequencies that I add up into a resultant waveform. Given that waveform what'd be the mathematical operation to get at its individual component square waves? Is there any?
 
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Surely you just mean the 'inverse Fourier transform'?
 
HallsofIvy said:
Surely you just mean the 'inverse Fourier transform'?

I think not; but now I'm confused. I'll read / think more and get back. Thanks!
 

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