Getting the components of a sum of square waves

In summary, if you have a periodic function that is a sum of sine functions, you can use a Fourier Transform to obtain the individual component functions. However, if you have a resultant waveform composed of square waves with varying amplitudes and frequencies, there is no direct mathematical operation to obtain its individual component square waves. You may be thinking of the inverse Fourier Transform, but this is not applicable in this case. Further reading and thinking may clarify this confusion.
  • #1
rollingstein
Gold Member
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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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  • #2
Surely you just mean the 'inverse Fourier transform'?
 
  • #3
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!
 

FAQ: Getting the components of a sum of square waves

1. What are square waves and how do they relate to a sum of square waves?

Square waves are a type of periodic waveform that consists of alternating high and low values, creating a square shape. A sum of square waves is the combination of multiple square waves with different frequencies and amplitudes.

2. How do you get the components of a sum of square waves?

The components of a sum of square waves can be obtained by breaking down the waveform into its individual square wave components using Fourier series analysis.

3. What is Fourier series analysis and how does it work?

Fourier series analysis is a mathematical method used to break down a complex periodic waveform into its individual sine and cosine components. This is done by expressing the waveform as a sum of sine and cosine functions with different frequencies and amplitudes.

4. What tools or techniques can be used to analyze a sum of square waves?

Aside from Fourier series analysis, other tools and techniques that can be used to analyze a sum of square waves include signal processing software, oscilloscopes, and spectral analyzers.

5. What are some real-life applications of sum of square waves?

The sum of square waves has various applications in electronics, such as in signal processing, audio and video encoding, and electronic music synthesis. It is also commonly used in the design of electronic circuits and communication systems.

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