It has been found that any repeating, non-sinusoidal waveform can be equated to a combination of DC voltage, sine waves, and/or cosine waves (sine waves with a 90 degree phase shift) at various amplitudes and frequencies.

Above excerpt from allaboutcircuits.com. I understand that a non-sine wave can be broken down into a combination of harmonic sine waves. What I dont understand is how it states above that it can also be from DC voltage which isnt alternating like a sine wave.

Could someone help clarify? Thanks

  • \$\begingroup\$ There's an 'and' missing from that sentence. ... a combination of DC voltage and sine waves .... \$\endgroup\$
    – brhans
    Feb 11, 2020 at 0:47
  • \$\begingroup\$ If the repeating waveform has a DC offset, then it had a DC component (essentially a sin wave of zero frequency). \$\endgroup\$ Feb 11, 2020 at 0:50
  • \$\begingroup\$ Consider a square wave. This has no DC offset and can be constructed from an infinite number of sinusoidal waves. Now consider something that resembles a square wave, but has 55% duty cycle instead of perfect 50% duty cycle. That cannot be reconstructed using sinusoidal waves unless a DC offset is added in also. \$\endgroup\$
    – user57037
    Feb 11, 2020 at 1:02
  • 1
    \$\begingroup\$ @brhans, there is an and in the sentence ... it is the comma \$\endgroup\$
    – jsotola
    Feb 11, 2020 at 1:07
  • \$\begingroup\$ After you see this, you'll realize that Fourier can represent just about ANYTHING you want. Everything imaginable is just circles all the way down. And you can easily see how one of the circle vectors can be just "positioned" and left there (as DC.) In fact, the very first picture drawn uses a DC vector, as well. \$\endgroup\$
    – jonk
    Feb 11, 2020 at 3:04

1 Answer 1


You are misinterpreting the statement. Note that is says "a combination of DC voltage, sine waves, and/or cosine waves". Some waveforms, when decomposed into a series of sine waves, still have a DC offset. Note that sine waves and cosine waves have an average value of 0. Thus if a given waveform has a DC offset, than that DC must be combined with the sine and cosine waves to create the original waveform. As a simple example, suppose the waveform in question is a single sine wave with a peak value of 1 volt but with a DC offset of 10 volts. Then, it can be decomposed as 2 components: a 1 volt peak sine wave and a 10 volt DC level. Again, the author is not claiming that all waveforms can be broken into DC, but only that some waveforms require a DC term in their decomposition to account for any DC offset in the original waveform.


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