Reply To: Clipped signals and the D/A stage

March 6, 2023 at 5:18 pm #5107
James Johnston

    Oh boy. You asked an interesting question. Ripples due to bandwith limiting come along with the digital realm. If I take a square wave, and filter it to a bandwidth where any of the appreciable harmonics are removed (or changed in phase) you will see “ripples”. These are a direct consequence of modifying the spectrum (by removing or changing phase) of the signal in question.  This is, however, not the issue with digital clipping of periodic signals.

    What’s more, “Gibbs Ears” is a term that refers to two things, one of which is a theoretical issue that can only happen with theoretically perfect square waves (which do not exist in the real world!), and the other of which, which looks somewhat similar, which is the result of bandwidth limiting, but which is NOT the same. “Gibbs Ears”, the zero power amplitude excursion in a theoretic Fourier transform, has a finite amplitude and zero width, yes, ZERO width, and thence has zero energy.  This does not happen in the real world, because one must have infinite bandwidth of the square wave, which literally can never exist int he real world.  That’s “Gibbs Ears”.


    The effect of bandwidth limiting (the ripples that have finite width as well as finite amplitude) are simple results of Fourier mathematics, and are not an ‘error’, they are what you SHOULD see when a wide-band signal is filtered to narrower bandwidth.

    NEITHER of these is clipping.

    The issue with clipping (a periodic signal is worst in this case) in the digital realm is that you will generate harmonics of the periodic signal that are OVER Fs/2 (Fs is sampling rate) and as such will promptly (instantly, no other option applies) alias back down into the baseband.

    For instance, let’s propose (for a really ugly example) a sine wave (using 44.1kHz sampling) that is set to (44100-1000)/3.  Yes, that means that the third harmonic of that sine wave, when you clip that waveform symmetrically, is 1000Hz. That is both anharmonic, extremely audible, and, well, a lot of other things, mostly “bad”.  If you clip assymmetrically, you also get kHz tone, too. Note, also NOT harmonic.  And yes, this continues up the harmonic number, splattering <redacted> all over your audio spectrum.

    This is why digital clipping is bad.

    There is a short graph of this in Bob’s book somewhere, wherein he says (at my urging, not that he had to be urged much) “don’t do that!”