Figure 2 provides a look at a series of audio files presented in two ways: the waveform on the left and the signal’s spectrum on the right. Note that I used a linear frequency scale for the spectrum analysis, which allows a visually natural spacing for the harmonics. We don’t hear this way, but it’s easier to see what’s going on.
In Figure 2A, the FFT confirms that our 1 kHz sine wave is pure and has all its energy concentrated about 1 kHz.
In Figure 2B, I applied only 0.5 dB of clipping using Audacity’s limiter. (Clipping and limiting are not exactly the same, and Audacity’s plugin offers both functions.) This slightly flattens the peaks of the waveform. The FFT reveals that even this small change results in the addition of significant energy at the first few odd harmonics, most prominently 3 kHz, 5 kHz, and 7 kHz.
Figure 2C shows the result of 3 dB of clipping, adding more energy further up into the spectrum.
Compare this with Audacity’s generated “no-alias” square wave (Figure 2D), a band-limited version of a square wave that avoids the visual nastiness of running a mathematically true square wave through an FFT with finite frequency resolution.
We see that as clipping becomes more severe, the signal increasingly resembles a square wave. Besides creating an unpleasant sound, there is the additional real-world ramification that square waves contain twice as much power (“area under the curve”) as sine waves of the same peak amplitude.
Running an amplifier into clipping can therefore cause a connected loudspeaker to overheat much faster.
Not Created Equal
It pays to bear in mind that we’re looking at digitally generated and manipulated test tones, and the real world is rarely so “cut and dry.” Accordingly, I also analyzed the clipped output signals from several actual audio devices.
Figure 3 depicts the same 1 kHz sine wave sent through an overdriven microphone preamp (A) and an entry-level headphone amplifier output cranked into distortion (B). The headphone amp is a particularly interesting case, creating a highly asymmetrical waveform. Note the presence of both even and odd harmonics in the signal’s spectrum. Another factor is that the spectrum of a clipped signal depends on the nature of the signal itself. We can’t dive into it here, but a clipped transient behaves much differently than a clipped steady tone.
If you were to look at a clipping plugin in your digital audio workstation (DAW) of choice, you’d likely see a multitude of options and algorithms. Not all clippers provide the same results, and at the peak of the recording industry “Loudness Wars,” plugins that could limit or clip peaks with less audible damage were a hot commodity in the race for hot masters.
Different devices distort in different ways, a concept which is likely at the heart of engineer preamplifier preferences. This means that not all distortion is created equal, and it also means I have to stop teasing my guitar-playing buddy about having so many distortion pedals in his rig. Yeah, right.
The author would like to thank Pat Brown and Langston Holland for their input on this piece.
