Waveform Distortion Worksheet

KEY CONCEPTS

What You Need to Know

A transfer function is a graph where the x-axis is the input amplitude and the y-axis is the output amplitude. A straight diagonal line (input = output) means the signal passes through unchanged — no distortion.

Any departure from that straight line reshapes the waveform, which adds frequencies that weren't in the original signal. These new frequencies are called harmonics.

SYMMETRY	HARMONICS	EXAMPLES
Symmetric	Odd harmonics (3rd, 5th, 7th...)	Hard clip, soft clip, foldback
Asymmetric	Even + odd harmonics (2nd, 3rd, 4th...)	Tube bias, half-wave rectify

Symmetric means the curve looks the same if you flip it around the center point (the origin). The positive and negative halves of the wave get the same treatment. Asymmetric means the positive and negative halves are shaped differently — this breaks the symmetry of the waveform and introduces even-numbered harmonics.

A pure sine wave has one frequency. After distortion, the spectrum shows the fundamental plus new harmonic peaks. The number and strength of those peaks tells you exactly what the distortion did to the waveform. The oscilloscope shows you the shape change; the spectrum shows you the harmonic consequence.

PART 1 — DISTORTION LAB

Counting Harmonics

Open the Waveform Distortion Lab. Set the source to OSC TEST with a SINE wave at 220 Hz. Set WET/DRY to 100% wet.

1

Select HARD clipping. Set the drive to about 70%. Look at the output oscilloscope — the top and bottom of the sine wave are flattened. Now look at the output spectrum. You should see new peaks above the fundamental.

Count the harmonic peaks. Hard clipping a sine wave creates odd harmonics — you should see peaks at 660 Hz (3rd), 1100 Hz (5th), 1540 Hz (7th), etc. The even slots (440, 880) should be empty or nearly so.

2

Now switch to SOFT (tanh). Same frequency, same drive. Compare the spectrum to hard clip. The harmonics should still be odd-only, but they roll off faster — fewer bright peaks, more warmth.

3

Switch to HALF RECTIFY. This is asymmetric — the negative half of the wave is removed entirely. Look at the spectrum now.

Both even and odd harmonics appear: 440 Hz (2nd), 660 Hz (3rd), 880 Hz (4th), etc. Asymmetric reshaping creates even harmonics because the positive and negative halves of the wave are no longer mirror images of each other.

4

Try FOLDBACK at high drive. Watch the oscilloscope — the waveform folds back on itself, creating complex zigzag shapes. The spectrum should show many strong harmonics extending far up.

5

Finally, try each algorithm with a SAWTOOTH wave instead of sine. A sawtooth already has all harmonics present. Notice how distortion redistributes the energy — it doesn't just add harmonics, it changes their relative strengths.

RESPONSE 1

Screenshot the output spectrum for (a) Hard Clip on a sine and (b) Half Rectify on a sine, both at the same drive setting. In 2–3 sentences, explain why the harmonic patterns differ. Use the words "symmetric" and "asymmetric."

PART 2 — DISTORTION LAB

The Octavia Effect

The Roger Mayer Octavia (1967) was the first octave-up fuzz, famously used by Hendrix. Its secret: a full-wave rectifier that folds the negative half of the wave onto the positive, doubling the frequency.

1

In the Distortion Lab, set a SINE at 220 Hz. Select HALF RECTIFY. Look at the spectrum — you should see a strong peak at 440 Hz (one octave up).

2

Now mentally predict: if you full-wave rectified (flipped the negative half instead of removing it), which harmonics would appear? Would the fundamental survive?

Full-wave rectification makes the waveform perfectly symmetric at double speed. The fundamental vanishes — the new "fundamental" is at 2× the original. That's why the Octavia sounds an octave up.

RESPONSE 2

In 2–3 sentences: why does full-wave rectification produce an octave-up effect? Why does half-wave rectification not sound as cleanly "one octave up"?

PART 3 — TRANSFER FUNCTION LAB

Seeing the Curve

Open the Transfer Function Lab. The orange curve in the center canvas is the transfer function — it maps input amplitude (x-axis) to output amplitude (y-axis). Start with a SINE at 220 Hz.

1

Click through each preset (Linear, Hard Clip, Soft Clip, Foldback, Half Rectify, Staircase, Dead Zone). For each one, observe three things simultaneously: the shape of the transfer curve, the output waveform on the oscilloscope, and the harmonic pattern on the spectrum.

Notice the correspondence: flat regions on the transfer curve create clipping on the waveform. Bends create smooth saturation. Steps create staircase quantization. Each shape has a distinct sonic character.

2

Select Hard Clip. The curve has flat horizontal sections at the top and bottom — these are the clipping ceilings. The middle section is a straight diagonal — signals below the threshold pass through unchanged.

3

Now select Soft Clip. The curve is an S-shape — it bends gradually instead of going flat abruptly. This is why tanh saturation sounds warmer: the waveform is rounded, not chopped, so the high harmonics are weaker.

RESPONSE 3

Screenshot the Transfer Function Lab showing the Foldback preset with its transfer curve, output waveform, and spectrum all visible. In 1–2 sentences: why does the zigzag shape of the foldback curve create so many harmonics?

PART 4 — TRANSFER FUNCTION LAB

Draw Your Own Distortion

Now it's your turn. You are going to draw custom transfer functions and hear what they sound like. Keep the source on SINE 220 Hz.

1

Click LINEAR to reset the curve. Now use the DRAW tool to bend the curve by hand. Try making a gentle S-curve — pull the top half slightly right and the bottom half slightly left. Listen as you draw.

Even small bends add harmonics. You should hear the tone brighten or change character as you deform the curve. The spectrum updates in real time.

2

Reset to LINEAR. Now draw something asymmetric — make the top half of the curve flat (clipped) but leave the bottom half linear (untouched). Check the spectrum: even harmonics should appear because the positive and negative halves are being treated differently.

3

Reset again. Try to draw a staircase by hand — a series of flat horizontal steps. Use the LINE tool: click at the start of a step, then click at the end. Build 6–8 steps. Compare with the STAIRCASE preset.

4

Now get creative. Draw the weirdest, most extreme transfer function you can think of. Zigzags, spirals, random scribbles. Switch to SAWTOOTH and SQUARE inputs and hear how your custom distortion sounds on different waveforms.

The crazier the curve, the more harmonics are generated — but at some point the sound becomes pure noise. There's a sweet spot between clean and chaos where interesting timbres live. That sweet spot is what circuit designers spend their careers searching for.

RESPONSE 4

Draw a transfer function that you think sounds interesting or musical (not just noise). Screenshot the curve, waveform, and spectrum together. In 2–3 sentences: describe what you drew and why it sounds the way it does. What features of the curve correspond to what you hear?

PART 5 — BOTH LABS

Real Sound

Distortion on a test oscillator is educational. Distortion on real sound is where things get interesting.

1

In either lab, switch the source to MIC IN or load an audio file. Try speaking, singing, clapping, or playing an instrument through your custom transfer function.

2

In the Transfer Function Lab, start with LINEAR (clean) and slowly deform the curve while listening. Find the threshold where the sound goes from "clean" to "warm" to "dirty" to "destroyed."

3

Compare the WET/DRY mix. At 50%, you hear the original and distorted signal blended. Many guitar amps and mixing engineers use partial distortion (called parallel saturation) to add warmth without losing clarity.

RESPONSE 5

Feed a sound you like (voice, instrument, audio file) through a distortion of your choice. Screenshot the before/after spectrogram. In 2–3 sentences: what happened to the spectrum? Where did new energy appear? Did the distortion make the sound more or less complex?

What to Turn In

Five responses with screenshots and short written explanations as described above. Submit as a PDF or series of images. Focus on connecting what you see (waveform shape, spectrum pattern, transfer curve) to what you hear.