A signal’s path, and two ways to see it.
On this page
A sound reaches a model through a chain of stages, from the microphone to the features a model reads. Each page covers one stage (Figure 4), and every stage can be judged in two domains, time and frequency.
A signal has two standard descriptions. The time domain shows when things happen; the frequency domain shows which frequencies are present.
The clip, made up for this page (illustrative) and sampled 8,000 times per second, holds a three-note chord and one click at 30 ms. Levels are in decibels (dB) against the loudest peak; 20 dB down is ten times smaller in amplitude.
A click holds every frequency at once, so it spreads into a flat floor. The Fourier transform moves a signal between the two domains; it is built from scratch on the Fourier transform page.
A graphic equalizer (EQ), the row of sliders in a music app, sets each band’s gain in decibels (Anushiravani 2016). Pushing its 1 kHz slider to +6 dB about doubles the amplitude in that band (exactly at 6.02 dB) and about quadruples its power.
The mark labels are example uses. A bel is one tenfold step in power and a decibel is a tenth of a bel, so gains that multiply add in dB: a +20 dB preamp and then the +6.02 dB slider give +26.02 dB. One more bit in the analog-to-digital converter (ADC) of section 2 doubles its number of levels, 6.02 dB.
Both lines give the slider’s +6.02 dB, from power ×4 or from amplitude ×2. Every dB value has a reference. On these pages it is the loudest frequency in a spectrum plot, the noise for an SNR (signal-to-noise ratio), or a filter’s input for its gain.
Later pages use the same scale for the SNR each ADC bit adds, how much a filter cuts, how far a window leaks and the PSD.
Samples taken at 8 kHz hold frequencies only up to half that rate, the 4 kHz Nyquist frequency, so an anti-alias filter must cut a 5.2 kHz whistle, added with some hiss to the made-up clip (illustrative), before the ADC samples. Any whistle the filter lets through folds back to the rate minus its frequency, 8 − 5.2 = 2.8 kHz, inside the speech band of an 8 kHz phone call or speech recognizer.
Figure 3. 1Nyquist, 4 kHz. 2Whistle, 5.2 kHz. 3Folded, 2.8 kHz.
Past 4 kHz the folded whistle survives every later stage, and at 2 kHz the band above 2 kHz is lost as well.
The thesis cited in Section 1.1 is about editing audio by example. Its methods take an example recording and make another recording sound like it in tone (the EQ), background noise and room. In this series, spectral subtraction and the Wiener filter reduce background noise, and equalization matching (Power Spectral Density, section 5) copies the tone of another recording, and Reverberation and Dereverberation measures a room and removes its late tail.
Five stages each have one classic failure, and each page explains its own.
| What you see | Cause | Fix |
|---|---|---|
| Flat-topped peaks | Input past the ADC’s range (clipping) | Lower the gain (ADC) |
| Tones never in the room | Sampling too slowly (aliasing) | Filter before sampling (Aliasing) |
| One tone smeared across frequencies | Abrupt edges of each short slice, or frame (leakage) | Taper each frame (STFT) |
| A click late or bent after filtering | The filter’s phase (its timing shift at each frequency) and delay | Linear or zero phase (Filters) |
| Short isolated tones after denoising | Noise peaks above the estimate (musical noise) | Subtract more, or keep a minimum gain (Spectral subtraction) |
The series starts with how a voltage becomes numbers, on ADC Fundamentals.