Glossary
Every term the lectures teach, with where each is explained.
- aliasing
- A frequency above the Nyquist frequency appearing, once sampled, as a lower frequency (its alias) that cannot afterwards be told apart from a real one.
- amplitude
- The height of a wave from its middle line to a peak. For a sound, a bigger amplitude is louder.
- analogue signal
- A signal that varies smoothly and continuously, as a likeness of the quantity it represents.
- analogue-to-digital converter
- A circuit that turns each sample's voltage into a binary number.
- anti-aliasing filter
- A low-pass filter placed before sampling that removes everything above the Nyquist frequency (in practice, cuts it down until any alias is too quiet to matter).
- digital signal
- A signal stored as a list of numbers, which can be copied, stored and sent without change.
- digital-to-analogue converter
- A circuit that turns binary numbers back into voltages.
- frequency
- The number of complete cycles of a wave each second, measured in hertz (Hz).
- image
- A copy of a sampled signal's spectrum around f_s, 2f_s and so on; a DAC's staircase output contains them.
- Nyquist frequency
- Half the sampling rate, f_s/2. Only frequencies below it can be captured; a tone exactly at it can vanish.
- oversampling
- Sampling much faster than the sampling theorem needs, so a gentle analogue filter is enough, then filtering digitally and keeping fewer samples.
- period
- The time a wave takes to go through one complete cycle, in seconds; the period T and frequency f are linked by f = 1/T.
- phase
- Where in its cycle a wave is at time zero, in degrees or radians. Phase decides whether added signals reinforce or cancel.
- pulse code modulation
- Sending a signal as a stream of binary numbers, one for each sample; the transmitter filters, samples, converts each sample to a number and sends its bits in series.
- quantisation
- Rounding each sample to one of a fixed set of levels; the second step of turning a signal into numbers, after sampling.
- reconstruction filter
- A low-pass filter after a DAC that removes the images above the Nyquist frequency, and corrects the slight droop a staircase DAC causes, leaving the original band-limited signal.
- sampling
- Measuring a signal at regular moments in time and keeping only those values, the samples.
- sampling period
- The time between samples, T_s = 1/f_s.
- sampling rate
- The number of samples taken each second, f_s, in hertz. A CD uses 44.1 kHz.
- sampling theorem
- To capture every frequency up to f_max, the sampling rate must be more than twice it: f_s > 2f_max.
- signal
- A quantity that changes over time and carries information; in audio, usually a voltage that follows a pressure wave.
- sinc function
- sinc(x) = sin(πx)/(πx), with sinc(0) = 1: equal to 1 at x = 0 and 0 at every other integer, the bump each sample contributes in exact reconstruction.
- transition band
- The range of frequencies over which a real filter goes from passing a signal to blocking it.
- Whittaker–Shannon interpolation formula
- x(t) = Σ x[n] sinc((t − nT_s)/T_s): the sum of every sample's sinc bump, which rebuilds a band-limited signal exactly from its samples.