DAQ (ADC)
A DAQ, an analogue-to-digital converter, samples its input at a set rate with a set number of bits over a set range. It shows what a computer recording the signal would see: aliases, quantisation and clipping.
Ports
One input, in, and one output, out, the signal as it reads it.
The model
Sampling and aliases
Sampled at \(f_s\), a tone at \(f\) is read at its alias in \(0\) to \(f_s/2\):
\[f_a = f \bmod f_s, \qquad f_a \to f_s - f_a \text{ if } f_a > f_s/2,\]with its phase reversed when it folds. A tone at a multiple of \(f_s\) reads as DC. The DAQ lists the tones above half its rate and where they land.
Quantisation and noise
\(b\) bits over \(\pm V_r\) give a step
\[\Delta = \frac{2V_r}{2^{b}}, \qquad \sigma_q = \frac{\Delta}{\sqrt{12}}.\]All the input’s noise, with the quantisation noise, folds into the band from 0 to \(f_s/2\), taken as flat there:
\[S_\text{out}(f) = \frac{\sigma_\text{in}^2 + \sigma_q^2}{f_s/2}, \qquad f \le f_s/2.\]Range
When the input’s peak passes the range, the DAQ says it would clip. The output is not clipped.
Settings
| Field | Default | Meaning |
|---|---|---|
rate | 10000 | Sample rate (S/s) |
bits | 16 | Bits |
range | 10 | Range, ± (V) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Readouts
The sample rate and the band it covers, the bits, one step and its quantisation noise, the aliases, then the signal as read: DC, tones and noise.
Assumptions
- No anti-aliasing filter: put a low-pass before it, as a real setup would.
- Ideal sampling: no aperture jitter, no differential non-linearity, and the input noise folded as if flat.
- Clipping is flagged, not modelled.
Related
- Low-pass filter, as an anti-aliasing filter.
- Electronics: non-linear blocks.