Band-pass filter
A band-pass filter passes a band about its centre frequency and cuts what is either side. It picks one beat note or harmonic out of a signal.
Ports
One input, in, and one output, out.
The model
The filter is the Butterworth low-pass of order \(n\) with \(s\) turned into
\[s \;\to\; \frac{s^2 + 1}{b\,s}, \qquad s = \frac{i f}{f_0}, \quad b = \frac{\Delta f}{f_0},\]for a centre \(f_0\) and a bandwidth \(\Delta f\). Its gain is 1 at the centre, and 3 dB down at two frequencies \(f_1\) and \(f_2\) with
\[f_2 - f_1 = \Delta f, \qquad f_1 f_2 = f_0^2,\]so the band is symmetric about \(f_0\) on a log axis. Outside it, the gain falls at \(6n\) dB an octave of the mapped frequency: an order-\(n\) band-pass has \(2n\) poles. DC is blocked.
Settings
| Field | Default | Meaning |
|---|---|---|
f0 | 1000 | Centre (Hz) |
bw | 100 | Bandwidth (Hz) |
order | 1 | Order: 1 (1), 2 (2), 3 (3), 4 (4) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Readouts
The panel gives its output in the steady state: the DC level, the five strongest tones (each one’s amplitude, rms and the phase of its cosine), and the noise, as a density at 1 kHz and in rms from 1 Hz to 1 GHz. Any notes, such as an input left unwired, are listed under it.
Assumptions
- An ideal Butterworth response, with no noise or loss of its own.
Related
- Low-pass filter and high-pass filter.
- Lock-in amplifier, a far narrower band about its reference.