This section is not intended as a tutorial for radio astronomy. It briefly summarises some key equations, with the intent of illustrating implementation choices made by this package.
This package works only in positive baseband frequencies, and is unaware of heterodyne systems. Where necessary, the signal will need to be mixed to this range before being provided as input. As an example, MeerKAT L-band digitisers receive signal in the range 856–1712 MHz, but mix it down to 0–856 MHz by negating every second sample (the digital equivalent of a 856 MHz mixing signal).
This has implications for :ref:`delay compensation <math-delay>`.
A wave with frequency f and wave number k is considered to have a phasor of
e^{(2\pi ft - kz)j}
where t is time and z is position. In particular, phase measured at a fixed position (an antenna) increases with time.
The delay sign convention is such that a input voltage sample with timestamp t will have an output timestamp of t + d (where d is the delay). In other words, the specified values are amounts by which the incoming signals should be delayed to align them.
To correctly apply delay with sub-sample precision, it is necessary to know the original ("sky") frequency of the signal, before mixing and aliasing to baseband. The user supplies this indirectly by specifying the phase correction that must be applied at the centre frequency, i.e. -2\pi f_c d, where f_c is the centre frequency. This calculation is provided by :class:`katpoint.delay.DelayCorrection`.