Signal processing is a branch of applied statistics concerned with analysis of functions of time that take on scalar or vector values. The functions are normally mixtures of a signal and a noise. A broad range of topics are considered in signal processing, including estimation of the signal parameters, hypothesis testing (e.g. detection of signals), filtering.
For example, the records of voltage 
at the output of sensors (like antennas or microphones) make a vector signal that is normally an additive mixture of a signal and noise
where
is the signal, that is often a known function of and ;- is the vector of unknown parameters, for example, coordinates of the signal source in space;
is the vector of noise.
Common problems in signal processing are estimation of parameters , or testing some hypothesis about the values of these parameters.