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
- 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.