In experimental data collection, a signal of data points will not be a perfect representation of the theoretical expectation.  Instead, the signal will contain some error, or noise.  When an image or audio signal is received after transmission over some distance, it is frequently contaminated by noise.  The simplest model for the acquisition of noise by a signal is additive noise, which has the form

   contaminated signal = original signal + noise.

The human ear can detect noise contained in an audio signal.  For instance, pop noise can be heard on old analog music records.  This noise sounds like random pops in the music recording.  Another type of noise is random noise which is usually characterized by values of the noisy signal alternating quickly up and down about a certain mean value.  Random noise usually causes a graph of data to look “fuzzy” like the graph in Figure 1, below.
 

Figure 1:   A noisy audio signal [8].

Random noise can also occur in short sections of the signal.  This is called localized random noise and can be caused by abrupt disruptions in the transmission of the signal.  In recent years, wavelets have been used to effectively remove all types of noise.