FIR / IIR and Wavelets
A filter applies a frequency-dependent gain to be applied to a signal. 

The process you describe - removing values below a certain threshold -  is not filtering in a DSP sense. 

A typical FIR filter is shown below. It consists of delays, z^-1, and gains, the $b$ terms.



Compare with the IIR filter shown below which has part of its output fed back into the delay structure (the gains are missing on this diagram).