Abstract
In this paper, we describe the method of filtering the frequency components of the signals and images, by using
the discrete signal-induced heap transforms (DsiHT), which are composed by elementary rotations or Givens
transformations. The transforms are fast, because of a simple form of decomposition of their matrices, and they
can be applied for signals of any length. Fast algorithms of calculation of the direct and inverse heap transforms
do not depend on the length of the processed signals. Due to construction of the heap transform, if the input
signal contains an additive component which is similar to the generator, this component is eliminated in the
transform of this signal, while preserving the remaining components of the signal. The energy of this component
is preserved in the first point, only. In particular case, when such component is the wave of a given frequency,
this wave is eliminated in the heap transform. Different examples of the filtration over signals and images by the
DsiHT are described and compared with the known method of the Fourier transform.
