Wavelet $p$-analogs of the discrete Haar transform

Two $p$-analogs (for $p>2$) of the discrete version of the Haar system in vector symbolism are proposed and fast algorithms are constructed based on them. The main wavelet principles for constructing these Haar-like systems are proposed, such as the presence of several parent functions, $p$-ary dilations and shifts. One of the systems retains an orthogonality property. The calculation procedure has been simplified for another almost orthogonal system. The developed algorithms are presented with decimation in time, methods of their representation with decimation in frequency are indicated.