Vasiliy Gai – Associate Professor, Department of Information Systems and Technologies, Institute of Radio Electronics and Information Technologies, Nizhniy Novgorod State Technical University n.a. R.E. Alekseev.
Address: 24, Minina str., Nizhny Novgorod, 603950, Russian Federation.
E-mail: vasiliy.gai@gmail.com

Generation of spectrum representation of signals is an essential phase in practically any digital signal processing. Such generation of spectrum representation is usually aimed at distinguishing properties of a signal as necessary for solving a particular task. The signal spectrum generation often employs wavelet transformation, Fourier transformation or discrete cosine transformation. This study proposes and analyzes algorithms of generation of a multi-level (coarse-to-fine) spectrum representation of signals based on U-transformation. Such representation is built using filters based on Walsh functions of the Harmuth’s system. It should be noted that there is also a fine-to-coarse approach of signal decomposition as implemented, for example, in wavelet transformation.

The benefits brought by U-transformation as compared to the existing methods of computing a spectrum representation lie in the use of addition and multiplication operators only in the computation process. In contrast to the Fourier transformation, U-transformation operates with real numbers instead of complex numbers. The spectrum decomposition generated using U-transformation shows invariance to the amplitude and frequency of signals being compared, i.e. if the compared signals have different frequency but the same form, then their decompositions will be similar.

U-transformation can be used for generation of spectrum representation in the applications of aural signal processing, vibration-based diagnostics, electrocardiogram analysis, etc. There are also opportunities to apply this type of transformation as a solution for qualitative behavior comparison of economic time series of varying length.