Юрій Семенович Манжос, Євгенія Віталіївна Соколова


The Internet of Things (IoT) is a modern paradigm consisting of heterogeneous intercommunicated devices that sending and receiving messages in various formats through different protocols. Thanks to the everywhere use of smart things, it is becoming common to collect large quantities of data generated by resource-constrained, distributed devices at one or more servers. However, the wireless transmitting of data is very expensive. For example in IoT, using Bluetooth Low Energy costs tens of millijoules per connection, while computing at full energy costs only tens of microjoules, and sitting idle costs close to one microjoule per second for STM processors. That is why additional data compression for smart devices can decrease the energy costs of IoT. There are methods of data compression without or with information loss. It is mathematically proved, that it is possible to construct as arbitrarily close approximations of a weighted sum of generalized orthogonal polynomials to an input function (IoT data). In this article, we are researching the Chebyshev and Fourier sequences as an approximation of source data. For a different type of data in the different sequences, we have a different compression for Chebyshev and Fourier approximation. Concurrent use of transformations allows selecting a maximal compression for different sequences. This article proposes a compression method especially suited for IoT devices. The proposed method is based on the simultaneous use of Chebyshev and Fourier transforms. To improve the compression performance was used a trigonometric optimization. The modification of Chebyshev transformation allows reducing energy costs by about four times. Trigonometric optimization replaces the direct use of the mathematical function cos(x) in a double loop by iteration expressions. A modified algorithm uses a one-time calculation of the cos(x) function. As a result, we have a slight increase of the source code and decrease of the computation time, and increasing energy effectiveness. The software implementation in C ++ of the modified Chebyshev transformation algorithm was proposed. The proposed method can be used not only in IoT but also for the accumulation of data on big servers.


Internet of Things; lossy signal compression; data approximation; general orthogonal polynomials; Fourier transformation; modification of Chebyshev discrete transformation; trigonometric optimization; energy effectiveness


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