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Application of the fractional Fourier transform in automotive system development: The problem of knock detection

The Fourier transform is undoubtedly one of the best known integral transforms. It has found uses in numerous applications and has become a fundamental tool in engineering science. The fractional Fourier transform (FRFT) can be viewed as the generalisation of the aforementioned transform with the order parameter. By exploiting the potential of an additional degree of freedom, it is possible to give a more general formulation of the problem or to improve the performance of existing methods by optimising the order parameter. This concept was introduced in the early 20th century in mathematics literature. However, no attention was paid to this subject in the signal processing community for a long time. This situation has changed in recent years. Thanks to new results concerning FRFTs such as rotation in the time-frequency domain and the relationship between the transform to the Wigner distribution, interest in the tool has increased over the past two decades. The transform has found applications in optics, signal and image processing, quantum mechanics etc. This paper extends and develops the results of a previous work (J. Fiolka, 2015), in which the author proposes using FRFT in an automotive application. The main topic addressed in the work concerns the detection of knocking combustion in spark ignition engines. As was shown, the proposed method allows the efficiency of the detection of knocks to be increased, particularly at high engine rotational speeds. Moreover, due to the low cost of the implementation because of the low computational complexity of the FRFT, the method can be attractive for automotive industry.