Abstract
Discrete Fourier transform (DFT) is a common analysis tool in digital signal processing. This transform is well studied and its shortcomings are known as well. Various window functions (e.g., Hanning, Blackman, Kaiser) are often used to reduce sidelobes and to spread the spectrum. In this paper, we introduce a transformation that allows removing the sidelobes of the Fourier transform and increasing the resolution of the DFT without changing the time sample. The proposed method is based on signal phase analysis. We give the comparison of the proposed approach with known methods based on window functions. The advantages and disadvantages of the proposed technique are explicitly shown. We also give a set of examples illustrating the application of our technique in some practical applications, including engine vibration analysis and a short-range radar system.
Highlights
It is often necessary to estimate the frequency of a mono-harmonic signal in spectral analysis or to detect the center frequency of a narrowband signal
Where N—the number of signal values measured over a period, as well as the number of decomposition components; xn, n = 0, . . . , N − 1—measured signal values
We propose a new method to reduce the sidelobes in the spectrum without increasing the width of the main lobe
Summary
It is often necessary to estimate the frequency of a mono-harmonic signal in spectral analysis or to detect the center frequency of a narrowband signal. Since the amplitudes are complex, it is possible to calculate both the amplitude and phase at the same time, k is the frequency index. The frequency of the k-th signal is equal to k/T, where T is the period of time during which the input data is taken. In this case, due to the spectral leakage, the mono-harmonic signal spectrum obtained by discrete
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