A Fast Spectral Analysis Method Based on Sparse Signals in Frequency Domain

In the oscilloscope for electronic testing, the traditional fast Fourier transform (FFT) faces problems such as high computational complexity, low frequency resolution, and unsuitability for sparse signals. To solve these problems, we propose a spectrum analysis method based on sparse Fourier transform (SFT). SFT is a new algorithm that uses the characteristics of the signal itself to obtain the signal spectrum, which is more efficient than the traditional
$\text{FFT}^{\underline{12}}$
. The main steps of SFT include spectrum rearrangement, filtering, subsampled FFT, localization and
$\text{evaluation}^{\underline{13}}$
. We use the theoretical framework of SFT to design a spectrum analysis method suitable for oscilloscopes, breaking through the limitations of the spectrum analysis function on the number of operation points in the existing system, and greatly improving the efficiency in sparse signal testing. We verify the effectiveness and superiority of our method through experiments and look forward to its application prospects in the field of electronic testing.