Efficient Computation of Sparse Spectra Using Sparse Fourier Transform
One of the recent research developments of obtaining faster computation of signal spectra is Sparse Fourier Transform (SFT). This paper aims at understanding signal sparsity in the frequency domain and its frequency spectra using SFT. In this paper, we show that given a time domain signal x which is sparse in the frequency domain with only a few number of significant frequency components, then x can be recovered completely by an iterative procedure wherein the largest frequency coefficients are extracted one by one till all the k largest frequency coefficients are retrieved. Later the algorithm was used to analyze the frequencies from a real time signal piano and the results are compared with FFT based analysis.
KeywordsDigital signal processing SFT Signal sparsity
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