FASTER THAN FFT ALGORITHM FOR SPARSE SIGNALS
NEHA SINGH ELECTRONICS AND COMMUNICATION ENGINEERING DEPTT BACHELOR OF TECHNOLOGY, PRE-FINAL YEAR BIPIN TRIPATHI KUMAON INSTITUTE OF TECHNOLOGY, DWARAHAT, DISTTALMORA, STATE-UTTARAKHAND, INDIA OMIKA ADHIKARI ELECTRONICS AND COMMUNICATION ENGINEERING DEPTT BACHELOR OF TECHNOLOGY, PRE-FINAL YEAR BIPIN TRIPATHI KUMAON INSTITUTE OF TECHNOLOGY, DWARAHAT, DISTTALMORA, STATE-UTTARAKHAND, INDIA KEYWORDS- Algorithm, DFT, FFT, Signal, Sparse. In digital signal processing, any irregular signal ( such as the voltage fluctuations in the wire that connects an mp3 player to a loudspeaker ), can be represented in Discrete Fourier Transform(DFT), as a combination of pure frequencies. It's universal in signal processing as well as can be used for applications such as the compression of images and audio files. The DFT is so prevalent due to the FFT algorithm which makes it possible to calculate Fourier transforms dynamically. Even then efforts to improve the calculation of DFT have a long and generally overlooked history, as today’s scenario demands increased speed of signal processing to meet some desired specific applications. In this regard, this paper presents a research about an even faster algorithm to compute the DFT of a sparse signal, which can speed up the original FFT by tenfold. The key idea behind the research is the division of signals into narrower slices of bandwidth, sized so that a slice will generally contain only one frequency with a heavy weight. Identification of the most heavily weighted frequency in that slice is done by repeatedly cutting the slice of spectrum into smaller pieces and keeping only those in which most of signal power is concentrated. Signals in which the DFT include a relatively small number of heavily weighted frequencies are called 'sparse' and the new algorithm determines the weights of a signal's most heavily weighted frequencies. The sparser the signal, greater the speed up can be provided by...
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