But as the researchers point out in their new paper, empirical studies show that on average, 57 of those frequencies can be discarded with minimal loss of image quality. An eight-by-eight block of pixels can be thought of as a 64-sample signal, and thus as the sum of 64 different frequencies. That’s why the Fourier transform is useful for compression. Indeed, many of the frequencies may have such low weights that they can be safely disregarded. “Weighted” means that some of those frequencies count more toward the total than others. The FFT takes a digital signal containing a certain number of samples and expresses it as the weighted sum of an equivalent number of frequencies.
#Fast fourier transform series
A digital signal is just a series of numbers - discrete samples of an analog signal, such as the sound of a musical instrument. Like the FFT, the new algorithm works on digital signals. The new algorithm could be particularly useful for image compression, enabling, say, smartphones to wirelessly transmit large video files without draining their batteries or consuming their monthly bandwidth allotments. Under some circumstances, the improvement can be dramatic - a tenfold increase in speed. At the Symposium on Discrete Algorithms (SODA) this week, a group of MIT researchers will present a new algorithm that, in a large range of practically important cases, improves on the fast Fourier transform.
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