Research Of Speech Compression Algorithm Based On Sparse Fast Fourier Transform

Speech signal is a special audio signal formed in the process of human communication, which is the support of human thinking. Speech signal processing is an interdisciplinary subject between the digital signal processing and phonetics. It not only affected by the technology of these disciplines, but also improved by these disciplines. Nyquist sampling theorem is the basic theory of digital signal processing at the present stage. With the rapid development of mobile Internet, speech services are also increasing significantly. The traditional Nyquist sampling will obtain huge sampling data, which bring tremendous pressure to the signal transmission and storage. If an algorithm can effectively reduce the amount of data that is needed for the transmission and storage, it not only can alleviate the pressure of hardware devices, but also can reduce the problem of time delay and improve the overall efficiency of information transmission.In 2012, an algorithm was proposed by four researchers of Massachusetts Institute of Technology Sparse Fast Fourier Transform(SFFT). Because of the low encoding complexity, less transmitted sampling points, independent of coding and decoding, the SFFT algorithm can achieve high data compression ratio and high SNR in processing of speech signal compression. In order to highlight the SFFT algorithm!s compression effect, this paper introduces compressed sensing(CS) algorithm and compares the segmental signal-to-noise ratio and data compression ratio, and evaluates the speech signal quality of these two algorithms by using perceptual evaluation of speech quality(PESQ).Firstly, we introduce the theory of speech signal in this paper, and understand the generation and characteristic of speech signal, the types of redundancy and compression method, perception and coding of speech signals, which provides theoretical basis for speech signals compression and reconstruction work. Then we focus on the research of the SFFT algorithm and CS algorithm, and make an improvement in the filter design of SFFT algorithm. Because the filter of the original SFFT algorithm has large ripple in the pass band and the stop band, there is a certain spectrum leakage in the operation process. In order to improve the accuracy, the original algorithm needs iterative processing. The improved algorithm applies Dolph-Chebyshev filter which is more smooth in the pass band and stop band and changes more quickly from pass band to the stop band, so the improved algorithm almost has no spectral leakage in the process. So the improved algorithms do not need to iterative processing, which improves the running efficiency of the SFFT algorithm. In CS algorithm research, the various sparse representation and reconstruction method are discussed in detail. We select the representative and low complexity discrete cosine transform sparse algorithm and orthogonal matching pursuit reconstruction algorithm for simulation. Both algorithms are simulated by applying the general periodic signal, non periodic signal and the speech signals.