中文摘要：

在音频变换编码中,一般采取均匀变换的方法进行频谱分析和心理声学模型计算,比如快速傅立叶变换（FFT）,移位离散傅立叶变换（SDFT）和改进离散余弦变换（MDCT）.但均匀频谱分析方法并不符合人耳听觉特性,需要进行额外的非线性映射,并且在低频段分辨率不足.本文在音频编码中引入非均匀快速傅立叶变换（NUFFT）,可以直接使频谱在不同频段具有不同的频率分辨率,非常有利于提高编码效率 同时根据音频编码的需求提出一种专门的近似求逆方法,尽管这种方法存在一定误差,但是可以证明这些误差主要与人耳不敏感的高频信息有关,并且采用此种近似求逆方法,NUFFT相对于FFT有更好的算法稳定性.最后给出了利用NUFFT和FFT进行变换操作的测试结果,从数据精度和客观音质评价两方面都说明在低码率下NUFFT的表现优于FFT.

英文摘要：

Usually uniform transforms, e. g., FFT （fast Fourier tranform）, SDFT （shifted discrete Fourier transform）, and MDCT（modified discrete cosine transform） are applied to analyze the speetra of the audio signal and to eompute the psychoaeoustie model in audio transform coding. However, the uniform transform suffers from insufficient resolution in low frequency range, and extra nonlinear mapping is always needed to fill the gaps between the uniform model and the human auditory system. In this paper, nonuniform fast Fourier transforms （NUFFT）, which benefits from flexible resolution in different frequency range, is applied in audio coding. According to the necessity of audio coding, we present a new inverse transform method. Although some calculation errors are inevitable, the errors eoncentrate at high frequency range, to which human ear is insensitive. It is also shown that the implementation of NUFFT has better stability than that of FFT, and comparatively larger quantization errors are permitted at low and middle frequency range. Experiments prove the superiority of NUFFT in both the numerical precision and the objective audio quality at low bit rates.