用周期Gabor基结合双正交交换，实现高效音频压缩。
Audio Compression using Periodic Gabor with Biorthogonal Exchange: Implementation Using the Zak Transform
- 构造周期Gabor基，利用Dirichlet函数正交性简化系数计算。
- 通过双正交交换实现高倍率压缩，显著优于STFT与多数DWT场景。
- 基于快速扎克变换，兼具低内存与高速度，适合实时音频处理。
本文提出一种基于新型Gabor基集的高效信号压缩方法。受Shimshovitz和Tannor工作启发，将传统Gabor函数与Dirichlet函数卷积，构建周期Gabor基（PG），该基对连续周期带限函数具有精确表示能力。利用Dirichlet函数的正交性，PG系数计算变得简单且数值稳定，但无法直接用于压缩。通过将PG基与其双正交基交换，采用局部化PG基计算系数（PGB），实现大压缩比。本文采用快速扎克变换（Fast Zak Transform）实现PGB形式，显著提升计算效率，在CPU和内存使用方面表现优异。在多种音频数据（包括音乐与语音）上对比了当前最先进的短时傅里叶变换（STFT）与离散小波变换（DWT）方法，结果表明本方法在所有测试中远超STFT，并在多数情况下超越DWT。
原文摘要 · Abstract (English)
An efficient new approach to signal compression is presented based of a novel variation on the Gabor basis set. Following earlier work by Shimshovitz and Tannor, we convolve the conventional Gabor functions with Dirichlet functions to obtain a Periodic Gabor basis set (PG). The PG basis is exact for continuous functions that are periodic band-limited. Using the orthonormality of the Dirichlet functions, the calculation of the PG coefficients becomes trivial and numerically stable, but its representation does not allow compression. Large compression factors are achieved by exchanging the PG basis with its biorthogonal basis, thereby using the localized PG basis to calculate the coefficients (PGB). Here we implement the PGB formalism using the Fast Zak Transform and obtain very high efficiency with respect to both CPU and memory. We compare the method with the state of the art Short-Time Fourier Transform (STFT) and Discrete Wavelet Transform (DWT) methods on a variety of audio files, including music and speech samples. In all cases tested our scheme surpasses the STFT by far and in most cases outperforms DWT.
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