论文标题
频量采样短时傅立叶变换
Frequency-Undersampled Short-Time Fourier Transform
论文作者
论文摘要
短时傅立叶变换（STFT）通常计算出与帧长度相同数量的频率组件，而相邻的时间帧则超过一半。结果，频谱矩阵的组件数量变为信号长度的两倍以上，因此很难将STFT用于信号压缩。此外，即使我们通过基于频谱图的信号处理将光谱图修改为所需的频谱图，只要它超出STFT范围，它也会在反转过程中重新变换。在本文中，为了在保持分析能力的同时减少频谱图的组件数量，我们提出了频率输入采样的STFT（FUSTFT），该频率仅计算频率成分的一半。我们还提出了有和没有周期性条件（包括其不同属性）的反转。在简单的音频信号示例中，我们确认了Fustft和反转的有效性。
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix becomes more than twice the signal length, and hence STFT is hardly used for signal compression. In addition, even if we modify the spectrogram into a desired one by spectrogram-based signal processing, it is re-changed during the inversion as long as it is outside the range of STFT. In this paper, to reduce the number of components of a spectrogram while maintaining the analytical ability, we propose the frequency-undersampled STFT (FUSTFT), which computes only half the frequency components. We also present the inversions with and without the periodic condition, including their different properties. In simple numerical examples of audio signals, we confirm the validity of FUSTFT and the inversions.
