In time series classification and regression, signals are typically mapped
into some intermediate representation used for constructing models. Since the
underlying task is often insensitive to time shifts, these representations are
required to be time-shift invariant. We introduce the joint time-frequency
scattering transform, a time-shift invariant representation which characterizes
the multiscale energy distribution of a signal in time and frequency. It is
computed through wavelet convolutions and modulus non-linearities and may
therefore be implemented as a deep convolutional neural network whose filters
are not learned but calculated from wavelets. We consider the progression from
mel-spectrograms to time scattering and joint time-frequency scattering
transforms, illustrating the relationship between increased discriminability
and refinements of convolutional network architectures. The suitability of the
joint time-frequency scattering transform for time-shift invariant
characterization of time series is demonstrated through applications to chirp
signals and audio synthesis experiments. The proposed transform also obtains
state-of-the-art results on several audio classification tasks, outperforming
time scattering transforms and achieving accuracies comparable to those of
fully learned networks.

通过计算基于小波卷积和模量非线性的联合时频散射变换，作者提出了一种具有时间平移不变性的信号表示方法，并且通过应用于鸣号信号和音频综合实验，证明了其适用于时序分类问题，并且在音频分类任务中获得了与全连接网络可比的高准确率。

联合时频散射

Joint Time-Frequency Scattering

A scattering transform defines a locally translation invariant representation
which is stable to time-warping deformations. It extends MFCC representations
by computing modulation spectrum coefficients of multiple orders, through
cascades of wavelet convolutions and modulus operators. Second-order scattering
coefficients characterize transient phenomena such as attacks and amplitude
modulation. A frequency transposition invariant representation is obtained by
applying a scattering transform along log-frequency. State-the-of-art
classification results are obtained for musical genre and phone classification
on GTZAN and TIMIT databases, respectively.

通过小波卷积和模运算，计算多阶调制谱系数，得到一种可以稳定处理时间扭曲的局部平移不变表示，可用于音乐类型和电话语音方面的分类，并取得了最新的分类结果。