Download Wavelet scattering along the pitch spiral We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic operator which cascades wavelet convolutions and modulus nonlinearities. It is derived from the pitch spiral, in that convolutions are successively performed in time, log-frequency, and octave index. We give a closed-form approximation of spiral scattering coefficients for a nonstationary generalization of the harmonic source-filter model.
Download The Shape of RemiXXXes to Come: Audio Texture Synthesis with Time-frequency Scattering This article explains how to apply time–frequency scattering, a convolutional operator extracting modulations in the time–frequency domain at different rates and scales, to the re-synthesis and manipulation of audio textures. After implementing phase retrieval in the scattering network by gradient backpropagation, we introduce scale-rate DAFx, a class of audio transformations expressed in the domain of time–frequency scattering coefficients. One example of scale-rate DAFx is chirp rate inversion, which causes each sonic event to be locally reversed in time while leaving the arrow of time globally unchanged. Over the past two years, our work has led to the creation of four electroacoustic pieces: FAVN; Modulator (Scattering Transform); Experimental Palimpsest; Inspection (Maida Vale Project) and Inspection II; as well as XAllegroX (Hecker Scattering.m Sequence), a remix of Lorenzo Senni’s XAllegroX, released by Warp Records on a vinyl entitled The Shape of RemiXXXes to Come.
Download Differentiable Time–frequency Scattering on GPU Joint time–frequency scattering (JTFS) is a convolutional operator in the time–frequency domain which extracts spectrotemporal modulations at various rates and scales. It offers an idealized model of spectrotemporal receptive fields (STRF) in the primary auditory cortex, and thus may serve as a biological plausible surrogate for human perceptual judgments at the scale of isolated audio events. Yet, prior implementations of JTFS and STRF have remained outside of the standard toolkit of perceptual similarity measures and evaluation methods for audio generation. We trace this issue down to three limitations: differentiability, speed, and flexibility. In this paper, we present an implementation of time–frequency scattering in Python. Unlike prior implementations, ours accommodates NumPy, PyTorch, and TensorFlow as backends and is thus portable on both CPU and GPU. We demonstrate the usefulness of JTFS via three applications: unsupervised manifold learning of spectrotemporal modulations, supervised classification of musical instruments, and texture resynthesis of bioacoustic sounds.