# Differentiable Signal Processing

Convolutional VocalTrax replaces the sample-by-sample tract recursion in differentiable articulatory synthesis with fixed-block convolution: it computes the exact frequency response of the same waveguide and applies it as a causal convolution in 5.8 ms blocks, so gradients pass through FFTs and a 43-step recursion along the tract. On 600 AudioMNIST recordings, the tract forward and backward pass runs 47 to 63 times faster on an A100, and a wav2vec 2.0 classifier trained only on real speech recognizes its reconstructions 14.5% of the time versus 10.0% for VocalTrax, although the log-mel distance is 11% higher.

Convolutional VocalTrax replaces the sample-by-sample tract recursion in differentiable articulatory synthesis with fixed-block convolution: it computes the exact frequency response of the same waveguide and applies it as a causal convolution in 5.8 ms blocks, so gradients pass through FFTs and a 43-step recursion along the tract. On 600 AudioMNIST recordings, the tract forward and backward pass runs 47 to 63 times faster on an A100, and a wav2vec 2.0 classifier trained only on real speech recognizes its reconstructions 14.5% of the time versus 10.0% for VocalTrax, although the log-mel distance is 11% higher.