Differentiable Digital Signal Processing is the application of differentiable programming, whereby a computer program may be differentiated end-to-end, to audio tasks. Coupled with gradientbased optimisation methods, differentiable signal processors are central to a variety of audio problems and can be incorporated into machine learning architectures.

In this paper it is shown that, using the environment expression and pattern matching abstraction, it is possible to write FAUST code that is differentiable end-to-end. A system for writing FAUST programs that are automatically differentiable in the forward-mode is developed and a parameter optimisation example presented. Differentiable programming in FAUST could serve as a platform for native approaches to machine learning problems in the audio domain.