Gradient Conversion Between Time and Frequency Domains Using Wirtinger Calculus

Hugo Caracalla; Axel Roebel
DAFx-2017 - Edinburgh
Gradient-based optimizations are commonly found in areas where Fourier transforms are used, such as in audio signal processing. This paper presents a new method of converting any gradient of a cost function with respect to a signal into, or from, a gradient with respect to the spectrum of this signal: thus, it allows the gradient descent to be performed indiscriminately in time or frequency domain. For efficiency purposes, and because the gradient of a real function with respect to a complex signal does not formally exist, this work is performed using Wirtinger calculus. An application to sound texture synthesis then experimentally validates this gradient conversion.
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