The chirp is created by the helper function helperEchirp. In this first example, we create a chirp signal with an exponentially increasing carrier frequency. With the introduction of automatic differentiation and differentiable signal processing, we can now use gradient descent with the usual convex loss functions to perform phase retrieval. Phase retrieval is, in general, ill-posed and prior iterative methods suffer from the non-convexity of the formulation and therefore convergence to an optimal solution is impossible to guarantee.

The techniques for doing this are referred to as phase retrieval. In these applications, it still may be useful or even necessary to recover an approximation of the original signal. In the latter case, the original complex-valued time-frequency representation no longer corresponds to the modified magnitude representation. This is most frequently done in speech processing where the underlying time-frequency representation is usually the short-time Fourier transform. In other applications, the required signal processing is optimally done by modifying the magnitudes of a time-frequency representation. This may lead people to retain only the magnitudes. One reason is simply that the complex-valued time-frequency representations containing phase information are difficult to plot and interpret. In a number of applications, the phase information in a time-frequency representation is discarded in favor of the magnitudes.

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