  The fast Fourier transform, FFT, is a useful and prevalent algorithm in
signal processing. It characterizes the spectral components of a signal, or is
used in combination with other operations to perform more complex computations
such as filtering, convolution, and correlation. Digital FFTs are limited in
speed by the necessity of moving charge within logic gates. An analog temporal
FFT in fiber optics has been demonstrated with highest data bandwidth. However,
the implementation with discrete fiber optic FFT components is bulky. Here, we
present and analyze a design of an optical FFT in Silicon photonics and
evaluate its performance with respect to variations in phase and amplitude. We
discuss the impact of the deployed devices on the FFTs transfer function
quality as defined by the transmission output power as a function of frequency,
detuning phase, optical delay, and loss.
