  A neural network is essentially a high-dimensional complex mapping model by
adjusting network weights for feature fitting. However, the spectral bias in
network training leads to unbearable training epochs for fitting the
high-frequency components in broadband signals. To improve the fitting
efficiency of high-frequency components, the PhaseDNN was proposed recently by
combining complex frequency band extraction and frequency shift techniques [Cai
et al. SIAM J. SCI. COMPUT. 42, A3285 (2020)]. Our paper is devoted to an
alternative candidate for fitting complex signals with high-frequency
components. Here, a parallel frequency function-deep neural network (PFF-DNN)
is proposed to suppress computational overhead while ensuring fitting accuracy
by utilizing fast Fourier analysis of broadband signals and the spectral bias
nature of neural networks. The effectiveness and efficiency of the proposed
PFF-DNN method are verified based on detailed numerical experiments for six
typical broadband signals.
