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A neural network is essentially a high-dimensional complex mapping model byadjusting network weights for feature fitting. However, the spectral bias innetwork training leads to unbearable training epochs for fitting thehigh-frequency components in broadband signals. To improve the fittingefficiency of high-frequency components, the PhaseDNN was proposed recently bycombining complex frequency band extraction and frequency shift techniques [Caiet al. SIAM J. SCI. COMPUT. 42, A3285 (2020)]. Our paper is devoted to analternative candidate for fitting complex signals with high-frequencycomponents. Here, a parallel frequency function-deep neural network (PFF-DNN)is proposed to suppress computational overhead while ensuring fitting accuracyby utilizing fast Fourier analysis of broadband signals and the spectral biasnature of neural networks. The effectiveness and efficiency of the proposedPFF-DNN method are verified based on detailed numerical experiments for sixtypical broadband signals.

Parallel frequency function-deep neural network for efficient complex broadband signal approximation