Parallel Frequency Function-Deep Neural Network for Efficient Approximation of Complex Broadband Signals

In recent years, with the growing popularity of complex signal approximation via deep neural networks, people have begun to pay close attention to the spectral bias of neural networks-a problem that occurs when a neural network is used to fit broadband signals. An important direction taken to overcome this problem is the use of frequency selection-based fitting techniques, of which the representative work is called the PhaseDNN method, whose core idea is the use of bandpass filters to extract frequency bands with high energy concentration and fit them by different neural networks. Despite the method's high accuracy, we found in a large number of experiments that the method is less efficient for fitting broadband signals with smooth spectrums. In order to substantially improve its efficiency, a novel candidate-the parallel frequency function-deep neural network (PFF-DNN)-is proposed by utilizing frequency domain analysis of broadband signals and the spectral bias nature of neural networks. A substantial improvement in efficiency was observed in the extensive numerical experiments. Thus, the PFF-DNN method is expected to become an alternative solution for broadband signal fitting.