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

arXiv: https://arxiv.org/abs/2106.10401 · HTML: https://mlsanity.com/paper/2106.10401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 19 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems](https://mlsanity.com/paper/1909.11759/) (2019)

## Abstract (arXiv)

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.