  Deep neural networks for image super-resolution (ISR) have shown significant
advantages over traditional approaches like the interpolation. However, they
are often criticized as 'black boxes' compared to traditional approaches with
solid mathematical foundations. In this paper, we attempt to interpret the
behavior of deep neural networks in ISR using theories from the field of signal
processing. First, we report an intriguing phenomenon, referred to as `the sinc
phenomenon.' It occurs when an impulse input is fed to a neural network. Then,
building on this observation, we propose a method named Hybrid Response
Analysis (HyRA) to analyze the behavior of neural networks in ISR tasks.
Specifically, HyRA decomposes a neural network into a parallel connection of a
linear system and a non-linear system and demonstrates that the linear system
functions as a low-pass filter while the non-linear system injects
high-frequency information. Finally, to quantify the injected high-frequency
information, we introduce a metric for image-to-image tasks called Frequency
Spectrum Distribution Similarity (FSDS). FSDS reflects the distribution
similarity of different frequency components and can capture nuances that
traditional metrics may overlook. Code, videos and raw experimental results for
this paper can be found in: https://github.com/RisingEntropy/LPFInISR.
