  In this paper, we provide a systematic approach for assessing and comparing
the computational complexity of neural network layers in digital signal
processing. We provide and link four software-to-hardware complexity measures,
defining how the different complexity metrics relate to the layers'
hyper-parameters. This paper explains how to compute these four metrics for
feed-forward and recurrent layers, and defines in which case we ought to use a
particular metric depending on whether we characterize a more soft- or
hardware-oriented application. One of the four metrics, called `the number of
additions and bit shifts (NABS)', is newly introduced for heterogeneous
quantization. NABS characterizes the impact of not only the bitwidth used in
the operation but also the type of quantization used in the arithmetical
operations. We intend this work to serve as a baseline for the different levels
(purposes) of complexity estimation related to the neural networks' application
in real-time digital signal processing, aiming at unifying the computational
complexity estimation.
