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.