Hardware-Efficient Decimation with Spectral Shape Approximating the Nth Power of a Dirichlet Kernel

In this paper, we introduce a proper approximation of the amplitude response of a digital filter to the Nth power of a Dirichlet kernel, which allows for the construction of efficient decimation architectures. We present an explicit formula to compute how this approximation affects the worst-case aliasing attenuation in the resulting spectral shape with respect to the exact function, such that the user can identify if the proposed approach is convenient for any given specifications. Additionally, a couple of digital decimation architectures are derived from this approximation. These architectures possess the easy reconfiguration capability of the state-of-the-art Cascaded Integrator-Comb (CIC) exact solution while exhibiting a higher maximum frequency of operation and a reduced utilization of hardware resources without practically affecting power consumption.