Connecting partitioned frequency-domain filters in parallel or in cascade

The efficient implementation of connected filters is an important issue in signal processing. A typical example is the cascade of two filters, e.g., an adaptive filter with a time-in-variant prefilter. The filtering and adaptation is carried out very efficiently in the frequency domain whenever filters with many coefficients are required. This is implemented as a block algorithm by using overlap-save or overlap-add techniques. However, in many real-time applications also, a short latency time through the system is required, which leads to a degradation of the computational efficiency. Partitioned frequency-domain adaptive filters, also known as multidelay adaptive filters, provide an efficient way for the filtering and adaptation with long filters maintaining short processing delays. This paper shows a computationally efficient way of implementing two or more partitioned frequency-domain filters in cascade or in parallel when their filter lengths are large. The methods presented require only one fast Fourier transform (FFT) and one inverse fast Fourier transform per input and output port, respectively. The FFT size can be even smaller than the length of the filters. The filters can be either time invariant or adaptive.