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., a n adaptive filter with a time-invariant prefilter, The filtering and adapta tion is carried out very efficiently in the frequency domain whenever filte rs with many coefficients are required. This is implemented as a block algo rithm by using overlap-save or overlap add techniques. However, in many rea l-time applications also, a short latency time through the system is requir ed, which leads to a degradation of the computational efficiency, Partition ed frequency-domain adaptive filters, also known as multidelay adaptive fil ters, provide an efficient way for the filtering and adaptation with long f ilters maintaining short professing delays. This paper shows a computationally efficient way of implementing two or mor e partitioned frequency-domain filters in cascade or in parallel when their filter lengths are large. The methods presented require only one fast Four ier transform (FFT) and one inverse fast Fourier transform per input and ou tput port, respectively, The FFT size can be even smaller than the length o f the filters. The filters can be either time invariant or adaptive.