Non-recursive half band filter with complex coefficients

摘要

The filter has complex coefficients to process a real value or complex value input signal. The complex coefficients of the filter and an odd filter length N have alternate purely real and purely imaginary values and no complex values in the usual sense. The complex coefficient is in the form h(0)=+/-h(0)(1+/-j)/sq.rt.2. The impulse response of a half band filter with only real coefficient values and the characteristic h(l)-h(-l) for all values of l less than or equal to (N-1)/2 and h(l)=) for l=plus or minus 2,4,... is modulated on a complex carrier of a frequency fm-(2m-1)fA/8 where m is 0, plus/minus 1,2,... fA-1/T is the reference sampling frequency of the filter.