Noncircularity

The letter examines the second-order noncircular properties of Fourier coefficients that are estimated from a time stationary sampled sequence. If X(m)=(1//spl radic/M)/spl Sigma//sub n=0//sup M-1/x(n)exp(i2/spl pi/mn/M), where x(n) is a time stationary data sequence, then the noncircular character of X(m) is shown by E[X/sup 2/(m)]=2A(m)csc(2/spl pi/m/M)exp (i2/spl pi/m/M), where A(m) is the sine transform of the autocorrelation function of x(n). The signal processing implications of this are not yet clear, but it appears that it could degrade the performance of a detector by as much as 1.5 dB.