Time-delay bias errors in estimating frequency response and coherence functions from windowed samples of continuous and transient signals

An investigation is reported of the bias effect introduced by time delays when frequency response and coherence functions are estimated from windowed time samples. The magnitude of the bias error for both functions is shown to be dependent on both the nature of the data capture window and the amount of delay. The bias is found to be more severe for random data processed through a Hanning window than through a "boxcar" window. For transient signals that are fully captured through a boxcar window, the bias error is shown to be zero. Experimental investigation verifies the derived estimates for both boxcar and Hanning windows.