A method for the polarization independent frequency domain equalization (FDE) chromatic dispersion compensation on polarization multiplexing (POLMUX) coherent systems. Operationally, time domain signals are converted to frequency domain signals such that time domain convolution can be done as simple multiplications in the frequency domain. These frequency domain signals then converted back to time domain for subsequent use. The input signal size and FFT size are advantageously designed so that the output signals can be continuous with some overlap between two successive frames.