Abstract: A complex filter minimizing mismatch error by averaging the mismatch error by integrating the real and imaginary input signals using the same integrator. A further advantage is that, as compared to known devices, the complex filter uses fewer number of components thereby reducing the consumed power. The complex filter may be used in a complex bandpass sigma-delta modulator, thereby increasing the performance of the sigma-delta modulator. The complex filter used in a sigma-delta modulator analog to digital converter increases performance of the analog to digital conversion since the mismatch noise is minimized. The complex bandpass sigma-delta modulator analog to digital converter include any number of complex filter stages.