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Complex coefficient FIR filters have applications in a variety of areas. The paper addresses the design of complex FIR filters using the frequency-response masking (FRM) approach, which is well known to be very efficient in the design and implementation of FIR filters with sharp transition bands. We first present a simple method for designing linear phase complex FIR filters using FRM and frequency shifting. We then propose a modified FRM structure for designing complex filters with approximately linear phases and reduced group delays. An illustrative example is included.