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This paper proposes a theory of harmonic filters and their mathematical models, applicable to periodically time varying (PTV) systems perturbed by a large periodic signal. The harmonic filters are based on a series of finite time delay and weighted sum operations, which allow selection or rejection of an input fundamental tone and/or its harmonics in a periodic manner. The harmonic filters are essentially array processors and can be analogous to digital FIR filters. The paper discusses optimum ways of choosing filter coefficients, time delays, and weights for the harmonic rejections and selections, equivalent to lowpass filters and highpass filters, respectively. Mathematical models for effects of hardware mismatches, weight and delay mismatches, on the filtering performance are provided and verified through ADS behavioral statistical simulations. The theory can be applicable to design quasi-sinusoidal mixers for a quality spectral purity, or harmonic carrier modulators and demodulators for high frequency applications .