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Frequency-domain equalization (FDE) is an effective technique for high-data-rate wireless communication systems suffering from very long intersymbol interference. Most of the existing FDE algorithms are limited to slow time-varying fading channels due to the lack of an accurate channel estimator. In this paper, we employ an interpolation method to propose new algorithms for frequency-domain channel estimation for both slow and fast time-varying fading. We show that least squares (LS)-based channel estimation and minimum mean square (MMSE)-based channel estimation with interpolations are equivalent under certain conditions. Noise variance estimation and channel equalization in the frequency domain are also discussed with fine-tuned formulas. Numerical examples indicate that the new algorithms perform very well for severe fading channels with long delay spread and high Doppler spread. It is also shown that our new algorithms outperform the recently developed frequency-domain least mean squares (LMS) and recursive LS (RLS) algorithms which are capable of dealing with moderate fading channels.