OFDM systems enable simple and effective schemes to mitigate frequency-selective fading channels. However, they are extremely sensitive to multiplicative fluctuations induced by time-varying multipath delays, carrier offsets and oscillators phase noise. Although the duration of OFDM symbols is chosen smaller than the channel coherence time to avoid, or reduce, channel time variations, this choice limits system efficiency. In this paper, we propose a generalized OFDM scheme capable of estimating and then compensating channel frequency selectivity and multiplicative noise effects using a deterministic method that exploits the redundancy added to the transmitted sequence in the form of pilot tones and null guard intervals in the frequency domain. The proposed method applies to channels modeled as the cascade of dispersive filters whose output is corrupted by both additive and multiplicative noise.