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A unified method is presented which allows to estimate dc-offset, all harmonic components and fundamental frequency in arbitrarily distorted single-phase grids using a Frequency Adaptive Observer (FAO) consisting of modified Second-Order Generalized Integrators (mSOGIs), an adaptive DC-Integrator (DCI) and a modified Frequency Locked Loop (mFLL). DCI and mSOGIs are tuned by pole placement which allows for an arbitrarily fast detection of dc-offset and harmonic components if the fundamental frequency is known. If the fundamental frequency must be estimated as well, an mFLL with Gain Normalization (GN), Rate Limitation (RL), Anti-Windup (AW) strategy and low-pass filters (LPF) must be employed. The effectiveness of the proposed FAO is validated by experimental results and its enhanced performance is shown and compared to existing estimation methods.