A unified method is presented which allows to estimate all harmonic components, DC-offset and fundamen- tal frequency in arbitrarily distorted single-phase grids us- ing a frequency-adaptive observer (FAO) consisting of modi- fied Second-Order Generalized Integrators (mSOGIs), a 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, a 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 by comparisons to existing estimation methods.