FFT flame monitoring for limit condition

A method for controlling operation of a fuel-fired heating appliance having a burner, a fuel flow control for controlling a fuel flow to the burner, and a combustion air blower for supplying combustion air to the burner, includes iteratively (1) determining the quality of combustion by sensing a flame at the burner and outputting a time-varying flame current signal that includes an ionization signal from the flame; sampling the flame current signal to obtain a time record of the flame current signal; using a Fourier transformation, transforming the time record into a frequency spectrum of frequency components that include frequency components of the ionization signal, the frequency spectrum having a spectrum shaped defined by various frequency components of the flame current signal; and determining whether the frequency spectrum indicates flame stability or instability. Upon determination of flame instability, adjusting at least one of the fuel flow control to decrease the fuel flow to the burner and the combustion air blower to increase the flow of combustion air to the burner, and shutting down the burner if flame stability is not determined within a predetermined interval.