The invention relates to a design of a recursive demodulator used for demodulating a signal containing Gaussian colored noise. The recursive demodulator comprises a sampling module, an error estimation module, a correlation calculation module and a differential demodulation module. A demodulation function of the recursive demodulator is implemented by the steps of: firstly, setting a sampling frequency, and sampling a signal to be detected; performing recursive estimation on the signal by means of the error estimation module, and calculating an estimation error; taking the estimation error as input, designing the correlation calculation module according to a set order of a colored noise model and an H infinite control operator, and performing recursive computation on a correlation matrix of the noise; and setting order parameters of the differential demodulation module according to a computation result of the correlation matrix after performing recursion for k times, performing demodulation calculation on a sampled signal, judging whether a demodulation result conforms to a precision requirement, and outputting the demodulation result if the requirement is achieved. The recursive demodulator has the advantages that: the whole demodulation process is implemented in a recursive iteration form, the recursion times can be selected flexibly according to the precision requirement of demodulation, and hardware implementation is facilitated; and the recursive demodulator can be used for signal demodulation of electrical tomography.