Method and sensor system for measuring the properties of a transmission path of a measuring system between a transmitter and a receiver

A method for measuring the transmission properties of a first transmission path of a measuring system based on feedback compensation between a first transmitter and a receiver, the method comprising:

• the first transmitter transmitting a first signal onto the first transmission path that is detected by the receiver after passing through at least a portion of the first transmission path;
• a compensation transmitter transmits a second signal onto a second transmission path that is detected by the receiver after passing through the second transmission path;
• the first signal and the second signal are superimposed in a linear manner in the receiver and a receiver output signal is formed therefrom;
• a supply signal is generated by a generator, wherein the supply signal and the receiver output signal each form a vector in a pre-Hilbert space and the supply signal is a band-limited supply signal different from zero that has an upper cutoff frequency ωmax and a lower cutoff frequency ωmin, the lower cutoff frequency ωmin being different from the upper cutoff frequency ωmax;
• feeding of the first transmitter with the supply signal;
• execution of a forward transformation through a Hilbert projection from the receiver output signal of the receiver to the supply signal to generate a projection image;
• forming an output signal based on the projection image signal, wherein the output signal comprises information about the transmission properties of the first transmission path;
• executing an at least partial inverse transformation of the output signal with the supply signal such that a pre-signal is formed;
• generating a compensation signal from the pre-signal;
• feeding of the compensation transmitter with the compensation signal for the feedback control of the receiver output signal.