We studied noise properties of microwave signals transmitted through the cryogenic resonator. The experiments were performed with the 11.342 GHz sapphire loaded cavity resonator cooled to 6.2 K. Based on the measured transmission coefficient of the cryogenic resonator we computed its noise suppression function. This was done via Monte-Carlo simulations some details of which are discussed in this Letter. Next, we measured technical fluctuations of a signal incident on the cryogenic resonator. Having processed these data with the previously computed noise filtering template we inferred noise spectra of the transmitted signal. We found that spectral densities of both phase and amplitude fluctuations of the transmitted signal were close to the thermal noise limit of -180 dB/Hz at Fourier frequencies F $ge$ 10 kHz. Such thermal noise limited microwaves allow more precise tests of special relativity and could be useful at some stages of quantum signal processing.
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