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We show analytically and experimentally that direct photodetection of a temporally-stretched and chirped optical pulse-train together with its time-delayed replica can be exploited to realize the generation of tunable continuous-wave microwave signals. The proposed scheme utilizes the chromatic dispersion of the standard single-mode-fiber (SMF) to temporally-stretch and chirp an optical pulse-train in such a way that the pulses overlap with each other. The temporally-stretched pulse-train is then sent to a Mach-Zehnder Interferometer (MZI) where it first splits and then recombines with a time-delayed replica of itself at the output. Proper management of both the dispersion in the system as well as the relative time-delay of the two arms of the MZI enables one to tune the frequency of the generated microwave signal to any integer multiple of the pulse source's repetition frequency which is within the bandwidth of the photodetector. Based on the proposed scheme, using an initial 2 GHz pulse-train, we demonstrate generation of tunable continuous-wave microwave signals from 4 GHz to 14 GHz.