This paper proposes a blind synchronization of ad-hoc microphone array in the short-time Fourier transform (STFT) domain with the optimized frame analysis centered at non-integer discrete time. We show that the drift caused by sampling frequency mismatch of asynchronous observation channels can be disregarded in a short interval. Utilizing this property, the sampling frequency mismatch and the recording start offset are estimated roughly by finding two pairs of the short intervals corresponding to the same continuous time. Using the estimate, STFT analysis is synchronized roughly between channels with optimized frame central. Since the optimized frame central is generally non-integer, we approximate the frame analysis by the linear phase filtering of the frame centered at the nearest integer sample. Maximum likelihood estimation refines the compensation of sampling frequency mismatch.