Detection and extraction of unknown signal in noise is an important issue in radar. When signal is an unknown transient, the representation in terms of basis functions which are localized in both time and frequency, such as Gabor representation, is very useful for signal detection. By taking time-frequency decomposition, the noise tends to spread its energy into entire time-frequency domain, while the signal often concentrates its energy within a small region with a limited time interval and frequency band. Therefore, the signal embedded in noise is much easier to be recognized in the time-frequency domain than that in either time or frequency domain. Constant false alarm rate (CFAR) processing is an optimal way to set up a threshold for detecting signals in noise environment. In this paper, we extend the CFAR processing to the time-frequency domain. By setting a CFAR threshold for the time-frequency Gabor coefficients, we can examine the Gabor coefficients and determine whether there is a signal. Then, the signal can be extracted by using the detected signal's Gabor coefficients. Therefore, the time location, the time duration, the frequency range, and other parameters of the unknown signal can be measured. The SNR of the extracted signal is improved about 10 - 12 dB over the observed noisy signal.