Conventional adaptive detectors assume independent and identically distributed (iid) secondary data vectors which is not contaminated with the target signal. Yet, the input to the adaptive detectors are produced by preprocessing the raw data in fast-time and slow-time dimensions, in general. This paper mainly aims to study the impact of fast-time matched filtering on the adaptive target detectors, namely Kelly's detector, adaptive matched filter (AMF) and adaptive coherence estimator (ACE). It is shown that the application of matched filtering prior to the adaptive detection violates the requirements of conventional adaptive detectors unless the range side-lobes of the radar pulse is zero at all lags. An alternative preprocessing method, based on an unitary transformation mapping, is suggested and it is shown the alternative approach exactly satisfies the requirements. Numerical comparisons are provided to examine the performance gain of the suggested approach in comparison with the conventional one, i.e. fast-time matched filtering.