In Nondestructive Evaluation (NDE) applications, the technique of split-spectrum processing (SSP) decomposes the received signal into many subbands, and then uses nonlinear processing techniques (such as minimization or polarity thresholding) to detect the flaws' signal and location. The resulting subband signals are coherently combined to obtain a high-resolution version of the original signal. In this paper, we introduce the notion of Polarity-Coincidence (PC) in the context of wideband-signal detection. In an appropriately designed filter bank, all subband signals display a common polarity at the time of a transient (flaw). Necessary and sufficient conditions on the filter banks with PC properties are derived. Various conventional filter banks are studied for their PC properties. It turns out that the cosine-modulated filter bank cannot be a PC filter bank whereas certain linear-phase and pairwise-mirror-image filter banks may be PC. Design methods and examples of PC filter banks are given. The use of these filter banks, together with a PC polarity thresholding and recomposition algorithm, is simulated on ultrasonics data.< >