A new technique is proposed to solve the simple binary signal-detection problem using a nonunity kernel time-frequency signal detector (GNKD). The GNKD is based on a Cohen time-frequency power spectrum, employing nonunity kernels only. This class of signal detectors includes the Choi-Williams detector (CWWD) and the recently proposed hyperbolic detector (HyD). This work extends the work done by Kumar and Carroll, who investigated the cross unity-kernel Wigner-Ville detector (CWD), which is a special case of the GNKD class. The discrete Moyal's formula for the nonunity kernel time-frequency distribution is derived. The performance of the GNKD is then compared to that of the CWD and the cross-correlator (CORR) detectors by calculating the signal-to-noise ratio (SNR) and the loss factor Q. The GNKD is shown to be better than both the CWD and the CORR with improvement in the SNR by a factor of ?2. The HyD can improve the SNR by about 18% compared to the CWWD. Detection of some practical nonstationary signals is also investigated to exemplify the proposed method.