The paper discusses the problem of detecting transient signals of unknown waveforms in white Gaussian noise. The signals are modeled as impulse responses of rational transfer functions with unknown parameters. A modified generalized likelihood ratio test (MGLRT) is proposed and its statistical properties are analyzed for both known and unknown noise variances. The MGLRT involves constrained maximum likelihood estimation of the signal parameters. The performance of the MGLRT is compared to that of an optimal matched filter and an energy detector, for some test cases. Also, the theoretical distributions of the likelihood ratios under H0and H1are compared to experimental distributions obtained by Monte Carlo simulations.