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 generalized likelihood ratio test (GLRT) is proposed and its statistical properties are analyzed. The GLRT involves constrained maximum likelihood estimation of the signal parameters. The distribution of the likelihood ratio is shown to be a central quadratic form under H0, and a noncentral quadratic form under H1.