The Fast Fourier Transform is the ubiquitous method of choice for spectral testing. However, its correct application to periodic signals requires either strict coherent sampling, or careful windowing, or other techniques that are computationally inefficient. This paper introduces a new method for achieving accurate spectral testing for periodic signals without the need for coherent sampling or windowing. Furthermore the method is computationally very efficient with only minimal addition to the computational complexity of FFT. The method is validated with both simulation data and experimental data. Extensive controlled simulation indicates that the method is very robust to errors in signal frequency, phase, amplitude, additive noise, and so on. Statistical analysis and comparative studies demonstrate that the proposed method achieves spectral testing accuracies similar to those obtained with perfect coherent sampling in an ideal noise-free environment.