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The Fast Fourier Transform is the standard approach for spectral testing. However, its correct application to sinusoidal signals requires either strict coherent sampling, or careful windowing, or other methods that are not computationally efficient. This paper introduces an improved method for achieving accurate and robust spectral testing for sinusoidal signals without the need for coherent sampling or windowing. Theoretical analysis, extensive simulation results, and experimental results show that the proposed method is always faster than the original method and robust when the signal frequency is close to Nyquist frequency. Statistical analysis and comparative studies demonstrate that the proposed algorithm achieves almost the same spectral testing accuracies as those obtained under perfect coherent sampling.