Sinusoidal signals have been always of interest because of their extensive applications in different areas of engineering and science. This research aims at generalizing the discrete Wirtinger inequalities and assessing their applicability in estimating the SNR of sinusoids of rational frequency [Special characters omitted.] it buried in additive noise.  The solution to the problem of estimating the SNR of a sinusoid of frequency [Special characters omitted.] , corrupted with additive white noise, has been provided in the form of an inequality-based method. The limitations of using the existing inequalities in the proposed method have been discussed and modifications have been made to the existing Wirtinger inequalities accordingly. Generalizations of the modified inequalities have been achieved by changing the structure of the filter's impulse response. Performance curves with wider non-saturated regions have been obtained. By using reordering and modulation, an arbitrary sinusoid of frequency [Special characters omitted.] , has been converted to a sinusoid of frequency [Special characters omitted.] , allowing the proposed method to estimate the SNR of sinusoids of higher frequencies as well. The computational complexity of the proposed method has been evaluated and compared with a DFT-based approach.  Extensive simulation results showing the capability of the proposed method in estimating the SNR of an arbitrary sinusoid of rational frequency [Special characters omitted.] have been provided. An advantage of the proposed method is that it can be adaptively adjusted to the length of the observed signal. In cases it is desired to evaluate the SNR of a sinusoid with a known frequency, the proposed method can be used as a computationally efficient option.