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In this paper, we propose a robust spectral representation for detecting formants in heavily degraded conditions. The method combines the temporal robustness of the stabilized weighted linear prediction (SWLP) with the robustness of group delay (GD) function in the frequency domain. Weighting of the cost function in linear prediction analysis with the short-time energy of the speech signal improves the robustness of the resultant spectrum. It also improves the accuracy of the estimated resonances as the weighting function gives more weightage to the closed phase of the glottal cycle, which is also the high SNR region of the signal. The group delay spectrum computed as the sum of individual resonances denoted by the roots of the SWLP coefficients, improves the robustness of weaker higher order resonances. The proposed SWLP-GD spectrum performs better than the conventional LP spectrum and the STRAIGHT spectrum in terms of spectral distortion measure and formant detection accuracies.