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In this paper we propose a new scheme for blind watermarking of speech and audio signals. We used the discrete wavelet transform (DWT) after framing the signal, and then we applied the discrete cosine transform (DCT) on each frame. For correlation purpose, sub-sampling is performed to decompose the frame into two segments. For security concern, Arnold transform is employed on the watermark image in order to save detection security. The fully blind detection is accomplished without using the original speech/audio signal and the insertion parameter is not required. Experimental assessment and comparisons with other published schemes demonstrate a good tradeoff between security, capacity, imperceptibility and robustness against various signal processing attacks for both audio and speech signals.