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An adaptive subband decomposition technique for efficient signal representation and compression is introduced and tested in a rate-distortion framework. The best wavelet packet bases exhibit a SFFT (short-time fast Fourier transform) subband decomposition at one source instance, a wavelet decomposition at another instance, or any intermediate wavelet packet decomposition at yet other instances to best match the signal's characteristics. For a given subband decomposition, commonly used information measures such as entropy, distortion (mse), and rate (no. of coefficients) are minimized over all subbands decomposition to search the most efficient wavelet packet tree of signal and a method to provide such a wavepacket tree is proposed. Image coding application results using the joint rate-distortion cost measure demonstrated superior performance over the entropy only information cost measure