The hyperbolic kernel and hyperbolic wavelet were shown to be useful and effective in time-frequency signal processing (Le et al., 2001 and 2003). We introduce the time-frequency wavelet power spectrum as a useful technique to study signal characteristics in which the hyperbolic and sym3 wavelets are employed. The hyperbolic wavelet power spectrum technique is employed for signals including electrocardiogram (ECG), sinusoidal, transient exponential, music, and speech. Comparisons between the Fourier power spectrum technique and hyperbolic wavelet power spectrum technique are also made.