D. B. (Don) Keele, Jr.
DBK Assoc., 536 W. Mishawaka Rd., Elkhart, IN 46517
A cycle-octave time-frequency display is created by plotting the magnitude of the wavelet transform, using a Morlet complex Gaussian wavelet, on a log-frequency scale versus time in number of cycles of the wavelet's center frequency. This type of display is quite well suited for plotting the decay response of wideband systems, such as the impulse response of a loudspeaker or room, because the time scale is long at low frequencies and short at high frequencies. If the response of typical filters are poltted on this type of display, the resultant 3-D responses are independent of the filter's center frequency, i.e., the decay response shape of a particular filter remains the same as it's center frequency is shifted up and down in log frequency. It can be shown that the wavelet transform of a system's impulse response is equivalent to an aggregate of the tone-burst responses of the system evaluated at equal-percentage-spaced frequencies, where the appropriately scaled and time-reversed mother wavelet acts as the tone-burst excitation signal.