A System Function Representation by Scale-Shift Transform
Iwao NAGASHIROt · 2000
Wavelet transform gies a time-frequency representation of a signal. But many applications show that more researches are needed for characterzing a time-varying system. In this paper, w edecribe a type of impulse response function with scale parameter a and shift parameter b. We also define a convolution operation with variable a and b. And for this type of system, w ecan prove that the scale-shift transform of output is giwn b y a product of scale-shift transform of input and a system function. As an application of scale-shift transform, we will show the system function of Doppler effect.