Quadratic-Phase Wave-Packet Transform in L2(R)

Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, so on. However, they seem to be inadequate representing those signals whose energy not well concentrated frequency domain. In pursuit of representations such signals, we propose novel time-frequency coined as quadratic-phase wave packet L2(R). The proposed aimed at rectifying conventional wavelet by employing Fourier with extra degrees freedom. Besides formulation all fundamental results, including orthogonality relation, reconstruction formula characterization range, also derive direct relationship between well-known Wigner-Ville distribution transform. addition, study wave-packet framework almost periodic functions. Finally, extend scope present work investigating composition transforms.