The linear canonical transform (LCT), a generalization of the Fourier transform (FT) and the fractional Fourier transform (
FRFT), is a very useful signal analysis tool.
When the parameter matrix A is with some special cases, the LCT reduces to FT,
FRFT, Fresnel transform, and scaling operation [24].
Although the
FRFT based MMSE outperforms the conventional MMSE receiver in terms of bit error rate (BER) [8], it assumes perfect channel knowledge at the receiver which in practice is never known apriori.
Zhang, "Study on integrated radar-communication signal of OFDM-LFM based on
FRFT," in Proceedings of the IET International Radar Conference 2015, pp.
To the best of our knowledge, Poisson sum formula has been generalized with many transforms such as
FRFT, LCT, fractional Laplace transform and fractional Hilbert transform [1, 2, 20, 21].
where u represents the frequency and K the
FRFT transformation kernel as
The fractional Fourier transform(
FrFT) was first defined mathematically by Namias [7] and by Mc-Bride and Kerr.
The fractional autocorrelation (FA) and fractional Fourier transform (
FrFT) were considered to solve the problem of polyphase code signal detection in [16] and [17], respectively.
Zhu, "Multi-LFM signal separation and parameter estimationbased on
FRFT," Journal of Communications Technology and Electronics, vol.