TY - JOUR
T1 - Sampling and sampling rate conversion of band limited signals in the fractional Fourier transform domain
AU - Tao, Ran Tao
AU - Deng, Bing
AU - Zhang, Wei Qiang
AU - Wang, Yue
PY - 2008/1
Y1 - 2008/1
N2 - The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.
AB - The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.
KW - Fractional Fourier transform (FRFT)
KW - Sampling rate conversion
KW - Sampling theorem
UR - http://www.scopus.com/inward/record.url?scp=37748999882&partnerID=8YFLogxK
U2 - 10.1109/TSP.2007.901666
DO - 10.1109/TSP.2007.901666
M3 - Article
AN - SCOPUS:37748999882
SN - 1053-587X
VL - 56
SP - 158
EP - 171
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 1
ER -