We have studied power density spectra ( PDS ) of 206 long Gamma-Ray Bursts ( GRBs ) .
We fitted the PDS with a simple power-law and extracted the exponent of the power-law ( \alpha ) and the noise-crossing threshold frequency ( f _ { th } ) .
We find that the distribution of the extracted \alpha peaks around -1.4 and that of f _ { th } around 1 Hz .
In addition , based on a sub-set of 58 bursts with known redshifts , we show that the redshift-corrected threshold frequency is positively correlated with the isotropic peak luminosity .
The correlation coefficient is 0.57 \pm 0.03 .