Aims. In the present study, the midrange periodicities are investigated in the data of sunspot numbers and solar flare index during solar cycle 23 for a time interval from August 23, 1997 to December 31, 2005. Methods. For spectral analysis of these data sets, the Date Compensated Discrete Fourier Transform (DCDFT) is used and this technique is applied separately for the data of total disk, northern and southern hemispheres of the Sun. Results. The power spectrums of the sunspot numbers exhibit several important midrange periodicities at 84.4, 113.7, 133.6 and 220.0 days which are consistent with the findings in previous studies made by several authors. Two peaks at 113.7 and 133.6 days detected from the whole disk data are contributed mainly by the southern and northern hemisphere, respectively. However, the results of this study show that the discrepancies in the periodic variations of the northern and southern hemispheres of the Sun display a kind of asymmetrical behavior. On the other hand, the flare index data covering the same time interval does not demonstrate any significant periodicity. This study shows that the DCDFT technique for the periodic analysis of solar time series is fairly useful.