The algorithm of 1[SX(]1[]2[SX)] dimension spectrum is introduced and the quadratic phase coupling is detected by the 1[SX(]1[]2[SX)] dimension spec tr um. The drawback of the traditional spectrum analysis, loss of phase information , is overcome by 1[SX(]1[]2[SX)] dimension spectrum. This method is also applied to the defect diagnosis of ball bearings. Experimental results show that the pro posed method is effective in the detection of defects of the ball bearings.