REPORTABLE SEGMENTS - Schedule of summary of reconciliation of segment profit before taxes and operations (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Segment Reporting Information [Line Items]
Subtotal	$ 317,174	$ 282,912	$ 245,942
Segment Adjusted EBITDA	296,688	257,684	210,838
Unallocated amounts, excluding depreciation	(49,054)	(48,262)	(47,231)
Adjusted EBITDA	247,634	209,422	163,607
Net interest expense	(62,735)	(65,795)	(67,513)
Depreciation and amortization	(52,302)	(52,100)	(51,517)
Restructuring charges	(21,418)	(13,670)	0
Loss from debt extinguishment	0	(7,925)	0
Acquisition contingent consideration	0	1,733	1,646
Acquisition costs	0	(2,960)	0
Income (loss) before taxes from continuing operations	111,179	68,705	46,223
Discontinued Operations, Held-for-sale | Defense Electronics
Segment Reporting Information [Line Items]
Less: Defense Electronics	20,486	25,228	35,104
Consumer and Professional Products
Segment Reporting Information [Line Items]
Segment Adjusted EBITDA:	115,673	104,053	90,677
Depreciation and amortization	(34,433)	(32,788)	(32,289)
Home and Building Products
Segment Reporting Information [Line Items]
Segment Adjusted EBITDA:	181,015	153,631	120,161
Depreciation and amortization	$ (17,370)	$ (18,361)	$ (18,334)