Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 435,739		$ 435,651
Accumulated amortization	(140,076)		(133,587)
Net	295,663		302,064
Amortization expense	6,957	$ 8,559
Goodwill	341,573		340,477
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,034		85,016
Accumulated amortization	(56,975)		(55,854)
Net	28,059		29,162
License Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	112		112
Accumulated amortization	(112)		(112)
Net	0		0
Patents and Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	39,773		39,711
Accumulated amortization	(18,266)		(17,666)
Net	21,507		22,045
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,220		309,212
Accumulated amortization	(63,123)		(58,355)
Net	246,097		250,857
Non-compete Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	600		600
Accumulated amortization	(600)		(600)
Net	0		0
Order backlog
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,000		1,000
Accumulated amortization	(1,000)		(1,000)
Net	0		$ 0
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 6,500	$ 6,300