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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Sep. 30, 2019
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 224,467		$ 121,093
Accumulated amortization	(93,494)		(90,426)
Net	130,973		30,667
Amortization expense	2,448	$ 2,540
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	71,772		57,699
Accumulated amortization	(52,097)		(50,986)
Net	19,675		6,713
License Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	102		102
Accumulated amortization	(81)		(74)
Net	21		28
Patents and Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	22,636		14,577
Accumulated amortization	(12,263)		(11,970)
Net	10,373		2,607
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	127,557		46,315
Accumulated amortization	(26,893)		(25,266)
Net	100,664		21,049
Non-compete Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	600		600
Accumulated amortization	(360)		(330)
Net	240		270
Order backlog
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,800		1,800
Accumulated amortization	(1,800)		(1,800)
Net	0		$ 0
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 2,448	$ 2,540

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