Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2020	Mar. 31, 2019	Sep. 30, 2019
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 226,081		$ 226,081		$ 121,093
Accumulated amortization	(96,831)		(96,831)		(90,426)
Net	129,250		129,250		30,667
Amortization expense			6,564	$ 4,609
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	75,662		75,662		57,699
Accumulated amortization	(52,802)		(52,802)		(50,986)
Net	22,860		22,860		6,713
License Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	102		102		102
Accumulated amortization	(88)		(88)		(74)
Net	14		14		28
Patents and Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	22,662		22,662		14,577
Accumulated amortization	(12,667)		(12,667)		(11,970)
Net	9,995		9,995		2,607
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	125,255		125,255		46,315
Accumulated amortization	(29,084)		(29,084)		(25,266)
Net	96,171		96,171		21,049
Non-compete Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	600		600		600
Accumulated amortization	(390)		(390)		(330)
Net	210		210		270
Order backlog
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,800		1,800		1,800
Accumulated amortization	(1,800)		(1,800)		(1,800)
Net	0		0		$ 0
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 4,100	$ 2,100	$ 6,600	$ 4,600