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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2021	Mar. 31, 2020	Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 226,029		$ 226,029		$ 225,059
Accumulated amortization	(112,487)		(112,487)		(103,811)
Net	113,542		113,542		121,248
Amortization expense			7,888	$ 6,564
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	76,517		76,517		76,011
Accumulated amortization	(58,133)		(58,133)		(55,482)
Net	18,384		18,384		20,529
License Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	112		112		112
Accumulated amortization	(112)		(112)		(112)
Net	0		0		0
Patents and Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	23,007		23,007		22,836
Accumulated amortization	(14,386)		(14,386)		(13,535)
Net	8,621		8,621		9,301
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	125,793		125,793		125,500
Accumulated amortization	(39,376)		(39,376)		(34,232)
Net	86,417		86,417		91,268
Non-compete Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	600		600		600
Accumulated amortization	(480)		(480)		(450)
Net	120		120		$ 150
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 3,900	$ 4,100	$ 7,900	$ 6,600

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- Definition

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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