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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($)
$ in Thousands
3 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount $ 225,926   $ 225,059
Accumulated amortization (108,534)   (103,811)
Net 117,392   121,248
Amortization expense 3,961 $ 2,448  
Purchased and Core Technology      
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount 76,473   76,011
Accumulated amortization (57,017)   (55,482)
Net 19,456   20,529
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 22,936   22,836
Accumulated amortization (13,968)   (13,535)
Net 8,968   9,301
Customer Relationships      
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount 125,805   125,500
Accumulated amortization (36,957)   (34,232)
Net 88,848   91,268
Non-compete Agreements      
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount 600   600
Accumulated amortization (480)   (450)
Net 120   $ 150
Cost of Sales and General and Administrative Expense      
Finite-Lived Intangible Assets [Line Items]      
Amortization expense $ 4,000 $ 2,400