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Goodwill and Other Intangible Assets - Summary of Gross Carrying Amounts and Accumulated Amortization of Intangible Assets by Major Class (Details) - USD ($)
$ in Thousands
6 Months Ended 12 Months Ended
Mar. 31, 2023
Sep. 30, 2022
Finite Lived Intangible Assets [Line Items]    
Gross Carrying Amount $ 197,665 $ 193,098
Accumulated Amortization (192,366) (183,398)
Net Carrying Amount 5,299 9,700
Customer Relationships    
Finite Lived Intangible Assets [Line Items]    
Gross Carrying Amount 107,913 104,498
Accumulated Amortization (102,925) (95,315)
Net Carrying Amount $ 4,988 $ 9,183
Weighted Average Remaining Life (Years) 2 years 1 year 8 months 12 days
Technology and Patents    
Finite Lived Intangible Assets [Line Items]    
Gross Carrying Amount $ 89,752 $ 88,600
Accumulated Amortization (89,441) (88,083)
Net Carrying Amount $ 311 $ 517
Weighted Average Remaining Life (Years) 8 months 12 days 1 year 2 months 12 days