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Restatement of previously reported unaudited interim consolidated financial statements - Schedule of Operations and Other Comprehensive Income (Loss) (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Thousands
 3 Months Ended 6 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Mar. 31, 2023
Mar. 31, 2022
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue $ 46,123 $ 33,510 $ 91,826 $ 65,982
Operating costs and expenses        
Selling and marketing 9,623 9,206 19,138 17,644
Research and development 7,373 7,095 15,043 13,502
General and administrative 10,059 6,073 18,538 12,037
Amortization and acquisition-related costs 4,274 4,005 9,095 6,284
Total operating costs and expenses 37,437 30,830 74,767 58,473
Operating income 8,686 2,680 17,059 7,509
Interest expense 2,163 2,040 4,300 4,048
Other income (expense), net 454 (225) 794 (90)
Income before income taxes 6,977 415 13,553 3,371
Income tax benefit (provision) (1,808) 20 (3,654) 188
Net income $ 5,169 $ 435 $ 9,899 $ 3,559
Net income per share – basic (in dollars per share) $ 0.11 $ 0.01 $ 0.22 $ 0.08
Net income per share - diluted (in dollars per share) $ 0.11 $ 0.01 $ 0.22 $ 0.08
Shares used in calculating net income per share – basic (in shares) 45,377 44,775 45,317 44,795
Shares used in calculating net income per share – diluted (in shares) 45,780 46,097 45,932 46,206
Other comprehensive income (loss)        
Net income $ 5,169 $ 435 $ 9,899 $ 3,559
Foreign currency translation adjustment 3,022 (1,862) 15,725 (3,129)
Unrealized gain (loss) on investments 296 (828) 648 (1,098)
Total other comprehensive loss 8,487 (2,255) 26,272 (668)
As Previously Reported        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   34,714   67,186
Operating costs and expenses        
Selling and marketing   9,206   17,644
Research and development   8,236   15,842
General and administrative   6,073   12,037
Amortization and acquisition-related costs   4,385   6,664
Total operating costs and expenses   31,210   58,853
Operating income   3,504   8,333
Interest expense   2,040   4,048
Other income (expense), net   (231)   (96)
Income before income taxes   1,233   4,189
Income tax benefit (provision)   (220)   (52)
Net income   $ 1,013   $ 4,137
Net income per share – basic (in dollars per share)   $ 0.02   $ 0.09
Net income per share - diluted (in dollars per share)   $ 0.02   $ 0.09
Shares used in calculating net income per share – basic (in shares)   44,775   44,795
Shares used in calculating net income per share – diluted (in shares)   46,097   46,206
Other comprehensive income (loss)        
Net income   $ 1,013   $ 4,137
Foreign currency translation adjustment   (1,862)   (3,129)
Unrealized gain (loss) on investments   (828)   (1,098)
Total other comprehensive loss   (1,677)   (90)
Total Adjustments        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   (1,204)   (1,204)
Operating costs and expenses        
Selling and marketing   0   0
Research and development   (1,141)   (2,340)
General and administrative   0   0
Amortization and acquisition-related costs   (380)   (380)
Total operating costs and expenses   (380)   (380)
Operating income   (824)   (824)
Interest expense   0   0
Other income (expense), net   6   6
Income before income taxes   (818)   (818)
Income tax benefit (provision)   240   240
Net income   $ (578)   $ (578)
Net income per share – basic (in dollars per share)   $ (0.01)   $ (0.01)
Net income per share - diluted (in dollars per share)   $ (0.01)   $ (0.01)
Shares used in calculating net income per share – basic (in shares)   0   0
Shares used in calculating net income per share – diluted (in shares)   0   0
Other comprehensive income (loss)        
Net income   $ (578)   $ (578)
Foreign currency translation adjustment   0   0
Unrealized gain (loss) on investments   0   0
Total other comprehensive loss   (578)   (578)
Software and hardware        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue 25,260 18,150 51,636 33,595
Operating costs and expenses        
Cost of revenue 219 310 388 688
Software and hardware | As Previously Reported        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   19,280   34,725
Operating costs and expenses        
Cost of revenue   310   688
Software and hardware | Total Adjustments        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   (1,130)   (1,130)
Operating costs and expenses        
Cost of revenue   0   0
Services and other        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue 20,863 15,360 40,190 32,387
Operating costs and expenses        
Cost of revenue $ 5,679 4,141 $ 10,579 8,318
Services and other | As Previously Reported        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   15,434   32,461
Operating costs and expenses        
Cost of revenue   3,000   5,978
Services and other | Total Adjustments        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Revenue   (74)   (74)
Operating costs and expenses        
Cost of revenue   $ 1,141   $ 2,340