Income Taxes - Income Tax Rate Reconciliation (Details)	12 Months Ended
	Oct. 02, 2022	Oct. 03, 2021	Sep. 27, 2020
Income Tax Disclosure [Abstract]
Tax at federal statutory rate	21.00%	21.00%	21.00%
State taxes, net of federal benefit	2.10%	2.30%	2.70%
Research and Development ("R&D") credits	(1.00%)	(2.60%)	(2.20%)
Tax differential on foreign earnings	1.00%	0.90%	0.70%
Non-taxable foreign interest income	0.00%	(1.00%)	(1.10%)
Goodwill	0.00%	0.00%	1.50%
Stock compensation	(2.00%)	(3.30%)	(2.20%)
Valuation allowance	0.20%	(9.30%)	1.60%
Change in uncertain tax positions	(1.10%)	1.70%	0.40%
Return to provision	1.40%	(3.70%)	0.80%
Disallowed officer compensation	1.90%	2.00%	0.20%
Cash repatriation	0.10%	2.10%	0.00%
Unremitted earnings	(0.20%)	1.00%	0.00%
Deferred tax adjustments	0.10%	0.80%	(1.30%)
Other	1.00%	0.90%	1.60%
Total income tax expense	24.50%	12.80%	23.70%