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Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Thousands |  | 12 Months Ended
--- | --- | ---
Apr. 28, 2020 | Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) |  | 7 years |  |
Gross Amount |  | $ 277,013 | $ 297,780 |
Accumulated Amortization |  | (158,035) | (146,050) |
Total Other Intangible Assets |  |  |  |
Gross Amount |  | 277,013 | 309,533 |
Removal of fully amortized intangible assets |  |  | 32,500 |
Amortization expense related to intangible assets |  | 44,505 | 42,569 | $ 37,734
Research and development |  |  |  |
Total Other Intangible Assets |  |  |  |
Amortization expense related to intangible assets |  | 32,319 | 31,351 | 27,858
Selling, general and administrative |  |  |  |
Total Other Intangible Assets |  |  |  |
Amortization expense related to intangible assets |  | $ 12,186 | 11,218 | $ 9,876
In-process research and development |  |  |  |
Not subject to amortization: |  |  |  |
Not subject to amortization |  |  | 11,753 |
Core and developed technology |  |  |  |
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) |  | 8 years |  |
Gross Amount |  | $ 238,092 | 243,739 |
Accumulated Amortization |  | $ (124,337) | (109,417) |
Customer relationships |  |  |  |
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) |  | 4 years |  |
Gross Amount |  | $ 27,450 | 41,270 |
Accumulated Amortization |  | $ (24,958) | (30,321) |
Customer relationships | Redpine Signals |  |  |  |
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) | 2 years |  |  |
Trademarks |  |  |  |
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) |  | 5 years |  |
Gross Amount |  | $ 11,471 | 12,771 |
Accumulated Amortization |  | $ (8,740) | $ (6,312) |
Trademarks | Redpine Signals |  |  |  |
Subject to amortization: |  |  |  |
Weighted-Average Amortization Period (Years) | 2 years |  |  |

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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. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274 + Details
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