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Goodwill and Intangible Assets (Tables) | 12 Months Ended
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Jan. 29, 2023
Goodwill and Intangible Assets Disclosure [Abstract] |
Goodwill balances | The carrying amounts of goodwill by applicable reporting unit were as follows:
(in thousands) | Signal Integrity |  | Advanced Protection and Sensing (f.k.a. Protection) |  | IoT System (f.k.a. Wireless and Sensing) |  | IoT Connected Services |  | Unallocated |  | Total
Balance at January 30, 2022 | $ | 274,085 |  |  | $ | 4,928 |  |  | $ | 72,128 |  |  | $ | — |  |  | $ | — |  |  | $ | 351,141 |
Reallocation | — |  |  | 10,546 |  |  | (10,546) |  |  | — |  |  | — |  |  | — |
Addition for acquisition | — |  |  | — |  |  | — |  |  | — |  |  | 931,397 |  |  | 931,397 |
Reduction for disposal | — |  |  | (835) |  |  | — |  |  | — |  |  | — |  |  | (835) |
Balance at January 29, 2023 | $ | 274,085 |  |  | $ | 14,639 |  |  | $ | 61,582 |  |  | $ | — |  |  | $ | 931,397 |  |  | $ | 1,281,703 |
Schedule of finite-lived intangible assets which continue to be amortized | The following table sets forth the Company’s finite-lived intangible assets resulting from business acquisitions, which are amortized over their estimated useful lives:
|  |  | January 29, 2023 |  | January 30, 2022
(in thousands) | Estimated Useful Life |  | Gross Carrying Amount |  | Accumulated Amortization |  | Net Carrying Amount |  | Gross Carrying Amount |  | Accumulated Amortization |  | Net Carrying Amount
Core technologies | 1-8 years |  | $ | 175,080 |  |  | $ | (21,156) |  |  | $ | 153,924 |  |  | $ | 26,300 |  |  | $ | (19,496) |  |  | $ | 6,804 |
Customer relationships | 1-10 years |  | 53,000 |  |  | (690) |  |  | 52,310 |  |  | — |  |  | — |  |  | — |
Trade name | 2-10 years |  | 9,000 |  |  | (132) |  |  | 8,868 |  |  | — |  |  | — |  |  | — |
Total finite-lived intangible assets |  |  | $ | 237,080 |  |  | $ | (21,978) |  |  | $ | 215,102 |  |  | $ | 26,300 |  |  | $ | (19,496) |  |  | $ | 6,804 |
Schedule of amortization expenses recorded in the Statements of Income | Amortization expense of finite-lived intangible assets was as follows:
(in thousands) | January 29, 2023 |  | January 30, 2022 |  | January 31, 2021
Core technologies | $ | 5,660 |  |  | $ | 4,942 |  |  | $ | 7,676 |
Customer relationships | 690 |  |  | — |  |  | 589 |
Trade name | 132 |  |  | — |  |  | — |
Total amortization expense | $ | 6,482 |  |  | $ | 4,942 |  |  | $ | 8,265 |
Schedule of future amortization expense | Future amortization expense of finite-lived intangible assets is expected as follows:
(in thousands) | Core Technologies |  | Customer relationships |  | Trade name |  | Total
Fiscal year 2024 | $ | 41,474 |  |  | $ | 16,029 |  |  | $ | 3,167 |  |  | $ | 60,670 |
Fiscal year 2025 | 39,535 |  |  | 4,050 |  |  | 1,722 |  |  | 45,307 |
Fiscal year 2026 | 32,427 |  |  | 4,050 |  |  | 500 |  |  | 36,977 |
Fiscal year 2027 | 17,566 |  |  | 4,050 |  |  | 500 |  |  | 22,116 |
Fiscal year 2028 | 13,555 |  |  | 4,050 |  |  | 500 |  |  | 18,105 |
Thereafter | 9,367 |  |  | 20,081 |  |  | 2,479 |  |  | 31,927 |
Total expected amortization expense | $ | 153,924 |  |  | $ | 52,310 |  |  | $ | 8,868 |  |  | $ | 215,102 |
Schedule of indefinite-lived intangible assets |

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