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INFORMATION ON REPORTABLE SEGMENTS - Financial Data (Details) - USD ($)
 3 Months Ended 6 Months Ended
Jul. 01, 2023
Jul. 02, 2022
Jul. 01, 2023
Jul. 02, 2022
Revenues:        
Revenues $ 423,300,000 $ 354,000,000.0 $ 823,100,000 $ 661,100,000
Income:        
Consolidated operating income 51,300,000 27,200,000 101,100,000 38,600,000
Acquisition-related and other costs 1,500,000 900,000 2,100,000 1,000,000.0
Amortization of intangible assets 11,500,000 7,100,000 17,800,000 16,400,000
Special charges, net 0 100,000 0 100,000
Other operating expense 0 1,900,000 0 1,000,000.0
ASPEQ Parent Holdings, Inc.        
Income:        
Acquisition-related and other costs 4,600,000   5,100,000  
ASPEQ Parent Holdings, Inc. | Cost of Sales | Step-Up of Inventory        
Income:        
Acquisition-related and other costs 1,100,000   1,100,000  
International Tower Lighting, LLC | Cost of Sales | Step-Up of Inventory        
Income:        
Acquisition-related and other costs   900,000   1,000,000.0
HVAC reportable segment        
Revenues:        
Revenues 269,000,000.0 218,700,000 520,600,000 411,800,000
Detection and Measurement reportable segment        
Revenues:        
Revenues 154,300,000 135,300,000 302,500,000 249,300,000
Operating Segments        
Revenues:        
Revenues 423,300,000 354,000,000.0 823,100,000 661,100,000
Income:        
Consolidated operating income 84,400,000 56,100,000 158,800,000 95,700,000
Operating Segments | HVAC reportable segment        
Revenues:        
Revenues 269,000,000.0 218,700,000 520,600,000 411,800,000
Income:        
Consolidated operating income 55,200,000 28,300,000 102,900,000 48,900,000
Special charges, net   100,000   100,000
Operating Segments | Detection and Measurement reportable segment        
Revenues:        
Revenues 154,300,000 135,300,000 302,500,000 249,300,000
Income:        
Consolidated operating income 29,200,000 27,800,000 55,900,000 46,800,000
Special charges, net   0   0
Corporate expense        
Income:        
Corporate expense 16,600,000 16,400,000 31,200,000 33,000,000.0
Segment Reconciling Items        
Income:        
Acquisition-related and other costs 1,500,000 900,000 2,100,000 1,000,000.0
Long-term incentive compensation expense 3,500,000 2,500,000 6,600,000 5,600,000
Amortization of intangible assets 11,500,000 7,100,000 17,800,000 16,400,000
Special charges, net 0 100,000 0 100,000
Other operating expense $ 0 $ 1,900,000 $ 0 $ 1,000,000.0