Signal Decomposition
Mathematical signal processing operating on variable scale windows provides time frequency representation for transient print defects. Continuous wavelet transform applies inner products between input signals from web inspection sensors and scaled mother wavelets to isolate localized spatial anomalies on moving substrates. High frequency components receive narrow time windows for precise spatial localization during rapid paper production runs, whereas low frequency background variations undergo wide window analysis.
The algorithm evaluates localized scaling coefficients across dilation parameters without downsampling constraints, yielding redundant output matrices that preserve shift invariance for downstream classification systems. Signal energy distributes continuously across scale space coordinates, allowing operators to distinguish random noise spikes from repeatable mechanical chatter originating at the calender stack.
Scale Resolution
Dilation parameters govern the spatial frequency resolution trade off during high speed web scanning procedures. Large scale factors capture broad basis weights fluctuations across jumbo reels, while fine scale parameters resolve micro formation defects such as pinholes or wire marks in lightweight packaging grades. Orthogonal mother wavelet selection dictates the mathematical leakage boundary, determining how effectively high frequency edge transients separate from smooth coating profiles.
Scaling functions integrate over finite spatial intervals to prevent boundary distortion at the edges of finite length sensor data arrays.
Coefficient Matrix
Redundant transformation outputs generate detailed coefficient matrices requiring thresholding algorithms to filter negligible background noise before converting raw sensor data into actionable defect maps. Matrix elements quantify local similarity between the reference wavelet and targeted substrate profiles, producing numerical values proportional to local variance intensity. Threshold filters discard coefficients falling below predetermined noise floors, preventing false rejection triggers on high speed sorting lines without losing true defect signatures.
Storage requirements expand considerably due to the redundant nature of uncompressed transformation output, demanding dedicated processing hardware alongside the inspection line.