Fixed Point Integer Math for Multipoint Sensor Calibration Matrices
Fixed-point Q-format calibration transforms multipoint sensor matrices without floating-point emulation by allocating intermediate guard bits in integer registers.
Scalar Product Truncation
Meaning
Arithmetic reduction method discards lower-order bits of a multiplied numerical result to fit the value into a restricted memory register. In embedded systems, scalar product truncation prevents arithmetic overflow during matrix multiplications or filter computations. This processing method allows low-power devices to perform complex digital signal processing without the need for high-end coprocessors.
Hardware Costing
The choice of computational accuracy directly affects the silicon surface area required for the processor core. By employing scalar product truncation, hardware designers can build smaller and cheaper arithmetic units. This reduction in silicon area lowers the wholesale price of the microchip, which in turn enhances the distributor’s margin.
Such competitive cost structures enable the distribution of smart industrial sensors into high-volume markets.
Performance Tradeoff
Reducing arithmetic precision can introduce quantization noise into the sensor data stream. If the scalar product truncation is too aggressive, the resulting calculation errors can cause system instability in precision machinery. Distributors must understand this tradeoff to properly advise their industrial customers on sensor suitability.
Technical support costs can rise if customers experience performance degradation due to calculation inaccuracies, which can lead to increased product return rates.
Product Quality
Quality control agreements require that the sensor output remains within defined limits under all operating conditions. The scalar product truncation algorithm must be verified to ensure it does not compromise the regulatory compliance of the device. Supply contracts often specify the minimum acceptable precision of the data streams.