Configuring Moving Average Filter Lengths for Decimated Signal Processing
Matching moving average filter length to the decimation factor eliminates alias leakage by placing transfer function zeros directly on downsampling fold points.
Two Complement
Binary Representation
Digital arithmetic uses a mathematical notation where the most significant bit holds a negative weight to represent both positive and negative integers in binary form. This two complement representation simplifies arithmetic circuits by allowing addition and subtraction to use the same logic hardware. The method avoids the dual representation of zero that occurs in other signed number formats.
Arithmetic Circuitry
Processor design utilizes the binary format to execute addition and subtraction using standard adder blocks. A subtraction is performed by inverting the bits of the subtrahend and adding one to the result before performing the addition. This process eliminates the need for separate subtraction logic, saving silicon area in the arithmetic unit.
Dynamic Range
Digital systems represent signed values within an asymmetric range that contains one more negative number than positive numbers. For an N-bit word, the values span from negative two raised to the power of N-minus-one to positive two raised to that power minus one. This asymmetry arises because zero is grouped with the positive numbers in the binary encoding.
When processing sensor data, the analog-to-digital converter must map its full-scale voltage range to fit within these digital limits. The binary values are monitored by software to ensure that the signals do not exceed these boundaries, preventing severe clipping or wrap-around distortion.
Overflow Prevention
Precision instrumentation implements overflow detection logic to identify when the result of an addition exceeds the representation range. If an overflow occurs, the system can saturate the output to the maximum or minimum value rather than allowing it to wrap around. This saturation prevents catastrophic feedback loop failures in digital control systems.