Summary: Finite word lengths introduce quantization error in fixed-point systems. Truncation quantization causes a larger maximum error and a negative bias compared to rounding, but is easier to implement in hardware. Similarly, wraparound overflow is typically worse than saturation, but also requires more hardware.
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The fractional
One method of quantization is rounding, which assigns the signal
value to the nearest level. The maximum
error is thus
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Another common scheme, which is often easier to implement in
hardware, is truncation.
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Overflow is the other problem. There are two common types: two's complement (or wraparound) overflow, or saturation overflow.
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"Real-Time DSP with MATLAB"