Product quantization error

In realization of filter structures, multipliers are used. The output (product) of a multiplier is stored in the registers. If the word length of the register is less than word length of the product then the product needs to be quantized by truncation or by rounding. The error due to the quantization of the output of the multiplier is referred to as Product Quantization Error.

Product quantization by rounding is preferred due to the following desirable characteristics:

1) In rounding the error signal is independent of the type of arithmetic employed.

2) Mean value of error signal due to rounding is zero.

3) Variance of error signal due to rounding is the least.

Product quantization error signal is treated as a random process with uniform probability density function.

In higher order IIR filters having number of noise sources, Output Noise variance (power) du to each source is computed separately.

Noise Transfer Function (NTF) is defined as transfer function from the noise source to the filter output. NTF is different for different noise source.

Total output noise power due to product quantization error (or Total round-off noise power) $\sigma_{e T o}^{2}=\sigma_{e 1 o}^{2}+\sigma_{e 2 o}^{2}+\ldots+\sigma_{e N o}^{2}$

Input error

For processing of CT signal using a digital system the analog signal has to be digitized by ADC (analog to digital converter). A/D conversion process produces two types of error viz. Quantization errors and Saturation errors. Quantization error is due to representation of the sampled signal by a fixed number of levels (Quantization levels). Saturation error occurs when the analog signal exceed the dynamic range of $A / D$ converter.