# What is the no overload region of a quantizer?

I was watching a video on quantization noise and the instructor kept referring to the "no overload" region of a quantizer? Could anyone please explain what that term means?

• never heard that term before, but I guess it's the area of the quantizer between its minimum and maximum input value boundary? – Marcus Müller Jul 21 '17 at 16:02
• Was it a sigma-delta modulator? In these one-bit quantizers, if the signal slope is too large, the converter can't keep up (it's overloaded). – MBaz Jul 21 '17 at 16:10
• My guess is that the overload region, is when the input amplitude is larger than the dynamic range of the converter. When this happens, some converters have a saturation recovery time associated with the overload, so there may be a period of time when the signal drops back into the dynamic range but the converter remains overloaded for some time. Since you saw the video, perhaps you could respond if this makes sense. – Stanley Pawlukiewicz Jul 21 '17 at 16:36
• @MBaz, delta modulation is not the same thing as sigma-delta. the latter doesn't have a problem with slope. – robert bristow-johnson Jul 21 '17 at 18:34
• @robertbristow-johnson Indeed I got them mixed up -- thanks for the correction. – MBaz Jul 22 '17 at 18:55

It is stated in chapter 5 (Scalar Quantization I: Structure and Performance) of the book "Vector Quantization and Signal Compression" by Gersho-Gray that

Associated with every $N$ point quantizer is a partition of the real line $\mathcal R$ into $N$ cells or atoms $R_i$, for $i = 1,2,\cdots, N$. The $i$th cell is given by $\mathcal R_i=\{x \in \mathcal R: Q(x) = y_i\} \equiv Q^{-1}(y_i)$, the inverse image of $y_i$ under $Q$. It follows from this definition that $\bigcup_i \mathcal R_i = \mathcal R$ and $R_i\bigcap R_j = \emptyset$ for $i \neq j$. A cell that is unbounded is called an overload cell. Each bounded cell is called a granular cell. Together all of the overload (granular) cells are called the overload region (granular region).

So in other words, the union of bounded regions (i.e. granular region) where saturation does not occur is referred to as the "no overload" region and is identified in the following picture

• the width of the "No overload (no saturation) region" is 7 units. i would widen it by $\frac12$ unit on both sides so that there are 8 valid levels. – robert bristow-johnson Jul 22 '17 at 22:16
• actually, for a three-bit word, there should be 4 negative levels and 4 non-negative levels (of which the zero level is one of them). so the nine-levels displayed is one too many. – robert bristow-johnson Jul 22 '17 at 22:17
• The picture shows a mid-tread quantizer with 9 levels (so it is not a 3-bit quantizer). Still, all 9 levels are valid (clipping occurs at the two extreme cells). The 3-bit quantizer you explained is a mid-riser which has four negative and four positive cells. But in that case there would be three positive and three negative "no overload" cells (6 in total). – msm Jul 23 '17 at 3:57
• i don't get "cells". for some value of input, the extreme positive and extreme negative outputs are still value. the overload occurs beyond those limits. – robert bristow-johnson Jul 23 '17 at 5:19
• i know about "mid-tread" and "mid-riser". but the issue is more general than that. for an 8-bit signed quantizer, there are legit inputs that will map to the codes for -128 and +127. but for input beyond those coded values, then the quantizer is overloaded or saturated. – robert bristow-johnson Jul 23 '17 at 5:21