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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.

The fractional B -bit two's complement number representation evenly distributes 2 B quantization levels between -1 and 1 2 B 1 . The spacing between quantization levels is then 2 2 B 2 B 1 B Any signal value falling between two levels is assigned to one of the two levels.

X Q Q x is our notation for quantization. e Q x x is then the quantization error.

One method of quantization is rounding , which assigns the signal value to the nearest level. The maximum error is thus B 2 2 B .

Another common scheme, which is often easier to implement in hardware, is truncation . Q x assigns x to the next lowest level.

The worst-case error with truncation is 2 B 1 , which is twice as large as with rounding. Also, the error is always negative, so on average it may have a non-zeromean (i.e., a bias component).

Overflow is the other problem. There are two common types: two's complement (or wraparound ) overflow, or saturation overflow.



Obviously, overflow errors are bad because they are typically large ; two's complement (or wraparound) overflow introduces more error than saturation, but is easierto implement in hardware. It also has the advantage that if the sum of several numbers is between -1 1 , the final answer will be correct even if intermediate sums overflow! However, wraparound overflow leaves IIR systemssusceptible to zero-input large-scale limit cycles, as discussed in another module. As usual, there are many tradeoffs to evaluate, andno one right answer for all applications.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital filter structures and quantization error analysis. OpenStax CNX. Jan 02, 2005 Download for free at http://cnx.org/content/col10259/1.1
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