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You will design a fourth-order notch filter and investigate the effects of filter-coefficient quantization. You will compare the response of the filter having unquantized coefficients with that of a filter having coefficients quantized as a single, fourth-order stage and with that of a filter having coefficients quantized as a cascade of two, second-order stages.

Filter-coefficient quantization

One important issue that must be considered when IIR filters are implemented on a fixed-point processor is that the filtercoefficients that are actually used are quantized from the "exact" (high-precision floating point) values computed byMATLAB. Although quantization was not a concern when we worked with FIR filters, it can cause significant deviationsfrom the expected response of an IIR filter.

By default, MATLAB uses 64-bit floating point numbers in all of its computation. These floating point numbers can typicallyrepresent 15-16 digits of precision, far more than the DSP can represent internally. For this reason, when creating filtersin MATLAB, we can generally regard the precision as "infinite," because it is high enough for any reasonable task.

Not all IIR filters are necessarily "reasonable"!
The DSP, on the other hand, operates using 16-bit fixed-point numbers in the range of -1.0 to 1.0 2 -15 . This gives the DSP only 4-5 digits of precision and only if the input is properly scaled to occupy the fullrange from -1 to 1.

For this section exercise, you will examine how this difference in precision affects a notch filter generated using the butter command: [B,A] = butter(2,[0.07 0.10],'stop') .

Quantizing coefficients in matlab

It is not difficult to use MATLAB to quantize the filter coefficients to the 16-bit precision used on the DSP. To do this, first take each vector of filtercoefficients (that is, the A and B vectors) and divide by the smallest power of two such that the resulting absolute value of the largest filtercoefficient is less than or equal to one. This is an easy but fairly reasonable approximation of how numbers outsidethe range of -1 to 1 are actually handled on the DSP.

Next, quantize the resulting vectors to 16 bits of precision by first multiplying them by 2 15 32768 , rounding to the nearest integer (use round ), and then dividing the resulting vectors by 32768. Then multiply the resulting numbers, which will bein the range of -1 to 1, back by the power of two that you divided out.

Effects of quantization

Explore the effects of quantization by quantizing the filter coefficients for the notch filter. Use the freqz command to compare the response of the unquantized filter with two quantized versions: first,quantize the entire fourth-order filter at once, and second, quantize the second-order ("bi-quad") sections separatelyand recombine the resulting quantized sections using the conv function. Compare the response of the unquantized filter and the two quantizedversions. Which one is "better?" Why do we always implement IIR filters using second-order sections instead ofimplementing fourth (or higher) order filters directly?

Be sure to create graphs showing the difference between the filter responses of the unquantized notch filter, the notchfilter quantized as a single fourth-order section, and the notch filter quantized as two second-order sections. Savethe MATLAB code you use to generate these graphs, and be prepared to reproduce and explain the graphs as part of yourquiz. Make sure that in your comparisons, you rescale the resulting filters to ensure that the response is unity (one)at frequencies far outside the notch.

Questions & Answers

what is the stm
Brian Reply
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
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Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Source:  OpenStax, Dsp laboratory with ti tms320c54x. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10078/1.2
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