# 5.16 Digital signal processing problems  (Page 6/6)

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1. What answer should Samantha obtain?
2. As a check, her group partner Sammy says that he computed the inverse DFT of her answer and got $\delta (n+1)+\delta (n-1)$ . Does Sammy's result mean that Samantha's answer is wrong?
3. The homework problem says to lowpass-filter the sequence by multiplying its DFT by $H(k)=\begin{cases}1 & \text{if k=\{0, 1, 7\}}\\ 0 & \text{otherwise}\end{cases}()$ and then computing the inverse DFT. Will this filtering algorithm work? If so, find the filteredoutput; if not, why not?

## Stock market data processing

Because a trading week lasts five days, stock markets frequently compute running averages each day over theprevious five trading days to smooth price fluctuations. The technical stock analyst at the Buy-Lo--Sell-Hibrokerage firm has heard that FFT filtering techniques work better than any others (in terms of producing moreaccurate averages).

1. What is the difference equation governing the five-day averager for daily stock prices?
2. Design an efficient FFT-based filtering algorithm for the broker. How much data should beprocessed at once to produce an efficient algorithm? What length transform should be used?
3. Is the analyst's information correct that FFT techniques produce more accurate averages than anyothers? Why or why not?

## Echoes

Echoes not only occur in canyons, but also in auditoriums and telephone circuits. In one situation where the echoed signal has been sampled, the input signal $x(n)$ emerges as $x(n)+{a}_{1}x(n-{n}_{1})+{a}_{2}x(n-{n}_{2})$ .

1. Find the difference equation of the system that models the production of echoes.
2. To simulate this echo system, ELEC 241 students are asked to write the most efficient (quickest) program that has the same input-output relationship. Suppose the duration of $x(n)$ is 1,000 and that ${a}_{1}=\frac{1}{2}$ , ${n}_{1}=10$ , ${a}_{2}=\frac{1}{5}$ , and ${n}_{2}=25$ . Half the class votes to just program the difference equation while the other half votes to program a frequency domain approach that exploits the speed of the FFT.Because of the undecided vote, you must break the tie. Which approach is more efficient and why?
3. Find the transfer function and difference equation of the system that suppresses the echoes. In other words, with the echoed signal as the input, what system's output is the signal $x(n)$ ?

## Digital filtering of analog signals

RU Electronics wants to develop a filter that would be used in analog applications, but that is implementeddigitally. The filter is to operate on signals that have a 10 kHz bandwidth, and will serve as a lowpassfilter.

1. What is the block diagram for your filter implementation? Explicitly denote which componentsare analog, which are digital (a computer performs the task), and which interface between analog anddigital worlds.
2. What sampling rate must be used and how many bits must be used in the A/D converter for theacquired signal's signal-to-noise ratio to be at least 60 dB? For this calculation, assume thesignal is a sinusoid.
3. If the filter is a length-128 FIR filter (the duration of the filter's unit-sample response equals128), should it be implemented in the time or frequency domain?
4. Assuming $H(e^{i\times 2\pi f})$ is the transfer function of the digital filter, what is the transfer function of your system?

## Signal compression

Because of the slowness of the Internet, lossy signal compression becomes important if you want signals to bereceived quickly. An enterprising 241 student has proposed a scheme based on frequency-domain processing.First of all, he would section the signal into length- $N$ blocks, and compute its $N$ -point DFT. He then would discard (zero the spectrum) at half of the frequencies, quantize them to $b$ -bits, and send these over the network. The receiver would assemble thetransmitted spectrum and compute the inverse DFT, thus reconstituting an $N$ -point block.

1. At what frequencies should the spectrum be zeroed to minimize the error in this lossycompression scheme?
2. The nominal way to represent a signal digitally is to use simple $b$ -bit quantization of the time-domain waveform. How long should a sectionbe in the proposed scheme so that the required number of bits/sample is smaller than that nominallyrequired?
3. Assuming that effective compression can be achieved, would the proposedscheme yield satisfactory results?

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles By     By By Anonymous User By Lakeima Roberts   