# 1.4 Introduction problems

 Page 1 / 1
Problems for introduction to signals and systems.

## Rms values

The rms (root-mean-square) value of a periodic signal is defined to be $s=\sqrt{\frac{1}{T}\int_{0}^{T} s(t)^{2}\,d t}$ where $T$ is defined to be the signal's period : the smallest positive number such that $s(t)=s(t+T)$ .

1. What is the period of $s(t)=A\sin (2\pi {f}_{0}t+\phi )$ ?
2. What is the rms value of this signal? How is it related to the peak value?
3. What is the period and rms value of the depicted square wave , generically denoted by $\mathrm{sq}(t)$ ?
4. By inspecting any device you plug into a wall socket, you'll see that it is labeled "110 volts AC". What isthe expression for the voltage provided by a wall socket? What is its rms value?

## Modems

The word "modem" is short for "modulator-demodulator." Modems are used not only for connecting computers totelephone lines, but also for connecting digital (discrete-valued) sources to generic channels. In thisproblem, we explore a simple kind of modem, in which binary information is represented by the presence orabsence of a sinusoid (presence representing a "1" and absence a "0"). Consequently, the modem's transmittedsignal that represents a single bit has the form $x(t)=A\sin (2\pi {f}_{0}t)\text{,}0\le t\le T$ Within each bit interval $T$ , the amplitude is either $A$ or zero.

1. What is the smallest transmission interval that makes sense with the frequency ${f}_{0}$ ?
2. Assuming that ten cycles of the sinusoid comprise a single bit's transmission interval, what is thedatarate of this transmission scheme?
3. Now suppose instead of using "on-off" signaling, we allow one of several different values for the amplitude during any transmission interval. If $N$ amplitude values are used, what is the resulting datarate?
4. The classic communications block diagram applies to the modem. Discuss how the transmitter mustinterface with the message source since the source is producing letters of the alphabet, not bits.

To transmit symbols, such as letters of the alphabet, RUcomputer modems use two frequencies (1600 and 1800 Hz) and several amplitude levels. A transmission is sentfor a period of time $T$ (known as the transmission or baud interval) and equals the sum of two amplitude-weighted carriers. $x(t)={A}_{1}\sin (2\pi {f}_{1}t)+{A}_{2}\sin (2\pi {f}_{2}t)\text{,}0\le t\le T$ We send successive symbols by choosing an appropriate frequency and amplitude combination, and sending themone after another.

1. What is the smallest transmission interval that makes sense to use with the frequencies given above?In other words, what should $T$ be so that an integer number of cycles of the carrier occurs?
2. Sketch (using Matlab) the signal that modem produces over several transmission intervals. Make sure youaxes are labeled.
3. Using your signal transmission interval, how many amplitude levels are needed to transmit ASCIIcharacters at a datarate of 3,200 bits/s? Assume use of the extended (8-bit) ASCII code.
We use a discrete set of values for ${A}_{1}$ and ${A}_{2}$ . If we have ${N}_{1}$ values for amplitude ${A}_{1}$ , and ${N}_{2}$ values for ${A}_{2}$ , we have ${N}_{1}{N}_{2}$ possible symbols that can be sent during each $T$ second interval. To convert this number into bits (the fundamental unit ofinformation engineers use to qualify things), compute $\log_{2}({N}_{1}{N}_{2})$ .

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
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