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
$s(t)=s(t+T)$ .
What is the period of
$s(t)=A\sin (2\pi {f}_{0}t+\phi )$ ?
What is the rms value of this signal? How is it
related to the peak value?
What is the period and rms value of the
depictedsquare wave , generically denoted
by
$\mathrm{sq}(t)$ ?
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.
What is the smallest transmission interval that
makes sense with the frequency
${f}_{0}$ ?
Assuming that ten cycles of the sinusoid comprise a
single bit's transmission interval, what is thedatarate of this transmission scheme?
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?
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.
Advanced modems
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.
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?
Sketch (using Matlab) the signal that modem produces
over several transmission intervals. Make sure youaxes are labeled.
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
$\log_{2}({N}_{1}{N}_{2})$ .
Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
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
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?