In principle, the parameters
f
_{s} (and hence
T ),
f
_{0} ,
L , and
M can be chosen arbitrarily. In fact, significant simplications to the implementation of the tuner occur if they are carefully chosen. To do this we must first develop a general equation for the decimated tuner output
$y\left(r\right)$ .
The undecimated filter output
$\overline{y}\left(k\right)$ can be written as the convolutional sum of
$\rho \left(k\right)$ and the filter pulse response
$h\left(k\right)$ :
Decimation by the factor
M is introduced by evaluating
$\overline{y}\left(k\right)$ only at the values of
k where
$k=rM$ . We denote the decimated output as
$y\left(r\right)$ , given by
Choosing various system parameters to simplify the general equation for the tuner output
Equation 4 holds for arbitrary choice of
L ,
M ,
f
_{0} , and
f
_{s} . To obtain the equations for the basic FDM-TDM transmultiplexer, we must first simplify the general equation for the output of the digital tuner. We do this by making the three key assumptions:
We assume that the sampling rate
f
_{s} and the tuning frequency
f
_{0} are integer multiples of the same
frequency step$\Delta f$ . In the case of FDM multichannel telephone systems for example,
$\Delta f$ is typically 4 kHz. We define the integer parameters
N and
n with the expressions
${f}_{s}\equiv N\xb7\Delta f$ and
${f}_{0}\equiv n\xb7\Delta f$ .
We next assume that the pulse response duration
L is an integer multiple of the factor
N defined above. We define the positive integer parameter
Q where
$L\equiv Q\xb7N$ . This is a nonrestrictive assumption since
Q can be chosen large enough to make it true for any value of
L . If
$QN$ exceeds the minimum required value of
L , then
$h\left(k\right)$ can be made artificially longer by padding it with zero values. The factor
Q turns out to be an important design parameter. The parameters
Q and
N are determined separately and the resulting value of
L follows from their choice.
We also assume that the decimation factor
M is chosen to be closely related to the parameter
N . Typical values are
$M=N$ and
$M=\frac{N}{2}$
We can now examine the effects of these assumptions. First, the relationship between
f
_{s} ,
f
_{0} , and
$\Delta f$ allows
$y\left(r\right)$ to be written as
We subscript the decimated output
$y\left(r\right)$ by the parameter
n to indicate that it depends on the tuning frequency
${f}_{0}=n\xb7\Delta f$ .
The second assumption, the definition of the parameter
Q , permits the single sum to be split into a nested double sum. To do this, define the new integer indices
q and
p by the expressions
Examination of
[link] shows that the pulse response running index
l has a unique value in the range from 0 to
$L-1$ for each permissible value of
p and
q . This permits the single convolutional sum over the index
l to be replaced (for reasons to be shown) with a double sum over the indices
p and
q . In particular,
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?
Source:
OpenStax, An introduction to the fdm-tdm digital transmultiplexer. OpenStax CNX. Nov 16, 2010 Download for free at http://cnx.org/content/col11165/1.2
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