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L = α f s δ f

where L , f s , and δ f are as just defined, and α is given by

α = 0 . 22 + 0 . 0366 · S B R

The validity of these simplified formulas depends on a number of assumptions, detailed in [link] , but all of them are sufficiently satisfied in this case to permit accuracy in the estimation of L within 5% or so.

Examination of [link] shows that δ f , the filter transition band, can be no larger than Δ f - B , the difference between the channel spacing and the bandwidth of each channel. Recalling also that N · Δ f = f s , we find that

L = N α Δ f δ f = N α 1 1 - B Δ f .

Thus, to first order, the pulse response duration of the required filter is proportional to the number of channels N and is hyperbolic in the percentage bandwidth , the ratio of the channel bandwidth B to the channel spacing Δ f . The effect of the proportionality to α will be examined shortly.

This graph consist of a horizontal line labeled Frequency spanning the length of the image with its extremes labeled -f_s/2 on the left and  f_s/2 on the right. There are five right triangles spaced at equal distances from each other sitting on the line. On top of the line there is also a waveform running across the horizontal line. The waveform continues past the first two triangles and then the wave and then ends at a large right triangle next to the middle smaller right triangle. On the other side of this triangle is another large right triangle that is turned the opposite direction with its right angle on the bottom left. The expanse between the far right of the large triangle of the left and the far left of the right triangle is labeled below the horizontal line and is labeled B. In the middle of the small middle triangle is a line that extends vertically and then intersect a line that connects the top corners of the large triangles. The middle line extending from the center circle is also crosses two parallel horizontal lines. An arrow points to these horizontal lines and labels it Passband Ripple PBR. The expanse between the beginning and the end of the right large triangle is labeled below the horizontal line as sf. The expanse from the center of the line to the middle of the second little triangle from the right. it is labeled delta f. On the right side of the large right triangle the waveform begins again. Between the right two triangles is labeled Stopband Ripple SBR.
Overlay of the Required Tuner Filter with the Generalized Response of an Optimal Linear Phase Equal-Ripple FIR Filter

Relationship to the design parameter Q

The development presented in the section Derivation of the equations for a Basic FDM-TDM Transmux defined the integer variable Q as the ratio of L and N . It was pointed out there without proof that in fact Q was an important design parameter, not just the artifact of two others. This can now be seen by combining the relationship L Q N with [link] to produce an expression for Q :

Q = α Δ f δ f = α 1 1 - B Δ f

Since N depends strictly on the number of channels into which the input band is divided, Q contains all of the information about the impact of the desired filter characteristics.

Continuation of the telegraphy demodulation example

Consider again the example of demodulating R.35 FDM FSK VFT canals discussed in the section Example: Using an FDM-TDM Transmux to Demodulate R.35 Telegraphy Signals . In that section, we determined that the following parameters would be appropriate: f s = 3840 Hz, N = 64 , and Δ f = 60 Hz. To determine Q , and hence the rate of computation needed for the data weighting segment of the transmultiplexer, we need to specify B and S B R , the degree of stopband suppression required.

Generally speaking, the filters in an FSK demodulator need to have unity gain at the mark or space frequency and zero gain at the space or mark frequency, respectively. A computer simulation used to verify the design of the demodulator showed that suppression of 50 dB was more than enough to provide the needed performance. At first glance it might appear that the transition band δ f can be allowed to equal the tone spacing Δ f = 60 Hz, making the percentage bandwidth equal to zero. Actual FSK VFT systems, however, sometimes experience bulk frequency shifts of several Hertz. In order to maintain full performance in the presence of such frequency offsets, the tuner filters need to be designed with a passband bandwidth of 15 Hz or so. Using S B R = 50 dB in [link] , we find with [link] that the required value of Q for this application is about 2.71. The actual value chosen for this application was 3, producing a pulse response duration of L = Q N = 192 , with the remaining degrees of freedom in the filter design used to widen the filter still more, allowing for even more frequency offset.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
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
why?
Adin
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?
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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