<< Chapter < Page Chapter >> Page >
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

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'An introduction to the fdm-tdm digital transmultiplexer' conversation and receive update notifications?