0.3 Example: using an fdm-tdm transmux to demodulate r.35 telgraphy  (Page 2/2)

A demodulator using these parameters is shown in [link] . When developed in 1985 it was termed the filter bank card and was used to simultaneously demodulate 24 voice grade channels, each containing 24 R.35 FSK canals. Thus $24·24·2=1152$ fllters were needed to isolate the mark and space energy of all FSK canals. When demodulating R.35 signals, each filter produces outputs at a rate of 320 per second. The input sampled waveforms are tuned and filtered by a preceding tuner to spectrally align the filter bank's bins with the mark and space frequencies of the R.35 signal.

Arrows in [link] point to the key computational elements on the filter bank card. One multiplier-accumulator device handled the window-and-fold, or preprocessing, function for all 24 voice channel inputs. The second computed the needed FFTs. When processing R.35 signals in all 24 channels, $320·24=76800$ FFTs of dimension $N=64$ were performed per second. The third arrow points to a floating-point processor used to measure the instantaneous power at the bandpass filter outputs and threshold their differences to produce binary decisions.

In passing, we note that this design exploits the fact that the FSK demodulator only requires knowledge of the magnitude of each filter output. Recalling the general transmux equation given in Equation 9 from "Derivation of the equations for a Basic FDM-TDM Transmux" and substituting the appropriate values of $N,Q$ , and M produces the equation:

The exponential preceding the sum has unity magnitude and therefore does not affect $|y_n\left(r\right)|.$ . It is therefore not necessary to compute the product of the exponential and the sum. The magnitude measurement is given by

This same filter bank card is also capable of demodulating FSK signals conforming to the R.37 and R.38A ITU-T recommendations. The R.37 signal, for example, uses 12 canals instead of 24, and each of them operates at twice the rate and with twice the mark-space frequency separation of the R.35 signal. Repeating the system design just performed yields the following:

• $\Delta f=120$ Hz
• $N=32$ and $f_s=3840$ Hz
• $L=96$ and $Q=3$
• $f_{out}=640$ Hz

Note that Q and f _s remain the same as for R.35, and that $\Delta f$ and $f_{out}$ double because of the increased mark-space separation and allowable baud rates, while L and N are halved. The impact of processing this additional signal can be assessed by using the formula for the number of multiply-adds required, specifically

It can be verified that the number of multiply-adds needed to perform the window-and-fold function for the filter bank is exactly the same as is needed for the R.35 signal, since the ratio $\frac{N}{M}$ holds constant. Moreover, the amount of computation needed for the radix-2 FFT is $\frac{5}{6}$ of that needed for R.35, the ratio between ${\log }_{2}32$ and ${\log }_{2}64$ . Thus a filter bank with the computational horsepower to handle R.35 can also handle R.37. The R.38A standard represents another factor of two in frequency separations and allowable baud rates. Once again it can be verified that the window-and-fold computation is the same and the FFT computation is smaller yet. Thus a properly designed filter bank processor capable of handling the R.35 standard can also handle R.37 and R.38A as well. A subtle difference is that the input signal must be tuned slightly differently for the three different standards.