# 0.4 The impact of digital tuning on the overall design of an fdm  (Page 5/7)

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By inspection it would appear that the proper value of $lo{g}_{2}\left(\frac{{f}_{s}}{\Delta f}\right)=lo{g}_{2}N$ is 8, 9, or 10. Assuming a nominal value of 9, we can use [link] to accurately estimate the optimum value of f s . Performing this calculation yields 437 kHz. In the actual design, this value was rounded up to 512 kHz, the next-higher power-of-two integer multiple of 4 kHz. The choice of ${f}_{s}=512$ kHz in turn means that the tuner decimation M t must equal 4 and the tuner's pulse response duration L t must equal at least 20.

The resulting tuner/transmultiplexer, shown in [link] and described in [link] , was built on a single circuit card. The 12-bit A/D module was mounted separately in the chassis. One multiplier chip operating at 4.096 megamultiplies/sec performed the tuner's quadrature downconversion. Two multiplier-accumulators (MACs) filtered and decimated the downconverted signal, preserving the center 248 kHz. Two more MACs perform the window-and-fold preprocessing for the transmultiplexer while a single MAC is used to compute the radix-2 FFT. Seven stages are used to compute the 128-point FFT and an additional one is used to perform sideband inversion on those voice channels designated by the user. This transmultiplexer also happens to use the so-called offset-bin DFT instead of the usual DFT. The motivation for this and the method for implementing it are discussed in Offset Bin Operation from "An Introduction to the FDM-TDM Digital Transmultiplexer: Appendix B" .

## Design of the fsk vft telegraphy demodulator

The section "Example: Using an FDM-TDM Transmux to Demodulate R.35 Telgraphy Signals" discussed the use of an FDM-to-TDM transmultiplexer as an integral part of a demodulator capable of handling all 24 FSK signals present in an FDM voice frequency telegraphy (VFT) system. The analysis developed in that section showed that, in absence of other system-level factors, the best input sampling rate to the transmux-based filter bank was 3840 Hz, 64 times the 60 Hz fundamental tone spacing in the R.35 standard. In this section, we re-examine that choice in terms of the tuner required to provide the VFT signal to the transmultiplexer.

To pass all 24 FSK components of an R.35 VFT signal, the tuner must have a passband B t of slightly more than 2880 Hz. The system must be able to accept real-valued digital samples from a commercial PCM link. These are provided at a rate of 8000 samples/sec This demodulator was also capable of digitizing real-valued analog inputs at a rate of 16 kHz. . From the section "Example: Using an FDM-TDM Transmux to Demodulate R.35 Telegraphy Signals" we recall that the other key parameters in the filter bank's design are: $Q=3$ , $M=12$ (assuming the input rate is 3840 Hz), $K=\frac{16}{3}$ , and $N=64$ . Using the values in [link] , and assuming a nominal value of 2.5 for α t , yields 3920 Hz as the optimal value of fs . This is very close to the best choice without taking the tuner into account. We therefore fix on 3840 Hz as the overall best choice.

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