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	  Text			  "Demonstration of a Wavelet Transmultiplexer"
" (WTM)\n\nThe wavelet transmultiplexer (WTM) provides\nan interesting example"
" of the perfect\nreconstruction property of the DWT.\n\nThis WTM combines thr"
"ee source signals for transmission\nover a single link, then separates the th"
"ree signals at the\nreceiving end of the channel.  The waveforms plotted in\n"
"each of the scope windows demonstrate the ability of wavelets\nto provide per"
"fect reconstruction of each of the three\nindependent signals, transmitted ov"
"er a single communications\nlink.  The error trace is displayed with an expan"
"ded vertical\nscale to demonstrate the absence of signal corruption.\nThis mo"
"del demonstrates a three-channel transmultiplexer,\nbut the method can be ext"
"ended to an arbitrary number of\nchannels.  Note that the total data rate is "
"limited\nby the Nyquist rate of the high-speed data link.\n\nThe operation of"
" a WTM is analogous to a frequency-domain\nmultiplexer (FDM) in several respe"
"cts.  In an FDM, baseband\ninput signals are filtered and modulated into adja"
"cent frequency\nbands, summed together, then transmitted over a single link."
"\nOn the receiving end, the transmitted signal is filtered to separate\nadjac"
"ent frequency channels, and the signals are demodulated\nback to baseband.  T"
"he filters also must strongly attenuate the\nadjacent signal to provide a sha"
"rp transition from the\nfilter passband to its stopband.  This process limits"
" the\namount of crosstalk (signal leakage) from one frequency band\nto the ne"
"xt.  In addition, often FDM employs\nan unused frequency band between the thr"
"ee modulated\nfrequency bands (known as a guard band) to relax\nthe requireme"
"nts on the FDM filters.\n\nIn a WTM, the filtering performed by the synthesis"
"\nand analysis wavelet filters is analogous to the\nfiltering steps in the FD"
"M, and the interpolation in the\nIDWT is equivalent to frequency modulation. "
" From a\nfrequency domain perspective, the wavelet filters\nare fairly poor s"
"pectral filters (as compared to the filters\nrequired by a FDM implementation"
"), exhibiting slow transitions\nfrom passband to stopband, and providing sign"
"ificant\ndistortion in their response.  What makes the WTM special\nis that t"
"he analysis and synthesis filters together\ncompletely cancel the filter dist"
"ortions and signal aliasing,\nproducing perfect reconstruction of the input s"
"ignals\nand thus perfect extraction of the multiplexed inputs.\nIdeal spectra"
"l efficiency can be achieved, since no guard\nband is required.  Practical li"
"mitations in the implementation\nof channel filters create out-of-band leakag"
"e and distortion.\nIn the conventional FDM approach, each channel within the"
"\nsame communications system requires its own filter and is\nsusceptible to c"
"rosstalk from neighboring channels.  With the\nWTM method, only a single band"
"pass filter is required\nfor the entire communications channel, while channel"
"-to-channel\ninterference is eliminated.\n\nNote that a noisy link can cause "
"imperfect reconstruction of the\ninput signals, and the effects of channel no"
"ise and other impairments\nin the recovered signals can differ in FDM and WTM"
".  This can be\nmodeled, for example, by adding a noise source to the high sp"
"eed link."
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