One of the problems in PCM (56K) modems is that the filters at the line cards and the transformers present in the analog portion of the telephone line put a null at DC frequency in the overall response of the channel. The filters at the line card also suppress frequency components around and near the Nyquist frequency (4 kHz for telephone lines). However, the problem is more severe at the DC and low frequencies as the transformers also exhibit non-linearity at such frequencies. These conditions make frequencies near DC and 4 kHz unusable for PCM modems. It is thus necessary to modify the spectrum of the output of the modems to match the channel.
Several proposals have been submitted to date to the TR-30.1 and ITU-T standard committee to modify the output spectrum. One promising submission by Motorola uses a convolutional code. See, Vedat Eyaboglu, "More on Convolutional Spectral Shaping," presented at the V.pcm Rapporteur Meeting, La Jolla, Calif., May, 5-7 , 1997, incorporated herein by reference. The code is generated through the use of a Viterbi decoder. The proposal uses a convolutional code with a very simple trellis.