Consider the implementation of a digital transmitter filter

Consider the implementation of a digital transmitter filter G_T(f) and a matched receiver filter G_R(f) as means to mitigate ISI, which distorts signal transmission over a band-limited channel. To that effect, the combined characteristics of the filters shall match those of a duobinary conversion filter. In addition, the impulse response of each filter shall have length N = 31. Find the frequency response H_DC(f) and the corresponding impulse response h_DC(t) of a duobinary conversion filter suited for an arbitrary bit interval T_b Given the results of part, use MATLAB to plot H_DC(f)/T versus normalized frequency fT over the interval (-1, 1). (c) Given the results of part, use MATLAB to plot hDC(t) versus normalized time t/T over the interval (-5, 5). (d) Determine the proper frequency responses G_T(f) and G_T-(f) that meet the design specifications. Use MATLAB to display the discrete-time impulse responses h_T[n] and h_R[n] of the digital filters for N = 31.

Solution

A multichannel digital receiver simultaneously down-converts a set of frequency-division-multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver, these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase M-path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple baseband aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator.