On digital single-sideband modulators

Designs and architectures of filter bank trees for spectrally efficient multi-user communications: review, modifications and extensions of wavelet packet filter bank trees

“…With the publication of [6], and the use of polyphase networks [11], what might be called the classic age, starting in about 1968 and continuing through about 1982 and probably dying out a year or so later, of digital transmultiplexers using single sideband channels emerged, and many improvements and modifications in designs and implementations thereof were explored [7][8][9][10][12][13][14][15][16][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][65][66][67], with significant numbers of these resulting in commercial equipment. Some novel ideas such as the use of wave digital filters [40][41][42][43][44]62,63], directional filters [64] and spread spectrum modulation were also explored and implemented [63].…”

“…Based on results in [4,5] Darlington [6] ushered in what it seems appropriate to call the classical age of digital transmultiplexers, from about 1969 through about 1982, by designing the first digital single sideband (SSB) modulators for multiple parallel channels. Various improvements in the designs of SSB transmultiplexers, such as more efficient hardware, filtering and processing, followed in quick succession [7][8][9][10].…”

“…A variety of improvements in the design of transmultiplexers and filter banks for multiuser communications, many (perhaps even most) with bases in the innovative papers [6,11], appeared in publications through to 1982 . In many of these ingenious and innovative techniques are used to gain design and performance advantages.…”

“…Knowledge of these references may be helpful as a source of ideas and techniques for detailed design improvements of modern transmultiplexers for use in multichannel broadband wireless systems using filter bank trees or M-band filter banks, and may also interest readers who wish to understand the evolution during this classical period in more detail. A succinct list of the detailed improvements advanced, for example, in [12][13][14][15][16][17][18], includes: improvement of coefficient sensitivity properties, permitting reduced parameter word length, more reliable implementation of higher order systems and increased flexibility in the design of channel characteristics [12]; based on [11], further new and clarifying analytical results and a transmultiplexer design using these [14]; a new design for a digital SSB-FDM modem using simpler hardware structures than those in [6,8,9,11,12] and the lowest multiplicative complexity among these, as well as a reasonably low required value of coefficient accuracy, due to the use of an efficient filtering technique, an FFT processor and a set of complex filters [15]; design improvements on those in [11] resulting in the design and performance evaluation of a 60-channel transmultiplexer relying heavily on DSP and prominently using polyphase networks as well as a DFT called the Odd-Time Odd-Frequency Discrete Fourier Transform (O 2 DFT); a new algorithm for a TDM-FDM transmultiplexer without FFT processors that uses ROM multipliers; and determination of the minimum number of bits for the filter and modulation coefficients as well as the data and arithmetic, using computational complexity theory [18].…”

“…The four categories based on the underlying algorithm described very thoroughly and clearly are: bandpass filter bank, lowpass filter bank, Weaver structure method, and multistage method. The list of criteria used in comparing the performance of the transmultiplexer methods is: (1) stability under looped conditions, (2) absolute value of the group delay, (3) computational and control complexity, (4) modularity, (5) intelligible crosstalk, (6) analogue frequency conversion, and (7) out-of-band signaling and pilots. The criteria are described, discussed, and applied to obtain a tabulated set of comparisons of various transmultiplexers.…”