Design of digital filters for an all digital frequency division multiplex-time division multiplex translator

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]. The digital SSB system described in [10] can be used in radio communications and telemetering as well as in channel banks.…”

“…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].…”

Structures for digital filter banks

“…An analogous convolutional encoder is seen to result from interconnecting U(zM) and V(zN), now assumed to be of the same dimension. The same block rate is then (1) employed throughout, so when MN, different z variables, say za and zb, exist in the two parts so that SaM = zbN. Likewise the L and R variables should be distinguished in the two parts and the internal X and Y vectors distinguished from the external X and Y vectors.…”

“…The design of high performance DFB's has followed several paths since its inception (1)(2)(3)(4). DFBs are often multi-rate structures with commensurate rates and can therefore be viewed as periodic, time-varying systems as described by Meyers and Burrus (5) -By considering a block with length equal to the period, the system can be viewed as a shift-invariant block processor, as suggested by Friedland (6,5).…”