## Filter banks in digital communications (2001)

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Venue: | IEEE CAS Mag |

Citations: | 10 - 2 self |

### BibTeX

@ARTICLE{Vaidyanathan01filterbanks,

author = {P. P. Vaidyanathan},

title = {Filter banks in digital communications},

journal = {IEEE CAS Mag},

year = {2001},

volume = {1},

pages = {4--25}

}

### OpenURL

### Abstract

Abstract. Digital signal processing has played a key role in the development of telecommunication systems over the last two decades. In recent years digital filter banks have been occupying an increasingly important role in both wireless and wireline communication systems. In this paper we review some of these applications of filter banks with special emphasis on discrete multitone modulation which has had an impact on high speed data communication over the twisted pair telephone line. We also review filter bank precoders which have been shown to be important for channel equalization applications. 1 1.

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Digital Communications
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Citation Context ...) can be regarded as a compex number,taking one of 2 b possible values from a rectangular constellation as demonstrated in part (b) for b = 4 bits (called 16-QAM). More efficient constellations exist =-=[14]-=-. The distance between the constellation words (e.g., s in part (a)) can be controlled to control the transmitted power. The model shown in Fig. 1 does not work in all situations. For example, mobile ... |

943 |
Multirate Systems and Filter Banks
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Citation Context ... 4. DECIMATORS, EXPANDERS, AND MULTIPLEXERS Before proceeding further we review a few standard building blocks and terminology used in multirate signal processing. Most of the details can be found in =-=[22]-=-. The building blocks ↑ M and ↓ M, shown in Fig. 5 are called the expander and decimator respectively. Their operation is explained in the figure caption. Two standard operations called “blocking” and... |

596 |
Multicarrier modulation for data transmission: an idea whose time has come
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Citation Context ... a practically flat power spectrum. A clever way to approximate optimal power allocation would be to divide the channel bandwidth into several subbands and transmit in each subband channel separately =-=[4,9]-=-. This already suggests a resemblance to frequency division multiplexing but the main difference now is that the different subband channels carry different parts of a single input stream. How this is ... |

499 | Wavelets and subband coding
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Citation Context ...conds. Background material on the DMT system and more generally on the use of digital filter banks in communications can be found in [1,5,9,21]. The DMT idea is similar in principle to subband coding =-=[7, 27, 22]-=- where a signal x(n) to be quantized is first decomposed into subbands. 7. BIORTHOGONALITY AND PERFECT DMT SYSTEMS Consider a linear time invariant system with impulse response h(n) and transfer funct... |

140 | Redundant Filterbank Precoders and Equalizers Part I: Unification and Optimal Designs
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Citation Context ...s. (b) An equivalent drawing where the number of filters is M instead of N. Note that the delay and advance operators have been relocated as well. Both configurations have been used in the literature =-=[15]-=-,[29]. 21sThere are many applications which can be described with the help of the filter bank precoder configuration. If s(n) comes from a finite field and all the arithmetic operations in the filteri... |

129 |
The multitone channel
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Citation Context ... a practically flat power spectrum. A clever way to approximate optimal power allocation would be to divide the channel bandwidth into several subbands and transmit in each subband channel separately =-=[4,9]-=-. This already suggests a resemblance to frequency division multiplexing but the main difference now is that the different subband channels carry different parts of a single input stream. How this is ... |

103 |
Frequency domain data transmission using reduced computational complexity algorithms
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Citation Context ...iform DFT filter bank. The channel equalizer 1/C(z) can be approximated well in many ways. An indirect but effective way to perform equalization is to introduce redundancies such as the cyclic prefix =-=[13]-=-. The popularity of the DFT based DMT filter bank arises from the fact that if M is chosen as a power of two (e.g., M = 512 which is typical) the DFT can be implemented very efficiently using the fast... |

48 |
Understanding digital subscriber line technology
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Citation Context ...s from many disciplines such as information theory, signal processing, linear system theory, and mathematics. The role of digital signal processing in communication systems has been quite significant =-=[17,18,6]-=-. In 1 Work supported in parts by the NSF grant MIP 0703755 and ONR grant N00014-99-1-1002. 1sthis paper we emphasize some of these, especially the role of filter banks. The aim here is to give an ove... |

45 | G.B.Giannakis, “Principal component filter banks for optimal multiresolution analysis - Tsatsanis - 1995 |

38 |
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Citation Context ... such that the channel is completely equalized (i.e., the received signal r(n) is equal to s(n) in absence of channel noise e(n)). In fact the well known class of fractionally spaced equalizers (FSE) =-=[19]-=- is a special case of the filter bank precoder with M = 1 and uses N-fold redundancy. The fascinating fact about the filter bank precoder is that even if M = N − 1itis almost always possible to have s... |

37 |
Multirate Digital Signal Processing
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Citation Context ... to give an overview of filter banks as applied to digital communication systems. Filter banks were originally proposed for application in speech compression more than 25 years ago (see references in =-=[7]-=-). Today they are used for the compression of image, video, and audio signals, and the story of their success can be found in many references. More recently filter banks have been used in digital comm... |

36 | Orthogonal transmultiplexers in communications: a review
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Citation Context ...ory of their success can be found in many references. More recently filter banks have been used in digital communication systems in many forms. Some of these include perfect digital transmultiplexing =-=[26, 1]-=-, filter-bank precoding for channel equalization [29, 15], equalization with fractionally spaced sampling [28], and discrete multitone modulation [18, 21, 23]. Filter banks have been used in high spee... |

36 | New precoding for intersymbol interference cancellation using nonmaximally decimated multirate filter banks with ideal FIR equalizers
- Xia
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Citation Context ...re recently filter banks have been used in digital communication systems in many forms. Some of these include perfect digital transmultiplexing [26, 1], filter-bank precoding for channel equalization =-=[29, 15]-=-, equalization with fractionally spaced sampling [28], and discrete multitone modulation [18, 21, 23]. Filter banks have been used in high speed DSL services for internet traffic [6]. They have also b... |

34 |
Filter bank modulation techniques for very high speed digital subscriber lines
- Cherubini, Eleftheriou, et al.
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Citation Context ...s from many disciplines such as information theory, signal processing, linear system theory, and mathematics. The role of digital signal processing in communication systems has been quite significant =-=[17,18,6]-=-. In 1 Work supported in parts by the NSF grant MIP 0703755 and ONR grant N00014-99-1-1002. 1sthis paper we emphasize some of these, especially the role of filter banks. The aim here is to give an ove... |

24 | Filter banks for blind channel identification and equalization
- Giannakis
- 1997
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Citation Context ...discrete multitone modulation [18, 21, 23]. Filter banks have been used in high speed DSL services for internet traffic [6]. They have also been considered for blind equalization in wireless channels =-=[8, 16]-=-. 2. THE NOISY CHANNEL In this paper we model the communication channel as a linear time invariant system with transfer function C(z) followed by an additive Gaussian noise source e(n) as shown in Fig... |

16 | Perfect discrete multitone modulation with optimal transceivers - Lin, Phoong - 2000 |

16 |
Perfect transmultiplexer
- Vetterli
- 1990
(Show Context)
Citation Context ...ory of their success can be found in many references. More recently filter banks have been used in digital communication systems in many forms. Some of these include perfect digital transmultiplexing =-=[26, 1]-=-, filter-bank precoding for channel equalization [29, 15], equalization with fractionally spaced sampling [28], and discrete multitone modulation [18, 21, 23]. Filter banks have been used in high spee... |

11 |
Minimum redundancy for ISI free FIR filterbank transceivers
- Lin, Phoong
- 2002
(Show Context)
Citation Context ...ast L − 1 rows are repetitions of the first L −1 rows. This results in a scheme called the cyclic prefix explained in detail in [13]. Further interesting extensions and deeper results can be found in =-=[11]-=-. 11.1. Filter Bank Precoders In a DMT system the symbols xk(n) are obtained by parsing binary data s(n) as shown earlier in Fig. 8(a). Instead of this, imagine that the symbols xk(n) are obtained by ... |

9 | A review of the theory and applications of optimal subband and transform coders
- Vaidyanathan, Akkarakaran
- 2001
(Show Context)
Citation Context ...f error in detecting xk(n) can be expressed in terms of the signal power Pk, noise variance σ 2 qk , and number of bits bk. The exact expression can be found in many references (e.g., see [14], [23], =-=[24]-=-). The main point is that this expression can be inverted to obtain the total power in the symbols xk(n). The result takes the form [23–24] P = M−1 � k=0 Pk = M−1 � k=0 � � β Pe(k),bk × σ 2 qk where t... |

8 | Theory of MIMO biorthogonal partners and their application in channel equalization
- Vrcelj, Vaidyanathan
- 2001
(Show Context)
Citation Context ...ication systems in many forms. Some of these include perfect digital transmultiplexing [26, 1], filter-bank precoding for channel equalization [29, 15], equalization with fractionally spaced sampling =-=[28]-=-, and discrete multitone modulation [18, 21, 23]. Filter banks have been used in high speed DSL services for internet traffic [6]. They have also been considered for blind equalization in wireless cha... |

7 |
A discrete multitone transreceiver system for HDSL applications
- Chow, Tu, et al.
- 1991
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Citation Context ... separated by bT seconds if s(n) and s(n + 1) are separated by T seconds. Background material on the DMT system and more generally on the use of digital filter banks in communications can be found in =-=[1,5,9,21]-=-. The DMT idea is similar in principle to subband coding [7, 27, 22] where a signal x(n) to be quantized is first decomposed into subbands. 7. BIORTHOGONALITY AND PERFECT DMT SYSTEMS Consider a linear... |

7 | Discrete multitone modulation with principal component filter banks
- Vaidyanathan, Lin, et al.
- 2002
(Show Context)
Citation Context ... uses only about 5.67 milliwatts for the same performance! For DMT systems with larger number of bands, the difference is less dramatic. In fact for very large M the performances are nearly identical =-=[25]-=-. It turns out that for a monotone decreasing (or increasing) power spectrum the ideal PCFB is precisely the brickwall filter bank. For a power spectrum with many variations, especially bumps and dips... |

6 |
Optimalilty of principal component filter banks for discrete multitone communication systems
- Vaidyanathan, Lin, et al.
- 2000
(Show Context)
Citation Context ... required power P is minimized. The KLT offers the optimal DMT solution if we compare all orthonormal DMT systems with FIR filters of length ≤ M. The proof follows as a special case of the results in =-=[23,24]-=-. q(n) effective noise z z z M M M T q (n) 0 q (n) 1 q (n) M−1 Fig. 15. Noise model for the DMT filter bank,redrawn in terms of the transform matrix T. If T is the DFT matrix, then this is the noise m... |

5 |
Vaidyanathan,“Filterbank optimization with convex objectives and the optimality of principal component forms
- Akkarakaran, P
- 2001
(Show Context)
Citation Context ... For an arbitrary class C such as the class of FIR orthonormal filter banks with length constrained by some integer, the PCFB may not in general exist. The detailed theory of the PCFB is available in =-=[2]-=-, and a tutorial review can be found in [24]. Assume that the error probabilities and total allowed power are fixed. It can then be shown that the bit rate, which is proportional to � k bk, is maximiz... |

3 | Discrete multitone communication with principal component filter banks
- Akkarakaran, Vaidyanathan
- 2001
(Show Context)
Citation Context ...ortional to � k bk, is maximized by the PCFB. Similarly, with appropriate theoretical modelling the information capacity (for fixed total power) is also maximized by the PCFB. Details can be found in =-=[3]-=-, [23], [25]. pcfb other subband 0 subbands 0 and 1 subbands 0,1 and 2 all subbands Fig. 16. This figure schematically explains what a principal component filter bank (PCFB) does. The dark blue column... |

2 |
Design of a 24-channel transmultiplexer
- Narasimha, Peterson
(Show Context)
Citation Context ...d unblocking. Similarly deinterleaving is also called blocking. 5. THE DIGITAL TRANSMULTIPLEXER Our next step would be to describe the operation of a filter bank structure called the transmultiplexer =-=[12,26,22]-=-. It was originally intended to convert data between time division multiplexed (TDM) format and frequency division multiplexed (FDM) format. Figure 7(a) shows a schematic of this in all-discrete langu... |

2 |
Digital signal processing in telecommunications
- Shenoi
- 1995
(Show Context)
Citation Context ...s from many disciplines such as information theory, signal processing, linear system theory, and mathematics. The role of digital signal processing in communication systems has been quite significant =-=[17,18,6]-=-. In 1 Work supported in parts by the NSF grant MIP 0703755 and ONR grant N00014-99-1-1002. 1sthis paper we emphasize some of these, especially the role of filter banks. The aim here is to give an ove... |