DFT Filter Banks Research Articles

Analysis of quantization errors in subband speech coding with modified DFT filter banks

The modified DFT filter bank is a highly efficient pseudo-QMF filter bank with almost perfect reconstruction, which is introduced in [N.J. Fliege, Modified DFT polyphase SBC filter banks with almost perfect reconstruction, in: Proceedings of the ICASSP, Australia, April 1994, vol. 3, pp. 149–152] and discussed in [N.J. Fliege, Computational efficiency of modified DFT-polyphase filter banks, in: Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, Asilomar, USA, November 1993; T. Karp, N.J. Fliege, MDFT filter bank with perfect reconstruction, in: Proceedings of the IEEE International Symposium on Circuits and System, Seattle, USA, May 1995]. Because of its comparable computational efficiency with cosine modulated filter banks and almost perfect reconstruction at the critical sampling rate, the MDFT filter bank can be used in subband speech coding. This paper aims at a theoretical analyses of the quantization errors in the subband speech coding with MDFT filter banks, and discusses how to design the prototype filter for an MDFT filter bank in order to minimize the quantization errors. A simplified and suboptimal procedure for the design of the prototype filter is presented.

Application of DFT filter bank to power frequency harmonic measurement

The paper presents a discrete-Fourier-transform (DFT) filter bank for power-system harmonic measurement. It has the ability to measure harmonic contents in time and frequency domains, and is ideal for long-term of observation harmonics. It can also overcome shortcomings of the windowed fast-Fourier-transform (FFT) algorithm. The subject of the DFT filter bank is closely related to multi-rate digital-signal-processing (DSP) technique. Hence, this method using the multi-rate technique is very efficient. Finally, an actual field test is implemented to measure power-frequency harmonics.

Iterative Method for the Design of DFT Filter Bank

Multirate adaptive filters have numerous advantages such as low computational load, fast convergence, and parallelism in the adaptation. Drawbacks when using multirate processing are mainly related to aliasing and reconstruction effects. These effects can be minimized by introducing appropriate problem formulation and employing sophisticated optimization techniques. In this paper, we propose a formulation for the design of a filter bank which controls the distortion level for each frequency component directly and minimizes the inband aliasing and the residual aliasing between different subbands. The advantage of this problem formulation is that the distortion level can be weighted for each frequency depending on the particular practical application. A new iterative algorithm is proposed to optimize simultaneously over both the analysis and the synthesis filter banks. This algorithm is shown to have a unique solution for each iteration. For a fixed distortion level, the proposed algorithm yields a significant reduction in both the inband aliasing and the residual aliasing levels compared to existing methods applied to the numerical examples.

On the Compensation of Delay in the Discrete Frequency Domain

The ability of a DFT filterbank frequency domain filter to effect time domain delay is examined. This is achieved by comparing the quality of equalisation using a DFT filterbank frequency domain filter with that possible using an FIR implementation. The actual performance of each filter architecture depends on the particular signal and transmission channel, so an exact general analysis is not practical. However, as a benchmark, we derive expressions for the performance for the particular case of an allpass channel response with a delay that is a linear function of frequency. It is shown that a DFT filterbank frequency domain filter requires considerably more degrees of freedom than an FIR filter to effect such a pure delay function. However, it is asserted that for the more general problem that additionally involves frequency response magnitude modifications, the frequency domain filter and FIR filters require a more similar number of degrees of freedom. This assertion is supported by simulation results for a physical example channel.

DSP Algorithms for On-Board Satellite Transmultiplexer and Receiver

This paper presents computationally efficient algorithms for a Digital Signal Processor (DSP) implementation of transmultiplexers, timing and carrier recovery, and detection of data for on-board satellite receiver. The transmultiplexer which generates a time domain sequence of a Frequency Division Multiplexed (FDM) signal is implemented using DFT filter banks. Carrier and timing recovery and data detection are implemented assuming no training sequence. It is very important to design efficient algorithms to perform these tasks so that computational requirements are kept to a minimum thereby saving power.The paper proposes a novel 4th power based algorithm to determine the carrier offset. It is based on the idea that if there are P samples per symbol, then one of them is closer to the ideal Nyquist sampling instant than others, and, has the least ISI. A recursive method to isolate this minimum-ISI sample is proposed. This sample is used to estimate the carrier phase. Since the method identifies the least ISI sequence, it is said to perform both the carrier and timing offset estimation. After compensating for constant frequency offset, timing recovery is performed using a modified Peak Average Energy Criterion (PAEC) algorithm. A Digital Phase Locked Loop (DPLL) is used to track the finer variation in frequency offset.Results of simulations evaluating performance of these algorithms are presented for a number of frequency and timing offset situations. It is seen that the computational load is maximum at “start-up”. We have proposed a particular start-up scheme and calculated its peak computational load in Millions of Instructions per second (MIPs).

A Hybrid Subband Adaptive System for Speech Enhancement in Diffuse Noise Fields

Performance of adaptive noise cancellation (ANC) degrades severely when uncorrelated noise components are present at the two inputs. Thus, practical background diffuse noises pose a serious problem for ANC systems. In this letter, we propose a new hybrid system that integrates subband adaptive filters (SAFs) and a Wiener filter. The hybrid system is implemented on an oversampled DFT filterbank that efficiently integrates the SAF and the Wiener filter components in the frequency-domain. Performance evaluation of the hybrid system in presence of diffuse noise interference shows that the proposed system is superior to both the Wiener filter and the SAF subsystems.

Design ofM-Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M-channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop-band attenuation, which is also taken care of in the proposed algorithm.

Filterbank design for oversampled subband adaptive filtering structures

A simple design procedure for uniform DFT filterbanks used in oversampled subband adaptive filtering structures is presented. The analysis prototype filter is designed with extended bandwidth to obtain fast convergence. The synthesis prototype filter is then optimised to reduce the mean square error. The resulting improvements in the convergence performance are verified through computer simulations.

Filter bank design for subband adaptive microphone arrays

This paper presents a new method for the design of oversampled uniform DFT-filter banks for the special application of subband adaptive beamforming with microphone arrays. Since array applications rely on the fact that different source positions give rise to different signal delays, a beamformer alters the phase information of the signals. This in turn leads to signal degradations when perfect reconstruction filter banks are used for the subband decomposition and reconstruction. The objective of the filter bank design is to minimize the magnitude of all aliasing components individually, such that aliasing distortion is minimized although phase alterations occur in the subbands. The proposed method is evaluated in a car hands-free mobile telephony environment and the results show that the proposed method offers better performance regarding suppression levels of disturbing signals and much less distortion to the source speech.

Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel.

Design of low‐delay perfect‐reconstruction filter banks using linear programming

AbstractIn many applications of filter banks, a low‐delay filter bank in which the system delay is small is desirable. In this paper, two new design methods are proposed for low‐delay perfect‐reconstruction filter banks. First, a design method is described for a two‐channel perfect‐reconstruction filter bank suitable for subband coding. In this method, a high‐pass filter for perfect reconstruction is designed for an arbitrary low‐pass filter. Next, a design method is described for an oversampling perfect‐reconstruction DFT filter bank suitable for subband adaptive filter. In this method, a prototype filter for a perfect‐reconstruction synthesizer is designed for the prototype filter for an arbitrary analyzer. The effectiveness of the present method is demonstrated by design examples. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(6): 30–39, 2001

Adaptive array processing for multipath fading mitigation via exploitation of filter banks

We propose subband adaptive array processing for mitigation of both intersymbol interference (ISI) and cochannel interference (CCI) in digital mobile communications. Subband adaptive array processing employs filter banks in a front end to an adaptive array receiver. By decomposing the signals into a set of subband signals, the analysis filters enhance the correlation of multipath rays in each subband. This enhancement is blind in the sense that no a priori knowledge of the temporal characteristics or spatial signatures of arriving signals is required. With the increased coherence, the desired signal can be effectively equalized by subsequent spatial processing. Further, the CCI signals and their multipaths can be suppressed with fewer degrees of freedom. The effects of quadrature mirror filter and discrete Fourier transform filter banks on multipath correlation are delineated.

Filterbank optimization with convex objectives and the optimality of principal component forms

This paper proposes a general framework for the optimization of orthonormal filterbanks (FBs) for given input statistics. This includes as special cases, many previous results on FB optimization for compression. It also solves problems that have not been considered thus far. FB optimization for coding gain maximization (for compression applications) has been well studied before. The optimum FB has been known to satisfy the principal component property, i.e., it minimizes the mean-square error caused by reconstruction after dropping the P weakest (lowest variance) subbands for any P. We point out a much stronger connection between this property and the optimality of the FB. The main result is that a principal component FB (PCFB) is optimum whenever the minimization objective is a concave function of the subband variances produced by the FB. This result has its grounding in majorization and convex function theory and, in particular, explains the optimality of PCFBs for compression. We use the result to show various other optimality properties of PCFBs, especially for noise-suppression applications. Suppose the FB input is a signal corrupted by additive white noise, the desired output is the pure signal, and the subbands of the FB are processed to minimize the output noise. If each subband processor is a zeroth-order Wiener filter for its input, we can show that the expected mean square value of the output noise is a concave function of the subband signal variances. Hence, a PCFB is optimum in the sense of minimizing this mean square error. The above-mentioned concavity of the error and, hence, PCFB optimality, continues to hold even with certain other subband processors such as subband hard thresholds and constant multipliers, although these are not of serious practical interest. We prove that certain extensions of this PCFB optimality result to cases where the input noise is colored, and the FB optimization is over a larger class that includes biorthogonal FBs. We also show that PCFBs do not exist for the classes of DFT and cosine-modulated FBs.

Simple design of oversampled uniform DFT filter banks with applications to subband acoustic echo cancellation

Subband adaptive filtering, which is the basis of modern acoustic echo cancellation (AEC) systems, is an important application of filter banks in which critical sampling cannot be used in general because of decimation aliasing effects. This leads to the use of oversampling schemes in the filter bank design wherein the perfect-reconstruction (PR) or near PR property is still required. In this work, a simple design technique for uniform DFT filter bank with near PR property is presented for the purpose of subband adaptive filtering. The prototype filter in the proposed filter banks is derived simply by performing an interpolation of a two-channel QMF filter, which can be obtained easily by computation or table look-up. An efficient implementation of the filter banks based on a weighted-overlap-add structure is described that allows flexibility in oversampling. The filter bank design technique presented in this paper is of particular interest in engineering applications, as demonstrated by design examples and experimental results in a real-time subband AEC application.

Design of stable, causal, perfect reconstruction, IIR uniform DFT filter banks

Design procedures for stable, causal and perfect reconstruction IIR parallel uniform DFT filter banks (DFT FBs) are presented. In particular a family of IIR prototype filters is a good candidate for DFT FB, where a tradeoff between frequency selectivity and numerical properties (as measured by the Weyl-Heisenberg frames theory) could be made. Some realizations exhibiting a simple and a massively parallel and modular processing structure making a VLSI implementation very suitable are shown. In addition, some multipliers in the filters (both the analysis and synthesis) could be made; powers or sum of powers of 2, in particular for feedback loops, resulting in a good sensitivity behavior. For these reasons as well as for the use of low order IIR filters (as compared with conventional FIR filters), the overall digital filter bank structure is efficient for high data rate applications. Some design examples are provided.

Software radio issues in cellular base stations

The use of the "software radio" concept in cellular applications is a topic of widespread interest. Two key issues in the implementation of software radios are the development of optimal receivers that require the minimum number of bits in the wide-band analog-to-digital converter (ADC) and efficient channelizers that extract individual channels from the digitized wide-band signal. In this paper, both of these issues are studied in detail for cellular base stations. A computationally efficient wide-band channelizer is presented. This channelizer is closely related to the discrete Fourier transform filter bank used in transmultiplexers. It is shown that the complexity of the proposed channelizer is significantly less (2-50/spl times/) than the complexity of conventional channelizers. An optimal receiver that explicitly takes into account the effect of the quantization noise of the wide-band ADC is also derived. The analysis of the ADC noise provides guidelines for specifying wide-band ADC for use in cellular applications. The development of the channelizer and the optimal receiver yield important insights into the implementation of cellular software radios. All of the key results of this paper are applied to a detailed example based on the Digital Advanced Mobile Phone System (D-AMPS, IS-54/IS-136) cellular standard. The bit-error rate (BER) performance simulations of a D-AMPS wide band receiver is presented as a part of this example.

Design of a family of stable causal perfect-reconstruction IIR uniform DFT filter banks with good numerical properties

A family of stable causal perfect reconstruction (PR) infinite-impulse response (IIR) discrete Fourier transform filter banks is presented, where a tradeoff between frequency selectivity and numerical properties is made. Some multipliers in both the analysis and synthesis filters could be made powers or sums of powers of two, in particular for feedback loops. Moreover, a simple scaling procedure that results in good sensitivity behavior is described. For these reasons, and also for the use of low-order IIR filters, the overall digital filter-bank structure is efficient for high data-rate applications. A design example, including quantization effects, is provided.

Modified DFT filter banks with perfect reconstruction

In this paper, essential features of the recently introduced modified discrete Fourier transform DFT (MDFT) filter bank are presented. First, it is shown that all analysis and synthesis filters-obtained by appropriate complex modulation of a low-pass prototype filter-are linear phase. This is important for subband image coding applications. Another important property is the structure-inherent alias cancellation: all odd alias spectra are automatically compensated in the synthesis filter bank. Further, the MDFT filter bank provides perfect reconstruction for the same prototypes as for cosine-modulated filter banks. Thus, the same design methods can be used. Finally, different mappings of the input signal into the subbands are discussed and a comparison to the well-known cosine-modulated filter banks is given.

Oversampled cosine modulated filter banks with perfect reconstruction

Oversampled filter banks (FBs) offer more design freedom and better noise immunity than critically sampled FBs. Due to the increased computational complexity caused by oversampling, oversampled FBs allowing an efficient implementation, such as cosine modulated filter banks (CMFBs), are of particular interest. So far, only critically sampled CMFBs have been considered. In this paper, we introduce oversampled CMFBs with perfect reconstruction (PR). Extending a classification of CMFBs recently proposed by Gopinath, we consider two types of oversampled CMFBs with PR. One of these types allows linear phase filters in all channels, and comprises CMFBs recently introduced by Lin and Vaidyanathan as well as Wilson-type CMFBs. For both types of oversampled CMFBs, we formulate PR conditions in the time, frequency, and polyphase domains. It is shown that any PR CMFB corresponds to a PR DFT FB with twice the oversampling factor and that (under a specific condition) the same PR prototype can be used for both CMFB types. We also show that the frame-theoretic properties of a CMFB and of the corresponding DFT FB are closely related. In particular, it is demonstrated that the minimum-norm synthesis prototype in an oversampled PR CMFB equals that in the corresponding DFT FB. Finally, we briefly address design methods and the efficient DCT/DST-based implementation of oversampled CMFBs.

Stable, causal, perfect reconstruction, IIR uniform DFT filter banks

A simple design procedure for stable, causal and perfect reconstruction infinite impulse response parallel uniform discrete Fourier transform filter banks (DFT FBs) based on a new polyphase decomposition, the ‘polyphase-oversampled’ FB, is presented. The proposed design results in causal and stable analysis and synthesis filters that are all derived from a single prototype filter, resulting in efficient realisations. A discussion of the FB numerical properties and some design examples are provided.