DFT Filter Banks Research Articles

Sparse Sensing With Co-Prime Samplers and Arrays

This paper considers the sampling of temporal or spatial wide sense stationary (WSS) signals using a co-prime pair of sparse samplers. Several properties and applications of co-prime samplers are developed. First, for uniform spatial sampling with M and N sensors where M and N are co-prime with appropriate interelement spacings, the difference co-array has O(MN) freedoms which can be exploited in beamforming and in direction of arrival estimation. An M -point DFT filter bank and an N-point DFT filter bank can be used at the outputs of the two sensor arrays and their outputs combined in such a way that there are effectively MN bands (i.e., MN narrow beams with beamwidths proportional to 1/MN), a result following from co-primality. The ideas are applicable to both active and passive sensing, though the details and tradeoffs are different. Time domain sparse co-prime samplers also generate a time domain co-array with O(MN) freedoms, which can be used to estimate the autocorrelation at much finer lags than the sample spacings. This allows estimation of power spectrum of an arbitrary signal with a frequency resolution proportional to 2π/(MNT) even though the pairs of sampled sequences xc(NTn) and xc(MTn) in the time domain can be arbitrarily sparse - in fact from the sparse set of samples xc(NTn) and xc(MTn) one can estimate O(MN) frequencies in the range |ω| <; π/T. It will be shown that the co-array based method for estimating sinusoids in noise offers many advantages over methods based on the use of Chinese remainder theorem and its extensions. Examples are presented throughout to illustrate the various concepts.

Joint use of DFT filter banks and modulated transmultiplexers for multicarrier communications

In this paper, new procedures for performing multicarrier modulation (MCM) are presented, based on using IFFT/FFT embedded in a filter bank-based transmultiplexer system. The IFFT/FFT blocks, along with the use of cyclic prefix or zero-padding strategies, enable easy equalization of the transmission channel. Additionally, the transmultiplexer system provides improved spectral discrimination, which can increases the transceiver robustness against mainly narrow-band interferences. Moreover, one of the proposed procedures presents an IDFT as the final stage of the MCM transmitter, and a DFT as the first stage of the receiver. This front-end is similar to standardized systems, enabling its compatibility. As it is illustrated by means of several examples, given a signal to noise ratio and comparing the new procedures to DFT-based MCM adopted in several digital communications standards, the following attractive features can be found: (a) greater spectral separation in the information transmitted over each subcarrier and (b) the robustness of the systems in noisy environments, mainly when narrow-band interferences appear, can be increased, allowing a reduction in the bit error probability.

Low complexity flexible filter banks for uniform and non-uniform channelisation in software radios using coefficient decimation

A new approach to implement computationally efficient reconfigurable filter banks (FBs) is presented. If the coefficients of a finite impulse response filter are decimated by M, that is, if every Mth coefficient of the filter is kept unchanged and remaining coefficients are replaced by zeros, a multi-band frequency response will be obtained. The frequency response of the decimated filter will have bands with centre frequencies at 2πk/M, where k is an integer ranging from 0 to M−1. If these multi-band frequency responses are subtracted from each other or selectively masked using inherently low complex wide transition-band masking filters, different low-pass, high-pass, band-pass and band-stop frequency bands are obtained. The resulting FB, whose bands’ centre frequencies are located at integer multiples of 2π/M, is a low complexity alternative to the well-known uniform discrete Fourier transform FBs (DFTFBs). It is shown that the channeliser based on the proposed FB does not require any DFT for its implementation unlike a DFTFB. It is also shown that the proposed FB is more flexible and easily reconfigurable than the DFTFB. Furthermore, the proposed FB is able to receive channels of multiple standards simultaneously, whereas separate FBs would be required for simultaneous reception of multi-standard channels in a DFTFB-based receiver. This is achieved through a second stage of coefficient decimation. Implementation result shows that the proposed FB offers an area reduction of 41% and improvement in the speed of 50.8% over DFTFBs.

Efficient iterative design of modified DFT filter banks

An iterative algorithm based on the Lagrange multiplier method is presented for designing modified discrete Fourier transform (MDFT) filter banks with perfect reconstruction (PR). The dominant work at each iteration is to solve a system of linear equations involving a symmetric block matrix. By exploiting its special structure, the block matrix is factored into the product of lower and upper triangular matrices, thus leading to improved efficiency. The main benefit of the proposed scheme is that it allows the efficient design of PR MDFT filter banks with a large number of channels and/or long prototype filters.

Analysis and Properties of Time-Varying Modified DFT Filter Banks

We provide a comprehensive analysis of the time-varying modified DFT (MDFT) filter bank based on the general time-varying filter bank theories (Wang, 2005, 2006, 2008, 2009) in both the time domain and frequency domain. We give firstly the description of the time-invariant MDFT filter bank including its perfect reconstruction (PR) condition, its mechanism of aliasing error cancellation and the relationship with the cosine-modulated filter bank in detail. Then, the time-varying MDFT filter bank is analyzed according to the time-domain description. Finally, the window switching method is introduced to design the prototype filter in the time-varying MDFT filter bank with examples. The error analysis shows that the introduced design approach is useful in practice.

Least-Squares Design of DFT Filter-Banks Based on Allpass Transformation of Higher Order

The allpass transformation of higher order is a very general concept to construct a frequency warped analysis-synthesis filter bank (AS FB) with nonuniform time-frequency resolution. In contrast to the more common allpass transformation of first order, the delay elements of the analysis filter bank are substituted by allpass filters of higher order to achieve a more flexible control over its frequency selectivity. Known analytical closed-form designs for the synthesis filter bank can ensure perfect reconstruction (PR), but the synthesis subband filters are not necessarily stable and exhibit no distinctive bandpass characteristic. These problems are addressed by a new least-squares error (LSE) filter bank design. The coefficients of the finite-impulse-response (FIR) synthesis filters are determined simply by a linear set of equations where the signal delay is an adjustable design parameter. This approach can achieve a perfect signal reconstruction with synthesis filters which are inherently stable and feature a bandpass characteristic. The proposed filter bank is of interest for various subband processing systems requiring nonuniform frequency bands.

Optimized Paraunitary Filter Banks for Time-Frequency Channel Diagonalization

We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS) channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.

Comment on "Parity-Check Matrix Calculation for Paraunitary Oversampled DFT Filter Banks

In a previous paper, Karp, Kieffer, and Duhamel have presented three methods to calculate the parity-check matrix of paraunitary oversampled DFT filter banks. Here is another.

A New Flexible Filter Bank for Low Complexity Spectrum Sensing in Cognitive Radios

Conventional filter bank-based spectrum sensing methods employ uniform discrete Fourier transform filter bank (DFTFB). In this paper, we propose a multi-stage coefficient decimation filter bank (MS-CDFB) for wideband spectrum sensing in cognitive radios. From an initial fixed-coefficient modal filter, a filter bank that has multiple passbands of either uniform or different passband widths can be obtained using coefficient decimation. Design examples show that proposed MS-CDFB offers a complexity reduction of about 30% over the DFTFB while giving a superior sensing accuracy than the latter. The complexity reduction of MS-CDFB over the DFTFB is 85%, if both the spectrum sensors are designed to produce identical sensing accuracies.

A Novel Filter Bank Design Method with CEM FRM Technique

Modulation filter banks can be obtained by modulating one or two prototype filters, which reduce the design complexity of the filter banks. Furthermore, this kind of filter can be realized by using DFT or FFT with very high computationally efficiency. The proposition of a modulation filter bank reduces the computation complexity of designing the filter bank consumedly, which has very high computation efficiency. However, with the increasing of channels, the request for transition of the prototype filter is very high. This makes the length of the prototype filter longer, which decreases the computation efficiency. Frequency-response masking technique, which was proposed by Lim in 1986, is a very efficient way for designing the sharp transition filter. It is composed of three sub-filters and a delay chain. The basic thought is designing a low complexity filter before compressing its frequency response, and then eliminating the useless periodic images of the prototype filter and its compensation filter by two masking filters. The complexity of the FRM filter can also be reduced by modifying its architecture. According to it, the paper deduces a Novel FRM low-pass filter based on Complex Exponential Modulation (CEM). The deduced filter is very suitable to the multi-rate digital signal process, apart from applying a single rate digital signal process. In the application of software defined radio, the most bandwidth needs to be separated because it may has many narrowband channels. The need is very stringent for the filter to attenuate the closer channels. The filter banks encounter a main problem when it is used to separate channels, which is that the prototype filter must be a sharp transition bandwidth filter. Furthermore, the length of the prototype filter becomes longer in the DFT filter banks when the number of sub-filters is large and the transition band is very sharp. So it is very important to use a high efficiency digital filter, which can reduce the number of coefficient observably. Based on the advantage of deduced novel low-pass filter, the paper proposes a new analysis filter bank architecture, which makes use of the high efficiency low-pass filter as a prototype filter. So it can decrease the computation complexity consumedly when the transition bandwidth of prototype filter is especially very sharp. It is the same with the alterable bandwidth system. At last, an eight channels filter bank design example is used to illustrate its feasibility. It reduces the computationally complexity of the sharp transition filter by using a CEM FRM prototype filter. At last, an application example has been given to illustrate the design of analysis filter banks, showing that the resulting filter bank reduces the computation complexity, which adapt to use in engineering implementation.

Design of a new DFT filter bank with modified sampling kernels and its application to arbitrary image scaling

Design of a new DFT filter bank with modified sampling kernels and its application to arbitrary image scaling

Harmonic power detection in wideband cognitive radios

An analysis for simultaneous sensing of multiple primary user activity in cognitive radios has been presented here from a signal-processing perspective. First, the drawbacks of using simple harmonic power detection in wideband cognitive radios is demonstrated. Then, the impact of preprocessing the received signal to improve detection performance is highlighted along with its tradeoff involving complexity and corresponding delays in cognitive radio networks. It has been shown that a polyphase DFT filter bank with an optimal window as prototype filter can lead to reliable as well as efficient sensing and detection architecture in cognitive radios with minimal overhead. A detailed account of challenges, performance limits and computational complexity comparisons for various spectrum-sensing solutions is also provided. The study is supported through simulations with parameters corresponding to the IEEE 802.22 standard.

Design of prototype filters for perfect reconstruction DFT filter bank transceivers

In recent years, multicarrier modulation techniques have stirred great interest among researchers. One specific form of multicarrier modulation, referred to as orthogonal frequency division multiplexing (OFDM), has been deployed in many applications. Despite their huge popularity, OFDM systems have a few, but important, drawbacks. In particular, OFDM relies on the inverse fast Fourier transform (FFT) for modulation purposes, which leads to a poor spectral containment and, consequently, to a high susceptibility to narrowband noise. To mitigate this problem, we propose to employ over-interpolated perfect reconstruction (PR) discrete Fourier transform (DFT) filter banks. The design of such filter banks is addressed using a novel method that guarantees the PR property to be satisfied while the spectral containment is being maximized. The equalization of frequency-selective channels exploits the fact that the filter banks do not contribute to any distortion due to its PR nature. A simple scheme, taking the form of an one-tap per subcarrier equalizer, is considered. Experimental results indicate that the spectral containment of the proposed PR DFT filter bank transceiver is indeed superior to the OFDM system. Moreover, simulations conducted in a digital subscriber line (DSL)-like environment contaminated by a narrowband noise show that the achievable bit rate of the proposed transceiver is significantly higher than that of a conventional OFDM system.

On the Optimization of Oversampled DFT Filter Banks

We use the general formula of the synthesis window of the oversampled discrete Fourier transform filter bank in terms of the minimum-norm solution and the null space of the perfect reconstruction condition matrix to optimize the window design. We give closed-form solutions to different optimization criteria, e.g., minimum out-of-band power, minimum quantization-error, and minimum window order

Arbitrary scaling of images using an M-channel DFT filter bank with optimized adaptive interpolation kernels

A new approach to arbitrary scaling of high quality images is proposed, whereby a 2-D M-channel DFT filter bank is designed along with its synthesis part being modified on the basis of a compactly supported sampling function. For that purpose, the 2-D down/up-sampling formulae in a closed form are derived and utilized. Also, an optimized adaptive interpolation technique is employed to compensate for quality degradation arising in scaled images. Finally, simulation results demonstrate that high quality images of arbitrary size can be obtained from the original image.

Application of uniform DFT filter bank in radar jamming system

The principle of uniform DFT filter bank is presented. Exploiting poly-phase structure, radar jamming system samples the intercepted wideband radar signals through analysis filter bank by different channels and linearly modulates the intercepted radar signal according to the theory of signal and system, then synthesizes the jamming signal through the synthesis filter bank. The method merely requires lower sample frequency, reduces the computational complexity and the data quantity to be processed. The un-ideal filter's influence to the result of signals processing is analyzed by simulating the match filter in radar jamming system.

An efficient digital implementation of multicarrier CDMA system based on generalized DFT filter Banks

In this paper, an efficient digital implementation of multicarrier transmission scheme based on generalized discrete Fourier transform (DFT) filter banks is presented for multicarrier code-division multiple-access (MC-CDMA) systems. Generalized DFT filter banks has been traditionally discussed for very high-speed digital subscriber lines (VDSL) wireline systems, received interest also for wireless applications. The design of the generalized DFT modulated filter banks is investigated and its fast implementation is derived in the time-domain for arbitrary integer sampling rate. Through the utilization of the generalized DFT modulated filter banks, one or more subcarriers, even noncontiguous subcarriers can be easily supported by system in both uplink and downlink, which facilitates the users to access the network in a frequency-division multiple-access manner. Simulation results show that the overall bit-error-rate performance of the proposed multicarrier transmission scheme well approaches that of a single-carrier system due to the negligible intercarrier interference introduced by an appropriate design of the generalized DFT modulated filter banks.

Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks

The recently introduced exponentially modulated filter bank (EMFB) is a -channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR) property if the prototype filter of an -channel PR cosine modulated filter bank (CMFB) is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT) type of implementation solutions are studied. The ELT-based EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs) when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems.

A hybrid method for the design of oversampled uniform DFT filter banks

Subband adaptive filters have been proposed to speed up the convergence and to lower the computational complexity of time domain adaptive filters. However, subband processing causes signal degradations due to aliasing effects and amplitude distortions. This problem is unavoidable due to further filtering operations in subbands. In this paper, the problem of aliasing effect and amplitude distortion is studied. The prototype filter design problem is formulated as a multi-criteria optimization problem and all the Pareto optima are sought. Since the problem is highly nonlinear and nonsmooth, a new hybrid optimization method is proposed. Different prototype filters are used and their performances are compared. Moreover, the effect of the number of subbands, the oversampling factors and the length of prototype filter are also studied. We find that prototype filters designed via Kaiser or Dolph–Chebyshev window provide the best overall performance. Also, there is a critical oversampling factor beyond which the improvement in performance is not justified. Finally, if the length of the prototype filter increases with the number of subbands, an increase in the subband level will not deteriorate the performance.

A systematic technique for designing linear-phase FIR prototype filters for perfect-reconstruction cosine-modulated and modified DFT filterbanks

This paper describes a systematic technique for designing prototype filters for generating perfect-reconstruction (PR) orthogonal cosine-modulated and modified discrete Fourier transform filterbanks. In the proposed design scheme, the stopband energy of the prototype filter is minimized, and the basic unknowns are the angles of a special lattice structure used for implementing the prototype filter so that the PR property is automatically satisfied independent of the angle values. This selection of the unknowns makes the overall optimization problem unconstrained. Due to the fact that there are several local optima, the design is performed in multiple steps in order to arrive at least at a very good suboptimal solution. First, for the given number of channels, the length of the channel filters, and the stopband edge of the prototype filter, the corresponding two-channel filterbank is designed based on the preoptimized data. Then, after knowing the angles for the optimized two-channel case, the prototype filter for the desired filterbank is generated by gradually increasing the number of channels and by properly using the result of the previous step as a start-up solution for the present step. The main benefit of the proposed design technique is that it enables one to effectively design prototype filters for filterbanks with very high-order analysis and synthesis filters.