Modified DFT Filter Banks Research Articles

Voice Analysis and Classification System Based on Perturbation Parameters and Cepstral Presentation in Psychoacoustic Scales

The paper describes an approach to design a system for analyzing and classification of a voice signal based on perturbation parameters and cepstral representation. Two variants of the cepstral representation of the voice signal are considered: based on mel-frequency cepstral coefficients (MFCC) and based on bark-frequency cepstral coefficients (BFCC). The work used a generally accepted approach to calculating the MFCC based on the time-frequency analysis by the method of discrete Fourier transform (DFT) with summation of energy in subbands. This method approximates the frequency resolution of human hearing, but has a fixed temporal resolution. As an alternative, a variant of the cepstral representation based on the BFCC has been proposed. When calculating the BFCC, a warped DFT-modulated filter bank was used, which approximates the frequency and temporal resolution of hearing. The aim of the work was to compare the effectiveness of the use of features based on the MFCC and BFCC for the designing systems for the analysis and classification of the voice signal. The results of the experiment showed that in the case when using acoustic features based on the MFCC, it is possible to obtain a voice classification system with an average recall of 80.6 %, and in the case when using features based on the BFCC, this metric is 83.7 %. With the addition of the set of MFCC features with perturbation parameters of the voice, the average recall of the classification increased to 94.1 %, with a similar addition to the set of BFCC features, the average recall of the classification increased up to 96.7 %.

Research of application of DFT-modulated filter bank in systems with significant spectral component amplification

The purpose of this article is to investigate the application of DFT-modulated filter bank in systems with significant spectral component amplification like hearing aid. There is a description of analysis / synthesis method based on short-time Fourier transform (STFT), which is used in most systems of speech information processing. It is shown that DFT-modulated filter bank is a generalization of STFT-method. In analysis / synthesis system based on DFT-modulated filter bank, the input signal is divided into subbands, passing through the analysis filter bank then each subband is amplified and the last step is to reconstruct the signal with synthesis filter bank. However, in digital systems with significant spectral component amplification, the resulting signal is distorted after reconstruction because of amplification factor difference in each subband. The article provides expressions for the distortion and the aliasing functions, allowing to estimate the distortion value, which appears in analysis / synthesis system of DFT-modulated filter bank. Efficient algorithms for calculating the distortion and the aliasing functions are also offered. In future it is planning to develop a procedure for optimizing the DFT-modulated filter bank based on the proposed efficient algorithms for calculating distortion and spectral aliasing in the filter bank.

Adaptive Time-Frequency Analysis for Noise Reduction in an Audio Filter Bank With Low Delay

In this paper, an adaptive time-frequency analysis scheme is proposed along with a synthesis scheme using an asymmetric window. The proposed scheme is suitable for audio noise reduction with a low delay in the range of 0 to 4 ms. The main novelty of the paper is the adaptive analysis scheme that can adapt to the incoming signal independently in both time and frequency by employing a complex filter on a DFT modulated filter bank. A number of adaptive time-frequency schemes are described that are suitable for low delay and low computational complexity. The adaptive time-frequency scheme is used for the computation of noise reduction gain factors, which are then adopted in a nonadaptive analysis/synthesis scheme. The synthesis scheme uses an asymmetric window to achieve a good tradeoff between low delay and a sharp frequency response. Examples are given of the adaptive analysis and measurements of the synthesis scheme are given to show that the filter bank has a gain dependent nonlinear phase response. Finally, a noise reduction task is performed that shows good performance compared to reference implementations in terms of segmental SNR and PESQ.

Design of FRM-based MDFT filter banks in the canonic signed digit space using modified meta-heuristic algorithms

An optimal totally multiplier-less sharp transition width Modified Discrete Fourier Transform (MDFT) filter bank is proposed in this work. Since, here, the aim is to design a low complexity sharp transition width MDFT filter bank, the filters of the filter bank are designed using Frequency Response Masking technique to reduce the number of multipliers and hence the complexity. To replace multipliers with adders and shifters, the filter coefficients are converted into the Canonic Signed Digit space. In order to reduce the number of adders and shifters in the multiplier-less implementation, restricted number of non-zero bits is used in the conversion. This may degrade the performances of the MDFT filter bank. The performances are improved using modified meta-heuristic algorithms. A new hybrid algorithm which combines the qualities of Harmony Search Algorithm and Gravitational Search Algorithm is proposed in this work to optimise the performance of the MDFT filter bank.

Theory and design of two-dimensional DFT modulated filter bank with arbitrary modulation and decimation matrices

It is well known that two-dimensional (2D) filter bank is far removed from a straightforward extension of one-dimensional (1D) filter bank. There are many challenging problems on the theory and design methods for the 2D filter bank. Among these problems, the perfect-reconstruction (PR) theory of the 2D DFT modulated filter bank with arbitrary modulation and decimation matrices remains an unsolved difficulty, which is the focus of this paper. The necessary and sufficient condition for perfect reconstruction (PR) is derived by using the polyphase decomposition of the analysis and synthesis filters, as well as the fast implementation structure of the filter bank. Then, the PR condition in frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF), which is utilized to formulate the design problem into an unconstrained optimization problem. An efficient iterative algorithm is proposed to solve the problem. Numerical examples are included to verify the validity of the PR condition and the effectiveness of the design method.

Design of low complexity sharp MDFT filter banks with perfect reconstruction using hybrid harmony-gravitational search algorithm

The design of low complexity sharp transition width Modified Discrete Fourier Transform (MDFT) filter bank with perfect reconstruction (PR) is proposed in this work. The current trends in technology require high data rates and speedy processing along with reduced power consumption, implementation complexity and chip area. Filters with sharp transition width are required for various applications in wireless communication. Frequency response masking (FRM) technique is used to reduce the implementation complexity of sharp MDFT filter banks with PR. Further, to reduce the implementation complexity, the continuous coefficients of the filters in the MDFT filter banks are represented in discrete space using canonic signed digit (CSD). The multipliers in the filters are replaced by shifters and adders. The number of non-zero bits is reduced in the conversion process to minimize the number of adders and shifters required for the filter implementation. Hence the performances of the MDFT filter bank with PR may degrade. In this work, the performances of the MDFT filter banks with PR are improved using a hybrid Harmony-Gravitational search algorithm.

Fast design of 2D fully oversampled DFT modulated filter bank using Toeplitz-block Toeplitz matrix inversion

This letter presents a low-complexity algorithm to design two-dimensional (2D) DFT modulated filter bank (DMFB) with nearly perfect reconstruction (NPR). The design problem is formulated into an unconstrained optimization problem whose cost function consists of the overall distortion and stopband energy. By exploiting the gradient information, the prototype filter (PF) coefficients are iteratively optimized with closed-form formula. At each iteration, the computational complexity is dramatically reduced by evoking Toeplitz-block Toeplitz matrix inversion and matrix inversion lemma, which makes the algorithm suitable for design 2D DMFB with a large number of channels and PF coefficients. Numerical example and comparison are included to show the effectiveness of the proposed design algorithm.

Elaborate analysis and design of filter-bank-based sensing for wideband cognitive radios

The successful operation of a cognitive radio system strongly depends on its ability to sense the radio environment. With the use of spectrum sensing algorithms, the cognitive radio is required to detect co-existing licensed primary transmissions and to protect them from interference. This paper focuses on filter-bank-based sensing and provides a solid theoretical background for the design of these detectors. Optimum detectors based on the Neyman-Pearson theorem are developed for uniform discrete Fourier transform (DFT) and modified DFT filter banks with root-Nyquist filters. The proposed sensing framework does not require frequency alignment between the filter bank of the sensor and the primary signal. Each wideband primary channel is spanned and monitored by several sensor subchannels that analyse it in narrowband signals. Filter-bank-based sensing is proved to be robust and efficient under coloured noise. Moreover, the performance of the weighted energy detector as a sensing technique is evaluated. Finally, based on the Locally Most Powerful and the Generalized Likelihood Ratio test, real-world sensing algorithms that do not require a priori knowledge are proposed and tested.

Efficient design of very large‐scale DFT modulated filter banks using M th band condition

This study presents several new properties of the discrete Fourier transform (DFT) modulated filter banks and efficient algorithm for designing the filter banks with very large-scale (with a very large number of subbands and very long filters). For DFT modulated filter bank, the authors derive the symmetric property of the overall transfer function and aliasing transfer functions which can be efficiently calculated by using the orthogonal property of the DFT matrix. By invoking the M th band condition and new property, an efficient algorithm is proposed to design DFT modulated filter banks. The convergence of the algorithm is also proved. Several numerical examples and comparison with the conventional methods are included to show the effectiveness of the proposed algorithm.

Performance Comparison of MDFT Filter Bank with OFDM in Multi-Carrier Systems

Based on the filter bank, the theory of multi-carrier modulation using Orthogonal Frequency Division Multiplexing (OFDM) and Modified Discrete Fourier Transform (MDFT) filter bank has been discussed and the detailed derivation process has been given. Following these discussions, the actual implementation of MDFT filter bank in multi-carrier modulation systems has been discussed, and then the comparison of their prototype functions, Peak to Average Power Ratio (PAPR) and Symbol Error Rate (SER) are drawn. Experimental results demonstrate that compared with the OFDM system, prototype functions of MDFT have obvious advantage in spectrum leakage. In terms of PAPR, they have similar performance. Whether using QPSK or 16QAM modulation, MDFT is superior to OFDM in symbol error rate as a whole and with increasing of filter length L, the advantage becomes more and more apparent.

Time-domain modified DFT modulated filter banks for multi-carrier transceiver systems

A time domain designing method is proposed for discrete Fourier transform (DFT) modulated filter banks (DFT-FBs) for application in multi-carrier transceiver systems. Instead of using the time-reversed pair limitation between the transmitting /receiving filter pair, the receiving filters in the proposed filter banks are derived from transmitting filters in accordance with the Moore-Penrose generalized inverse matrix. It can be freely obtained to design the transmitting prototype filter, which mainly affects the level of spectral containment. Furthermore, the symbol error rate (SER) performance of the proposed filter bank based trans-multiplexer with one tap equalizer is investigated in ideal channel and multi-path channel environments respectively. Simulation shows that the proposed approach can achieve significant SER reductions when square root raised cosine (RRC) prototype filter is used for comparing with the orthogonal frequency division multiplexing (OFDM) and the general DFT-FBs based applications.

Design of Multiplier-less Sharp Transition Width MDFT Filter Banks using Modified Metaheuristic Algorithms

The significant advantage of modified discrete Fourier transform (MDFT) filter banks over the conventional discrete Fourier transform (DFT) filter banks is the structure inherent alias cancellation in the former. When the number of channels is increased, the filters in the filter bank need to be of sharp transition width. This increases the complexity of the filters and hence that of the filter bank. Frequency Response Masking (FRM) approach is known to reduce the complexity of sharp transition width filters. This paper proposes a method to realize MDFT filter banks using FRM with much lesser complexity. To further reduce the complexity, the filter banks are made totally multiplier-less. This is done by converting the coefficients to the canonic signed digit (CSD) representation. Metaheuristic algorithms are used to improve the performance of the CSD represented filter banks. Modified integer coded genetic algorithm, differential evolution, artificial bee colony, harmony search and gravitational search algorithms are proposed to be used for the optimization of the proposed multiplier-less MDFT filter banks. This design method reduces the complexity, power consumption and chip area for the implementation of the uniform filter banks.

Design of two‐dimensional large‐scale DFT‐modulated filter bank

This study presents a novel property of the two-dimensional DFT-modulated filter bank and an efficient algorithm for designing the filter bank with large scale (with a large number of subbands and filters of large spatial support). It is firstly shown that the overall transfer function and aliasing transfer functions can be simply represented with the multiplication of the prototype filters and their modulated filters; a new property used to remarkably reduce the calculation of these functions. On the other hand, the design problem of the filter bank is formulated into an unconstrained optimisation problem. Based on the gradient vector, the conjugate gradient method is utilised to solve the design problem. The convergence of the proposed algorithm is analysed. Numerical examples and comparisons with other methods are included to show the performance of the algorithm.

Design of Oversampled Interleaved DFT Modulated Filter Bank Using 2Block Gauss-Seidel Method

In this paper, we present several new properties of the recently introduced interleaved DFT modulated filter bank and an efficient algorithm for designing the filter bank. The periodicity and symmetry properties of the overall transfer function and aliasing transfer functions are stated. Then the design of the filter bank is formulated into a constrained optimization problem that jointly minimizes the overall distortion and aliasing distortion subject to fixed bounds on the stopband energy, transition-band energy, and passband flatness of the prototype filters. The constrained optimization problem is solved by the 2block Gauss-Seidel method, which alternatively optimizes the analysis PF pair and the synthesis PF pair. Since the overall distortion and aliasing distortion are jointly minimized, the proposed algorithm can lead to filter banks with small reconstruction error, even when the filter banks behave with a low redundancy ratio and short PFs. The convergence of the proposed algorithm is proved. Numerical examples and comparisons with the existing method are included to demonstrate the performance of the proposed algorithm.

Low-Complexity Maximally-Decimated Multirate 3-D Spatio-Temporal FIR Cone and Frustum Filters

A low-complexity multirate 3-D spatio-temporal FIR cone and frustum filter structure is proposed having potential applications as a spatio-temporal directional filter. The cone filter structure employs a 1-D modified discrete Fourier transform (DFT) filter bank and 2-D spatial filters. The frustum filter having a double-frustum-shaped passband oriented along the temporal frequency axis is approximated by employing an appropriate subset of subbands. Low computational complexity is achieved by maximal decimation in the temporal dimension, and by employing the DFT-polyphase realization to implement the 1-D modified DFT filter bank. The cone and frustum filters are almost alias free, and provide near-perfect reconstruction. The reduction in computational complexity, relative to undecimated and under-decimated realizations, is numerically confirmed by means of a potential application involving the attenuation of strong broadband plane wave interference.

Efficient design of high-complexity interleaved DFT modulated filter bank

This paper presents several novel properties of the interleaved DFT modulated filter bank and efficient algorithm for designing the filter bank with a very large number of channels and very long filters (also known as high-complexity). For interleaved DFT modulated filter bank, we find a new property of the transfer function and aliasing transfer functions, by which the complexity of the calculation of these functions can be dramatically reduced over that by the traditional way. Also, a time-domain condition is derived for the filter bank to have no transfer function distortion. Based on new properties, a bi-iterative unconstrained quadratic program (BI-UQP) algorithm is proposed to design the filter bank. Numerical examples and comparisons with other method are included to demonstrate the effectiveness of the proposed method.

Oversampled perfect reconstruction DFT modulated filter banks for multi-carrier transceiver systems

In this work, we propose a novel method for the design of oversampled perfect reconstruction (PR) discrete Fourier transform (DFT) modulated filter banks (FB) for application to multi-carrier modulation (MCM). The PR property is enforced by employing a parametric class of paraunitary matrices to form the transmit/receive polyphase filters of the transceiver system. Specifically, the polyphase filters are formed by cascading special types of paraunitary matrices characterized by a limited set of design parameters. To reduce the number of these parameters, three different factorization methods are employed and compared. Through the optimization of these design parameters, the stop-band energy of the subband filters can be minimized which leads to improved spectral containment. The performance of the proposed system is investigated in a multi-carrier transceiver application, where it is compared with OFDM and other recently proposed FB structures. Numerical results show that the proposed scheme leads to a clear advantage not only in additive white Gaussian noise (AWGN) and frequency selective channels, but also in the presence of channel impairments such as narrow band interference or carrier frequency offset. In particular, it is found that a significant reduction in the bit error rate can be achieved by employing the proposed scheme.

Optimization and Implementation for the Modified DFT Filter Bank Multicarrier Modulation System

The modified Discrete Fourier Transform (MDFT) filter bank is a Nearly Perfect Reconstruction (NPR) system based on pseudo-QMF filter bank. In this paper, we introduce an optimized algorithm to implement the MDFT filter bank based multicarrier modulation system. The system based on this optimization algorithm has the low error rate and system delay. To verify the designed system we have compared the MDFT multicarrier modulation system with the OFDM modulation system. The results show that at high speed communication the data error rate in the MDFT filter bank multicarrier modulation system is clear improved in comparison with OFDM systems.  Index Terms—MDFT filter bank, NPR, Error rate, Optimization algorithm

Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.

Design of 2D oversampled linear phase DFT modulated filter banks via modified Newton's method

In this paper, the structure of the 2D oversampled DFT modulated filter banks is analyzed and a spatial-domain condition of a filter bank without transfer function distortion is derived. Based upon the spatial-domain condition, a modified Newton's method is presented for fast design of 2D oversampled linear phase (LP) DFT modulated filter banks with nearly perfect reconstruction (NPR). We formulate the design problem into an unconstrained optimization with a fourth-order objective function, which is the weighted sum of the transfer function distortion of the filter bank and the stopband energy of the prototype filter (PF). The optimization is solved by the modified Newton's method, where each of iterations updates the PF by a set of linear equations. It is proved that the iteration process fast converges to a stationary point of the objective function. Compared with the existing methods, the new method is fast in computation and can design 2D filter banks with a large number of subbands.