INTRODUCTION During the last two decades, the research on efficient design of filter banks especially 2-channel QMF banks, has received considerable attention because of its wide applications in numerous fields. Filter bank design is a multi-objective optimization problem. Consequently, the condition for perfect reconstruction can be written as S. K. Agrawal, O. P. Sahu, "Two-Channel Quadrature Mirror Filter Bank: An Overview", International Scholarly Research Notices, vol. Quadrature Mirror Filter (QMF) banks have been of great interest since their introduction by Croisier, Estebari and Calsnd [3], [4].These find applications in situations where a If the pass band edge is too small as in curve 2, then dips around . The Quadrature Mirror Filter (QMF) basically is a parallel combination of a High Pass Filter (HPF) and Low Pass Filter (LPF), which performs the action of frequency sub division by splitting the signal spectrum into two spectra. Different design techniques for nearly perfect reconstruction and perfect reconstruction QMF banks have been discussed. Differential evolution (DE) is one of the most powerful evolutionary algorithm (EAs) and has been used for various signal processing applications. Johnston [26] minimized AMD, in ALD and PHD free QMF bank, by optimizing the coefficients of the low-pass filter , such that the amplitude of the distortion function becomes as flat as possible and at the same time the stop band energy of was minimized. It is shown that, for a bank of M filters of length L, PR can be obtained when L = 2KM, for any positive integer K, whereas previous results guaranteed PR only for K = 1. Simultaneously, an application of these Z-window based FIR filters in designing two-channel quadrature mirror filter (QMF) bank has been presented. About | where are the relative weights and , , , and mor are the mean square error in pass band, mean square error in stop band, square error of the overall transfer function at , and measure of ripple, respectively. Thus QMF finds wide applications in many signal processing tasks such It is believed that this arrangement would reduce the hardware complexity, the cost and the workload of the 253–361, April 1984. 0.0. Comparison of various nearly PR algorithms for design of two-channel QMF bank based on significant parameters for. The Quadrature Mirror Filter (QMF) basically is a parallel combination of a High Pass Filter (HPF) and Low Pass Filter (LPF), which performs the action of frequency subdivision by splitting the signal spectrum into two spectra. A two-band, linear phase, quadrature mirror filter … Better values of reconstruction and aliasing errors have been achieved in contrast to the Kaiser window based QMF bank. There is a need for suitable algorithms for finding optimum solutions for these significant parameters. QMF is listed in the World's largest and most authoritative dictionary database of abbreviations and acronyms The Free Dictionary Finally future research trends are discussed in Section 5, followed by conclusion in Section 6. CANCEL Filter bank has applications in areas like video and audio coding, data communication, etc. The input audio signal is first decomposed into 64 sub-band signals using QMF decom-position. Therefore, AMD is eliminated and we then have Home Further, each decimated subband is filtered again along column using analysis filters of next stage, which results in four subbands. Digital Butterworth, Chebyshev and Elliptic filters are special cases [21, 53, 54] of the form given by (26). Two-channel QMF was first used in subband coding and then find applications in various signal processing fields. In this paper a Quadrature Mirror Filter is implemented in VHDL, for wireless communication applications. In this method, again analysis filters and synthesis filters are related as in (3) and (4) so that aliasing is completely canceled. (c)Classical optimization methods may fail to achieve optimal design as they do not guarantee for convergence on the global optimum. Following fidelity assessment parameters can be used to analyze the satisfactory reconstruction of original image [32]. (d)Hybrid optimization methods may be used to design QMF banks for improved performance. View Notes - QMF from ECE 595 at Purdue University. The QMF implementation is carried out on FPGA platform. As we have already discussed in Section 1, QMF bank has been of great interest during the past two decades due to its various applications in different signal processing fields. [31] presented a new algorithm to design two-channel QMF bank using the Marquardt optimization method. The algorithm ensures good stop band attenuation for each of the analysis filters. The design techniques for QMF bank can be classified as optimization-based or nonoptimization based. This method does not require manual intervention or repeated trials with different start-up guesses as in method [26]. dio applications based on the predictability of the temporal evolution of Quadrature Mirror Filter (QMF) sub-band signals. Retrospective Theses and Dissertations The reconstructed signal suffers from three types of errors: aliasing distortion (ALD), amplitude distortion (AMD), and phase distortion (PHD), due to the fact that the filters , , , and are not ideal [25]. Looking for online definition of QMF or what QMF stands for? Abstract - In this paper a Quadrature Mirror Filter is implemented in VHDL, for wireless communication applications. If the pass band edge is too large means and have too much overlap as in curve 1, then there is peaking effect in around . To obtain FIR linear phase PR QMF banks, it is necessary to give up [21] the power complementary condition of (13) as well as the constraints . Electronics Letters 26, 906–907 (1990) CrossRef Google Scholar. A great amount of different filter bank approaches have been developed over last fifteen years. The lattice structure has the hierarchical property that a higher order PR QMF bank can be obtained from a lower order PR QMF bank, simply by adding more lattice sections. In this work, a novel sub-band ABA hardware configuration is proposed. Several applications are described, including subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrowband filter coefficients. Tree structure QMF bank can be used for 1-D filter. Quadrature mirror filter is presented. Enkanayake and Premaratne et al. Quadrature Mirror Filter (QMF) banks for narrow band signals [2]. Select a Web Site. For multiple part number look-up, separate with a comma. Przewiń w dół i kliknij, aby zobaczyć każdy z nich. (e)QMF banks are used extensively in designing efficient subband coders for speech, image, and video signals. or https://stars.library.ucf.edu/rtd/4292, Home | This research is about QMF lter bank design using nonlinear optimization methods. It can be completely removed by defining the synthesis filters as given below: Subband coding of signals is an effective method to achieve bandwidth compression when the signal energy is dominantly concentrated in a particular region of frequency. MODULATED QMF FILTER BANKS WITH PERFECT RECONSTRUCTION Henrique S. Malvar Necessary and sufficient conditions for perfect reconstruction (PR) in a modu-lated filter bank are derived. In the flexible systems, to identify the frequencies of disturbances filter banks and quadrature mirror filter are employed. There are two types of tree structures, namely, uniform and octave filter bank structures. (b)If the characteristics of prototype filter are assumed to be ideal in its pass band and stop band regions, consequently, reconstruction error lies only in transition band. The coefficients of are optimized in order to minimize . Tree structure QMF bank can be used in wireless communication as interference canceler [, A. Croisier, D. Esteban, and C. Galand, “Perfect channel splitting by use of interpolation/decimation/tree decomposition techniques,” in, D. Esteban and C. Galand, “Application of quadrature mirror filter to split band voice coding schemes,” in, S. C. Chan, C. K. S. Pun, and K. L. Ho, “New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases,”, M. Sablatash, “Designs and architectures of filter bank trees for spectrally efficient multi-user communications: review, modifications and extensions of wavelet packet filter bank trees,”, M. J. T. Smith and S. L. Eddins, “Analysis/synthesis techniques for subband image coding,”, J. W. Woods and S. D. O’Neil, “Sub-band coding of images,”, M. G. Bellanger and J. L. Daguet, “TDM-FDM transmultiplexer: digital polyphase and FFT,”, M. Vetterly, “Perfect transmultiplexers,” in, Y.-P. Lin and S.-M. Phoong, “ISI-free FIR filterbank transceivers for frequency-selective channels,”, J. H. Husøy and T. Gjerde, “Computationally efficient sub-band coding of ECG signals,”, S. O. Aase, “Filter bank design for sub-band ECG compression,” in, S. Chandran, “A novel scheme for a sub-band adaptive beam forming array implementation using quadrature mirror filter banks,”, T. Painter and A. Spanias, “Perceptual coding of digital audio,”, V. X. Afonso, W. J. Tompkins, T. Q. Nguyen, and S. Luo, “ECG beat detection using filter banks,”, G. Gu and E. F. Badran, “Optimal design for channel equalization via the filterbank approach,”, R. V. Cox, D. E. Bock, K. B. Bauer, J. D. Johnston, and J. H. Synder, “The analog voice privacy systems,”, R. E. Crochiere, “A novel approach for implementing pitch prediction in sub-band coding,” in, A. J. Barabell and R. E. Crochiere, “Sub-band coder design incorporating quadrature filters and pitch prediction,” in, R. Bregovic and T. Saramaki, “A general-purpose optimization approach for designing two-channel fir filterbanks,”, R. Bregovic and T. Saramaki, “Two-channel FIR filterbanks—a tutorial review and new results,” in, M. J. T. Smith and T. P. Barnwell III, “Exact reconstruction techniques for tree structured sub-band coders,”, M. J. T. Smith and T. P. Barnwell III, “A procedure fo designing Exact reconstruction filter bank for tree structured sub-band coders,” in, P. P. Vaidyanathan, “Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial,”, J. D. Johnston, “A filter family designed for use in quadrature mirror filter banks,” in, V. K. Jain and R. E. Crochiere, “Quadrature mirror filter design in time domain,”, C. K. Chen and J. H. Lee, “Design of quadrature mirror filters with linear phase in the frequency domain,”, H. Xu, W.-S. Lu, and A. Antoniou, “An improved method for the design of fir quadrature mirror-image filter banks,”, W.-S. Lu, H. Xu, and A. Antoniou, “A new method for the design of FIR quadrature mirror-image filter banks,”, O. P. Sahu, M. K. Soni, and I. M. Talwar, “Marquardt optimization method to design two-channel quadrature mirror filter banks,”, A. Kumar, G. K. Singh, and R. S. Anand, “An improved method for the design of quadrature mirror filter banks using the Levenberg-Marquardt optimization,”, J. Upendar, C. P. Gupta, and G. K. Singh, “Design of two-channel quadrature mirror filter bank using particle swarm optimization,”, A. Kumar, G. K. Singh, and R. S. Anand, “A closed form design method for the two-channel quadrature mirror filter banks,”, A. Gupta and S. K. Agarwal, “Designing of two channel polyphase quadrature mirror filter bank using power optimization method,” in, O. P. Sahu, M. K. Soni, and I. M. Talwar, “Designing quadrature mirror filter banks using steepest descent method,”, O. P. Sahu, M. K. Soni, and I. M. Talwar, “On the design of two channel quadrature mirror filter,”, K. Swaminathan and P. P. Vaidyanathan, “Theory and design of uniform DFT, parallel QMF banks,”, Y.-D. Jou, “Design of two-channel linear-phase quadrature mirror filter banks based on neural networks,”, A. Kumar, S. M. Rafi, and G. K. Singh, “A hybrid method for designing linear-phase quadrature mirror filter bank,”, L. Andrew, V. T. Franques, and V. K. Jain, “Eigen design of quadrature mirror filters,”, S. Nalbalwar, S. D. Joshi, and R. K. Patney, “A novel approach to design of signal matched QMF and DFT filter bank,” in, M. Li and C.-W. Kok, “Norm induced QMF banks design using LMI constraints,” in, A. Ghosh, R. Giri, A. Chowdhury, S. Das, and A. Abraham, “Two-channel quadrature mirror bank filter design using a Fitness-Adaptive Differential Evolution algorithm,” in, F. Cruz-Roldán, I. Santamaría, and Á. M. Bravo, “Frequency sampling design of prototype filters for nearly perfect reconstruction cosine-modulated filter banks,”, P. Ghosh, S. Das, and H. Zafar, “Adaptive-differential-evolution-based design of two-channel quadrature mirror filter banks for sub-band coding and data transmission,”, C. Y.-F. Ho, B. W.-K. Ling, L. Benmesbah, T. C.-W. Kok, W.-C. Siu, and K.-L. Teo, “Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming,”, G. S. Baicher, “Towards optimal implementation of a class of quadrature mirror filter using genetic algorithms,” in, Y. C. Lim, R. H. Yang, and S.-N. Koh, “Design of weighted minimax quadrature mirror filters,”, C.-K. Goh, Y. C. Lim, and C. S. Ng, “Improved weighted least squares algorithm for the design of quadrature mirror filters,”, S. K. Agrawal and O. P. Sahu, “Two-channel quadrature mirror filter bank design using FIR polyphase component,”, M. M. Ekanayake and K. Premaratne, “Two-channel IIR QMF banks with approximately linear-phase analysis and synthesis filters,”, P. P. Vaidyanathan, S. K. Mitra, and Y. Neuvo, “A new approach to the realization of low sensitivity IIR digital filters,”, P. P. Vaidyanathan, P. Regalia, and S. K. Mitra, “Design of doubly complementary IIR digital filters using a single complex all pass filter, with Multirate applications,”, T. A. Ramstad, “IIR filter bank for sub band coding of images,” in, T. Q. Nguyen, T. I. Laakso, and R. D. Koilpillai, “Eigenfilter approach for the design of allpass filters approximating a given phase response,”, M. M. Ekanayake and K. Premaratne, “Two-channel IIR QMF banks with approximately linear-phase analysis and synthesis filters,” in, P. P. Vaidyanathan and P.-Q. Nonuniform filter banks are also related to the so-called dyadic wavelets [77], especially useful in signal compression. Such systems are called Linear Phase Filter Banks. Some future research trends in designing of QMF banks and its applications have also been discussed which may be helpful for the researchers. Finally, the image signal is decomposed into four bands labeled by XX, YX, XY, and YY. Construction Experienced fleet managers count on Donaldson filters to protect equipment in gritty construction and aggregate environments. In most cases, they are not able to find global optimum solution. They can also be used for efficient subband coding of ECG and ultrasonic signals [75, 76]. If the characteristics of prototype filter are assumed to be ideal in its pass band and stop band regions, consequently, reconstruction error lies only in transition band. Two-channel filter banks can be classified into three types: quadrature mirror filter banks, orthogonal filter banks, and biorthogonal filter banks [20]. Some of design methods lead to nearly perfect reconstruction (NPR) filter banks while others lead to perfect reconstruction (PR) filter banks. [30] have proposed a new algebraic method for the design of two-channel quadrature mirror-image filter. Using advanced arithmetic concepts such as distribute arithmetic, reduced adder graph, or residue number system VARIOUS METHODS TO IMPLEMENT L/2 FILTERS 23. Nearly perfect reconstruction QMF banks can be further divided into two types: design of linear phase QMF banks and nonlinear QMF banks. The first step generates a good initial starting point using an existing design method and during the second step the optimization of the filter bank using modified Dutta-Vidyasagar algorithm [69] was performed. The reversed signs indicates a phase shift of π radians, which is the same as multiplying the DFT by e i π . where is filter length and is the amplitude function. The objective function “” was minimized by optimizing the coefficients of , subject to unit energy constraint, and is given as Consequently, the proposed approach leads to the same QMF banks as the approach of [6] but requires a significantly lower The temporal envelopes in critically sampled QMF sub-bands are approximated using frequency domain linear prediction applied over The objective function “” was minimized by optimizing the coefficients of : 2013, Article ID 815619, 10 pages, 2013. https://doi.org/10.1155/2013/815619, 1Department of Electronics and Communication Engineering, National Institute of Technology, Kurukshetra, Haryana 136119, India. In the time domain, the QMF constraint becomes , i.e., all odd-index coefficients are negated. These subband signals are decimated by a factor of two to achieve signal compression or to reduce processing complexity. where and are all pass filters of the form Due to nonlinearity and nonconvexity of the objective functions, conventional numerical/mathematical methods may find difficulty to achieve an optimal design. However, during the computation of odd numbered output samples, the structure is simply resting. The constraint on by (26), where and are given by (27), is necessary to become and all pass which in turn makes (25) to be all pass. In many cases, words that are keywords in database management systems cannot be used as the name of a table, view, column, or index in a QMF SQL query unless they are enclosed in double quotation marks. Hybrid optimization methods may be used to design QMF banks for improved performance. QMF can refer to: . Filter design relationships have been established and included in this paper. DSP applications in the consumer market, such as bioinformatics, the MP3 audio format, and MPEG-based cable/satellite television have fueled a desire to understand this technology outside of hardware circles. If is FIR, then due to the constraint , we cannot achieve the perfect reconstruction [21]. In the similar way, the bottom channel of Figure 1 can be described. Są one wymienione po lewej stronie. Quadrature Mirror Filter Banks find use in applications where a signal must be slipt into subbands operated on then reconstructed in the output. There is a need for suitable algorithms for finding optimum solutions for these significant parameters. A great amount of different filter bank approaches have been developed over last fifteen years. Now the analysis filter is constraining the form: The another approach to design QMF … In typical filter bank applications, ... (11) and are possible when the filter bank is constructed as a QMF (quadrature mirror filter) filter bank or CQF (conjugate quadrature filter) filter bank. By designing analysis filters in two-channel module, we can make the wavelet basis as smooth as possible [78]. The decimated signals are typically coded and transmitted. Therefore, in this case after eliminating ALD and PHD completely, we can only minimize amplitude distortion by optimizing the coefficients of . Malvar, H.: Modulated qmf filter banks with perfect reconstruction. This example shows the existence of FIR PR QMF banks. This choice ensures that is a good high-pass filter, if is good low-pass filter. These filters are called "pseudo-QMF" because these are approximate, not exact. Review articles are excluded from this waiver policy. Table 2 shows the comparison among three types of QMF banks. Eventually, at some point in the process, the subband signals are recombined so that the original signal is properly reconstructed [3]. QMF banks are used extensively in designing efficient subband coders for speech, image, and video signals. A filter. To obtain the perfect reconstruction QMF bank, PHD and AMD should also be eliminated; that can be possible if the reconstructed signal is simply made equal to a scaled and delayed version of the input signal . Several recent methods are also included. Yang, J.-H. Lee, and B.-C. Chieu, “Perfect-reconstruction filter banks having linear-phase fir filters with equiripple response,”, T. Q. Nguyen and P. P. Vaidyanathan, “Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters,”, K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, “Time-domain filter bank analysis: a new design theory,”, R. Bregovic and T. Saramaki, “New method for the design of two-channel perfect-reconstruction linear-phase FIR filter banks,” in, E. Abdel-Raheem, F. El-Guibaly, and A. Antoniou, “Design of low-delay two-channel FIR filter banks using constrained optimization,”, A. K. Soman, P. P. Vaidyanathan, and T. Q. Nguyen, “Linear phase paraunitary filter banks: theory, factorizations and designs,”, M. S. Spurbeck and C. T. Mullis, “Least squares approximation of perfect reconstruction filter banks,”, C.-K. Goh and Y. C. Lim, “An efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks,”, M. Vetterli and D. Le Gall, “Perfect reconstruction FIR filter banks: some properties and factorizations,”, S. R. K. Dutta and M. Vidyasagar, “New algorithms for constrained minimax optimization,”, M. Vetterli, “Multi-dimensional sub-band coding: some theory and algorithms,”, S. Das and P. N. Suganthan, “Differential evolution: a survey of the state-of-the-art,”, S. Hara, T. Matsuda, K. Ishikura, and N. Morinaga, “Co-existence problem of TDMA and DS-CDMA systems - application of complex multirate filter bank,” in, S. Hara, H. Masutani, and T. Matsuda, “Filter bank-based adaptive interference canceler for co-existence problem of TDMA/CDMA systems,” in, M. Konstantinos, A. Adamis, and P. Constantinou, “Receiver architectures for OFDMA systems with subband carrier allocation,” in, T. D. Tran and T. Q. Nguyen, “On M-channel linear phase FIR filter banks and application in image compression,”, T. Xia and Q. Jiang, “Optimal multifilter banks: design, related symmetric extension transform, and application to image compression,”. [52] presented computationally simple method to obtain IIR analysis and synthesis filters that possess negligible phase distortion. The input audio signal is first decomposed into 64 sub-band signals using QMF decomposition. In the design of QMF bank, the coefficients of the filters , , , and are obtained in such a way so that the three distortions ALD, AMD, and PHD are minimized or eliminated. Having eliminated aliasing and phase distortion, we can only minimize amplitude distortion systematically [21]. By using input-output relationship of decimator and interpolator, we can write , which describe the aliasing effect in the top channel of Figure 1, and , which describe the imaging effect [25]. The objective function was formulated as weighted sum of errors: Therefore all the four filters are completely determined by the low-pass analysis filter only. Kumar et al. Popular swarm intelligence approach, known as particle swarm optimization (PSO), has also been applied in [33] to design QMF bank by Upendar et al. Tree structure QMF bank can be used in wireless communication as interference canceler [72, 73] for coexistence problem of TDMA/CDMA systems, which can jointly cancel both wideband interference (CDMA signals in terms of TDMA signal) and narrowband interference (TDMA signals in terms of CDMA signal). The individual subbands can be processed according the required applications. or Thus by constraining to be linear phase and selecting the synthesis filters as in (3), PHD and ALD are eliminated completely. The Quadrature Mirror Filter (QMF) basically is a parallel combination of a High Pass Filter (HPF) and Low Pass Filter (LPF), which performs the action of frequency subdivision by splitting the signal spectrum into two spectra. Malvar, H.: Extended lapped transforms: fast algorithms and applications. At the receiver, the two subband signals are decoded and then interpolated by a factor of two and finally passed through low-pass and high-pass synthesis filters, and , respectively. Because of their structure, lattice filters do this very well and allow perfect reconstruction, even when the lattice coefficients must be quantized. Designing analysis and synthesis filters of a QMF filter bank. 4292. the polyphase components can be expressed as. IBM DB2 Query Management Facility for z/OS (DB2 QMF) V12.1 expands the data sources it supports and adds this comprehensive access to its QMF TSO and CICS client. In earlier proposed design techniques, suitable modifications can be made in such a way that the reconstruction error and computational complexity will reduce by using new algorithms. The QMF bank optimization based on IIR all-pass filters is first simplified as the problem of solving a set of linear equations. The overall transfer function of the analysis filter/synthesis filter system is a delay, and the aliasing cancellation has all the significant aliasing terms canceled. M-channel pseudo-quadrature-mirror-filter (QMF) banks using a prototype filter having a linear-phase spectral-factor of a 2M th band filter. Among those filter banks, Cosine Modulated filter banks [1]-[3] are very popular because they are easy to implement and can provide perfect reconstruction (PR). (d)QMF based subband coders [18, 19] provide more natural sounding, pitch prediction, and wider bandwidth than earlier subband coders. If direct form implementation is used for decimation filter, then only the even numbered output samples are computed and that requires () multiplications per unit time (MPUs) and additions per unit time (APUs). If the polyphase components and are selected to be IIR all pass [21, 25], then from (25), would also be all pass, which means AMD is eliminated. In the time domain, the QMF constraint becomes , i.e., all odd-index coefficients are negated. Introduction Filter banks are often used in signal processing applications for division of a signal into frequency bands and the reconstruction of the signal from the individual bands. The main difficulty comes in transition band region ; therefore, the reconstruction error must be controlled in this region. Such a property ensures freedom from aliasing, This paper proposes an analysis technique for wide-band audio applications based on the predictability of the temporal evolution of Quadrature Mirror Filter (QMF) sub-band signals. The objective function is minimized directly, using nonlinear unconstrained method. Results of the proposed method were also compared with other methods in terms of significant parameters, that is, , , stop band edge attenuation and reconstruction error. The Quadrature Mirror Filter (QMF) basically is a parallel combination of a High Pass Filter (HPF) and Low Pass Filter (LPF), which performs the action of frequency subdivision by splitting the signal spectrum into two spectra. Sahu et al. This has also been extended to wideband signals [2, 3]. A generalization of the QMF filter bank to many channels exists, and is called the Pseudo-Quadrature Mirror Filter Bank (PQMF). All products. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. The temporal envelopes in critically sampled QMF sub-bands are approximated using frequency domain linear prediction applied over The reconstructed signal is therefore just a time delayed version of the input signal ; that is, for some nonzero constant and some positive integer . With a single extra adder, it is possible to obtain a highpass response in addition to the lowpass response and use the two responses for the filter bank implementation. Retrospective Theses and Dissertations. If the low-pass filter is written in the polyphase form of (16), then system function , of the QMF bank can be written as If filter characteristics of are assumed ideal in pass band and stop band regions then the overall amplitude response of the QMF bank will be constant in the pass bands of and . This application lets you run queries and procedures as QMF batch jobs rather than interactively. There are mainly two research areas in design of QMF banks [22]. V. K. Jain and R. E. Crochiere, “Quadrature Mirror Filter Design in the Time Domain”, IEEE Trans. Application of the lattice filter is presented along with a design program and example of its use to implement a QMF. XX subband can be further decomposed for multilevel decomposition. Inne znaczenia QMF Oprócz Kwadratura lustro filtr, QMF ma inne znaczenia. To implement the PSO algorithm, a Matlab program was developed and performance of the proposed method had been illustrated by examples [33]. Keywords: Quadrature Mirror Filter (QMF), Filter Bank, Variable Window, Combinational Window 1.