Frequency Transformation

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Masayuki Kawamata - One of the best experts on this subject based on the ideXlab platform.

  • high performance variable band pass band stop state space digital filters using gramian preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • High-performance variable band-pass/band-stop state-space digital filters using Gramian-preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • adaptive iir band pass band stop filtering using high order transfer function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

  • Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters
    Digital Filters and Signal Processing, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Masayuki Kawamata
    Abstract:

    Frequency Transformation is one of the well-known techniques for design of analog and digital filters [1, 2]. This technique is based on variable substitution in a transfer function and allows us to easily convert a given prototype low-pass filter into any kind of Frequency selective filter such as low-pass filters of different cutoff frequencies, high-pass filters, band-pass filters, and band-stop filters. It is also well-known that the transformed filters retain some properties of the prototype filter such as the stability and the shape of the magnitude response. For example, if a prototype filter is stable and has the Butterworth magnitude response, any filter given by the Frequency Transformation is also stable and of the Butterworth characteristic. Due to this useful fact, the Frequency Transformation is suitable not only to the filter design but also to the real-time tuning of cutoff frequencies, which can be applied to design of variable filters [3] and to adaptive notch filtering [4, 5]. Hence the Frequency Transformation plays important roles in many modern applications of signal processing from both the theoretical and practical points of view.

  • Adaptive IIR Band-Pass/Band-Stop Filtering Using High-Order Transfer Function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

Shunsuke Koshita - One of the best experts on this subject based on the ideXlab platform.

  • high performance variable band pass band stop state space digital filters using gramian preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • High-performance variable band-pass/band-stop state-space digital filters using Gramian-preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • adaptive iir band pass band stop filtering using high order transfer function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

  • Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters
    Digital Filters and Signal Processing, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Masayuki Kawamata
    Abstract:

    Frequency Transformation is one of the well-known techniques for design of analog and digital filters [1, 2]. This technique is based on variable substitution in a transfer function and allows us to easily convert a given prototype low-pass filter into any kind of Frequency selective filter such as low-pass filters of different cutoff frequencies, high-pass filters, band-pass filters, and band-stop filters. It is also well-known that the transformed filters retain some properties of the prototype filter such as the stability and the shape of the magnitude response. For example, if a prototype filter is stable and has the Butterworth magnitude response, any filter given by the Frequency Transformation is also stable and of the Butterworth characteristic. Due to this useful fact, the Frequency Transformation is suitable not only to the filter design but also to the real-time tuning of cutoff frequencies, which can be applied to design of variable filters [3] and to adaptive notch filtering [4, 5]. Hence the Frequency Transformation plays important roles in many modern applications of signal processing from both the theoretical and practical points of view.

  • Adaptive IIR Band-Pass/Band-Stop Filtering Using High-Order Transfer Function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

Masahide Abe - One of the best experts on this subject based on the ideXlab platform.

  • high performance variable band pass band stop state space digital filters using gramian preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • High-performance variable band-pass/band-stop state-space digital filters using Gramian-preserving Frequency Transformation
    Digital Signal Processing, 2014
    Co-Authors: Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata
    Abstract:

    This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the Frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L"2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving Frequency Transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving Frequency Transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of Frequency Transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

  • adaptive iir band pass band stop filtering using high order transfer function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

  • Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters
    Digital Filters and Signal Processing, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Masayuki Kawamata
    Abstract:

    Frequency Transformation is one of the well-known techniques for design of analog and digital filters [1, 2]. This technique is based on variable substitution in a transfer function and allows us to easily convert a given prototype low-pass filter into any kind of Frequency selective filter such as low-pass filters of different cutoff frequencies, high-pass filters, band-pass filters, and band-stop filters. It is also well-known that the transformed filters retain some properties of the prototype filter such as the stability and the shape of the magnitude response. For example, if a prototype filter is stable and has the Butterworth magnitude response, any filter given by the Frequency Transformation is also stable and of the Butterworth characteristic. Due to this useful fact, the Frequency Transformation is suitable not only to the filter design but also to the real-time tuning of cutoff frequencies, which can be applied to design of variable filters [3] and to adaptive notch filtering [4, 5]. Hence the Frequency Transformation plays important roles in many modern applications of signal processing from both the theoretical and practical points of view.

  • Adaptive IIR Band-Pass/Band-Stop Filtering Using High-Order Transfer Function and Frequency Transformation
    Interdisciplinary Information Sciences, 2013
    Co-Authors: Shunsuke Koshita, Masahide Abe, Yuki Kumamoto, Masayuki Kawamata
    Abstract:

    Received April 24, 2013; final version accepted October 22, 2013This paper proposes a new unified framework for the adaptive IIR band-pass/band-stop filtering for detectionand enhancement/suppression of an unknown narrowband signal immersed in a broadband signal. In most of theconventional methods, which are well-known as the adaptive notch filtering, the adaptive band-pass/band-stopfilter is restricted to a low-order transfer function. On the other hand, our proposed method can be applied toarbitrary high-order band-pass/band-stop transfer functions in a simple manner. We derive this simple adaptivemechanism with the help of the Frequency Transformation and its block diagram representation. In addition, weprove that this result includes the conventional all-pass-based adaptive notch filters as special cases. Moreover, wedemonstrate a significant property that the use of high-order adaptive band-pass/band-stop filters yields muchbetter signal-to-noise ratio (SNR) improvement than the conventional low-order filters.KEYWORDS: signal processing, adaptive digital filtering, narrowband signal, high-order transferfunction, Frequency Transformation

Shi Yan - One of the best experts on this subject based on the ideXlab platform.

  • State-space formulation of 2-D Frequency Transformation in Fornasini–Marchesini second model
    Multidimensional Systems and Signal Processing, 2017
    Co-Authors: Shi Yan, Lijun Sun, Yunze Cai, Qinglin Zhao
    Abstract:

    This paper presents a state-space formulation for the two-dimensional (2-D) Frequency Transformation in the Fornasini–Marchesini second (FM II) model. Specifically, by introducing some new state vectors, an equivalent description of the FM II model will be first established. Then based on this new description, a state-space formulation of the 2-D Frequency Transformation in the FM II model is derived by revealing the substantial input and output relations among the state vectors of the prototype filter, all-pass filters and the transformed filter. The resultant formulation owns an elegant and general expression, and can be viewed as a natural extension of its counterpart in the Roesser model. Furthermore, as one of the various possible applications of the proposed formulation, a 2-D zero-phase IIR filters design procedure will be shown, by which the desired 2-D zero-phase IIR filters can be constructed in a more flexible way to avoid the kind of image distortions caused by the nonlinear phase of the used filter. Three typical image processing examples as well as the computational complexity analysis will be given to show the effectiveness and efficiency of the proposed procedure.

  • ICICS - State-space formulation of 2-D Frequency Transformation base on Fornasini-Marchesini second model
    2013 9th International Conference on Information Communications & Signal Processing, 2013
    Co-Authors: Shi Yan, Yanyan Wei, Qinglin Zhao
    Abstract:

    This paper presents a state-space formulation of two-dimensional (2-D) Frequency Transformation for 2-D digital filters based on the Fornasini-Marchesini second (FM II) model. It will be shown that the FM II model can be interpreted as an equivalent model which has a similar form to the Roesser model. Then based on such a new equivalent model, the state-space formulation of the 2-D Frequency Transformation based on FM II model is derived by investigating the substantial input and output relations of the prototype filter, all-pass filters and the transformed filter such that the FM II model of the transformed filter can be directly obtained without using any realization approach. Moreover, it turns out that the resultant formulation owns a elegant and general expression so that it can be viewed as a natural extension of its counterpart in Roesser model. A non-trivial example is given to show the effectiveness of the proposed formulation.

  • ICARCV - Invariance of second-order modes of 2-D digital filters under 2-D Frequency Transformation
    2012 12th International Conference on Control Automation Robotics & Vision (ICARCV), 2012
    Co-Authors: Yafei Tian, Fanyong Zhang, Shi Yan
    Abstract:

    The so-called second-order modes, which are the square roots of the eigenvalues of the product of the controllability Gramian and observability Gramian of the filters, scale the minimal attainable value of roundoff noise of one-dimensional (1-D) and two-dimensional (2-D) filters. This paper carries out a preliminary investigation on the invariance property of the second-order modes of 2-D digital filters under 2-D Frequency Transformation based on the state-space formulation of 2-D Frequency Transformation proposed by the co-authors. Some nontrivial numerical examples are given to show that, compared with the results given in the 1-D Frequency Transformation for 2-D separable digital filters case, the similar invariance property may also hold for the 2-D Frequency Transformation of 2-D digital filters, i.e., the horizontal second-order modes keep invariant when only horizontal 2-D Transformation is applied while the vertical second-order modes keep invariant when only vertical 2-D Transformation is applied.

  • Derivation of a novel state-space formulation of 2-D Frequency Transformation by LFT techniques
    2008
    Co-Authors: Natsuko Shiratori, Shi Yan
    Abstract:

    This note derives a novel alternative state-space formulation of 2D Frequency Transformation for 2D digital filters by utilizing linear fractional Transformation (LFT) techniques. It turns out that the obtained new state-space formulation is much simpler than the existing result. Moreover, all the known 1D and 2D formulations can be unified by the proposed formulation as special cases. Numerical examples are given to illustrate the effectiveness of the proposed formulation.

  • New results on state-space formulation of 2-D Frequency Transformation
    2008 Chinese Control and Decision Conference, 2008
    Co-Authors: Shi Yan, Natsuko Shiratori
    Abstract:

    This paper presents a new state-space formulation of 2-D Frequency Transformation for 2-D digital filters. By investigating the inherent structural relations among the prototype filter, the all-pass Transformation filters and the transformed filter, a concise and elegant state-space formulation of 2-D Frequency Transformation is derived, which unifies all the existing results for both 1-D and 2-D cases. Numerical examples are given to illustrate the effectiveness of the proposed formulation.

Moeness G. Amin - One of the best experts on this subject based on the ideXlab platform.