This paper proposes a comb filter design method which utilizes two linear phase FIR filters for flexibly adjusting the comb filter's frequency response. The first FIR filter is used to individually adjust the notch gains, which denote the local minimum gains of the comb filter's frequency response. The second FIR filter is used to design the elimination bandwidths for individual notch gains. We also derive an efficient comb filter by incorporating these two FIR filters with an all-pass filter which is used in a conventional comb filter to accurately align the nulls with the undesired harmonic frequencies. Several design examples of the derived comb filter show the effectiveness of the proposed comb filter design method.

Simple and accurate formulations are employed to represent discrete-time infinite impulse response (IIR) processes of first-order differentiator and integrator. These formulations allow them to be eligible for wide-band applications. Both first-order differentiator and integrator have an almost linear phase. The new differentiator has an error of less than 1% for the range 0-0.8π of normalized frequency and the new integrator has an error of less than 1.1% for the range 0-0.8π of normalized frequency.

All optical analog-to-digital converter consisting of an optical polarization modulator using nonlinear phase shift and switches based on polarization is proposed. The principle of operation is discussed using Jones matrix. Optical polarization states through the system and limit of resolution are evaluated. The resolution is optimized by maintaining the polarization state in the converter and refining the polarization of incident sampling signal. Parallel usage of converter modules is proposed to increase the dynamic range, where cyclic nature of optical phase plays an important roll. Application to photonic routing of our converter is also proposed.

R-regular Mth band filters are an important class of digital filters and are used in constructing Mth-band wavelet filter banks, where the regularity is essential. But this kind of filter has larger stopband peak errors compared with a minimax filter of the same length. In this paper, peak errors in stopband of R-regular 4th-band filters are reduced by means of superimposing two filters with successive regularities. Then the stopband peak errors in the resulting filters are compared with the original ones. The results show that the stopband peak errors are reduced significantly in the synthesized filter that has the same length as the longer one of the two original filters, at the cost of regularity.

This paper proposes a new theory and design method for a class of recombination nonuniform filter banks (RNFBs) with linear phase (LP) filters. In a uniform filter bank (FB), consecutive channels are merged by sets of transmultiplexers (TMUXs) to realize a nonuniform FB. RNFBs with LP analysis/synthesis filters are of great interest because the analysis filters for the partially reconstructed signals, through merging, are LP and hence less phase distortions are introduced to the desired signals. We analyze the spectrum supports of the analysis filters of these LP RNFBs. The conditions on the uniform FB and recombination TMUXs of an LP RNFB with good frequency characteristics are determined. These conditions are relatively simple to be satisfied and the uniform FB and recombination TMUXs can be designed separately without much degradation in performance. This allows dynamically recombination of different number of channels in the original uniform FB to give a flexible and time-varying frequency partitioning. Using these results, a method for designing a class of near-perfect-reconstruction (NPR) LP RNFBs with cosine roll-off transition band using the REMEZ algorithm is proposed. A design example is given to show that LP RNFBs with good frequency responses and reasonably low reconstruction errors can be achieved.

The even-odd transform (EOT) converts a complex sequence set into another one with even and odd correlation distributions exchanged. The Fukumasa-Kohno-Imai transform (FKIT) converts a real-valued sequence set into a complex one with improved generalized even-odd-equivalent (EOE) correlation distributions. In this work, the EOT is generalized for asynchronous M-PSK/CDMA. A subclass of the generalized EOTs coincides with the FKITs. New bounds on the correlation gains achievable by the FKITs are then derived.

In this paper, we propose a projection based design of near perfect reconstruction QMF banks. An advantage of this method is that additional design specifications are easily implemented by defining new convex sets. To apply convex projection technique, the main difficulty is how to approximate the design specifications by some closed convex sets. In this paper, introducing a notion of Magnitude Product Space where a pair of magnitude responses of analysis filters is expressed as a point, we approximate design requirements of QMF banks by multiple closed convex sets in this space. The proposed method iteratively applies a convex projection technique, Hybrid Steepest Descent Method, to find a point corresponding to the optimal analysis filters at each stage, where the closed convex sets are dynamically improved. Design examples show that the proposed design method leads to significant improvement over conventional design methods.

This paper presents a 7th-order channel-select filter for a spread-spectrum wireless receiver operating with a minimum power supply of 2.5 V. The channel-select filter implements a sharp transition from 2 MHz to 4 MHz and a stopband attenuation of 50 dB. The 7th-order filter is realized by a cascade of a passive RC integrator, a 3rd-order leapfrog filter, an operational amplifier based differentiator, a 2nd-order notch filter, and a 1st-order allpass filter. It is designed in a 0.35 µm single-poly BiCMOS process. Simulation results show feasibility of the proposed filter.

In this paper, we present a numerical design method for two-dimensional (2-D) FIR linear-phase (LP) quincunx filter banks (QFB) with equiripple magnitude response and perfect reconstruction (PR). The necessary conditions for the filter length of analysis filters are derived. A dual affine scaling variant (DASV) of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters and an approximation scheme is introduced to satisfy the PR constraint for the 2-D filter banks (FB). The simulation examples are included to show the effectiveness of this proposed design technique.

Since IIR filters have lower computational complexity than FIR filters, some design methods for IIR filter banks have been presented in the recent literatures. Smith et al. have proposed a class of linear phase IIR filter banks. However this method restricts the order of the numerator to be odd and has some drawbacks. In this paper, we present two design methods for linear phase IIR filter banks. One is based on Lagrange-Multiplier method, and optimal IIR filter banks in least squares sense are obtained. In an other approach, IIR filter banks with the maximum number of zeros are derived analytically.

An ultra-broadband optical parametric amplification can be attained by a noncollinear phase-matching. The group-velocity matching of the signal and idler reduces the signal-pulse width to 14-fs in an optical parametric amplifier based on a β-BaB2O4 crystal pumped by a second harmonics of a Ti: sapphire regenerative amplifier. This simple novel method shows the potential light source of a tunable sub-10-fs pulse in a visible region.

This paper describes a design technique of perfect reconstruction (PR) two-channel IIR filter bank. M.J.T. Smith et al., gave two types of PR IIR filter bank systems. One is the system such that the analysis and synthesis filters with nonlinear phase are implemented with all-pass polyphase filters and satisfy the power complementary condition approximately. The other is the system such that all the analysis and synthesis filters have liner phase responses and do not satisfy the power complementary condition. To improve coding performance, we propose a filter bank system such that all the analysis and synthesis filters have linear phase and satisfy the power complementary condition approximately.

In this paper, we present a novel way to design biorthogonal and paraunitary linear phase filter banks. The square error of the perfect reconstruction of the filter bank is expressed in quadratic form of filter coefficients and the cost function is minimized by solving linear equation iteratively without nonlinear optimization. With some modifications, this method is extended to the design of paraunitary filter banks. Furthermore, the lattice structure of odd-channel paraunitary filter banks is also derived. Design examples are given to validate the proposed method.

We present a systematic theory for the optimum sub-band interpolation using a given analysis or synthesis filter bank with the prescribed coefficient bit length. Recently, similar treatment is presented by Kida and quantization for decimated sample values is contained partly in this discussion [13]. However, in his previous treatment, measures of error are defined abstractly and no discussion for concrete functional forms of measures of error is provided. Further, in the previous discussion, quantization is neglected in the proof of the reciprocal theorem. In this paper, linear quantization for decimated sample values is included also and, under some conditions, we will present concrete functional forms of worst case measures of error or a pair of upper bound and lower limit of those measures of error in the variable domain. These measures of error are defined in Rn, although the measure of error in the literature [13] is more general but must be defined in each limited block separately. Based on a concrete expression of measure of error, we will present similar reciprocal theorem for a filter bank nevertheless the quantization for the decimated sample values is contained in the discussion. Examples are given for QMF banks and cosine-modulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosine-modulated FIR filter banks by using reciprocal relation and new transformation called cosine-sine modulation in the design of filter banks.

It is known that an anticausal IIR filter can be realized in real time by using the time reversed section technique. When combined with a casual IIR filter, the overall transfer function can yield exact linear phase characteristic in theory. This paper presents a new method for designing complex IIR digital filters with exact linear phase. The design problem of IIR filters with exact linear phase can be reduced to magnitude-only filter design. The proposed procedure is based on the formulation of an eigenvalue problem by using Remez exchange algorithm. By solving the eigenvalue problem to compute the real maximum eigenvalue, the solution of the rational interpolation problem can be achieved. Therefore, the optimal filter coefficients are easily obtained through a few iterations. The proposed design algorithm not only retains the speed inherent in Remez exchange algorithm, but also Simplifies the interpolation step because is has been reduced to the computation of the real maximum eigenvalue. Several examples are presented to demonstrate the effectiveness of the proposed method.

A novel method is presented for designing discrete coeffcient FIR linear phase filters using Hopfield neural networks. The proposed method is based on the minimization of the energy function of Hopfield neural networks. In the proposed method, the optimal solution for each filter gain factor is first searched for, then the optimal filter gain factor is selected. Therefore, a good solution in the specified criterion can be obtained. The feature of the proposed method is that it can be used to design FIR linear phase filters with different criterions simultaneously. A design example is presented to demonstrate The effectiveness of the proposed method.

The approximation of the gain characteristics of linear phase FIR digital filters is reduced to the approximation by cosine polynomials. Therefore we can easily obtain an optimum solution under the LMS of Chebyshev error criterion. However the optimum solution does not always meet practical specifications, especially in the case where the gain is specified strictly at some angular frequencies. On the other hand in such a case, it is known that interpolation technique can be suitably applied for the approximation mentioned above. However, in this case, we encounter another difficulty in the approximation caused by interpolation. In order to overcome the above difficulty, this paper proposes a new method utilizing both of the interpolation and LMS techniques. Some parameters included in approximating functions are used to satisfy prescribed interpolating conditions and the other parameters are used to minimize the approximation error under the LMS criterion. In addition, interpolation technique is extended to include the case in which also higher derivatives are taken into interpolation conditions to make smooth interpolation. An example is shown to illustrate the effectiveness of the proposed method.