In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.

Recent trends in designing filters involve development of sparse filters with coefficients that not only have real but also zero values. These sparse filters can achieve a high performance through optimizing the selection of the zero coefficients and computing the real (non-zero) coefficients. Designing an infinite impulse response (IIR) sparse filter is more challenging than designing a finite impulse response (FIR) sparse filter. Therefore, studies on the design of IIR sparse filters have been rare. In this study, we consider IIR filters whose coefficients involve zero value, called sparse IIR filter. First, we formulate the design problem as a linear programing problem without imposing any stability condition. Subsequently, we reformulate the design problem by altering the error function and prepare several possible denominator polynomials with stable poles. Finally, by incorporating these methods into successive thinning algorithms, we develop a new design algorithm for the filters. To demonstrate the effectiveness of the proposed method, its performance is compared with that of other existing methods.

In this paper, challenges regarding the provision of channel state information (CSI) and carrier frequency synchronization for orthogonal frequency division multiplexing (OFDM) systems with null subcarriers are addressed. We propose novel maximum likelihood (ML) based schemes that estimate the aggregate effects of the CFO and channel by using two successive OFDM preambles. In the presented scheme, CFO is estimated by considering the phase rotation between two consecutive received OFDM preambles. Both single input single output (SISO) as well as multiple input multiple output (MIMO) OFDM systems are considered. The mean squared errors (MSE) of the channel and CFO are used to evaluate the performance of our proposed scheme. By using two successive OFDM preambles, the estimation of channel and the estimation of CFO are decoupled, which leads to a simple estimation method. Simulation results show that the BER performance of the proposed estimators is comparable to that of known channel state information and the CFO MSE performance achieves the Cramer-Rao bound (CRB) of the fully loaded OFDM system.

In this paper, we propose a new error feedback (EF) structure for 2-D separable-denominator digital filters described by a rational transfer function. In implementing two-dimensional separable-denominator digital filters, the minimum delay elements structures are common. In the proposed structure, the filter feedback-loop corresponding to denominator polynomial is placed at a different location compared to the commonly used structures. The proposed structure can minimize the roundoff noise more than the previous structure though the number of multipliers is less than that of previous one. Finally, we present a numerical example by designing the EF on the proposed structure and demonstrate the effectiveness of the proposed method.

For copyright protection, a watermark signal is embedded in host images with a secret key, and a correlation is applied to judge the presence of watermark signal in the watermark detection. This paper treats a discrete wavelet transform (DWT)-based image watermarking method under specified false positive probability. We propose a new watermarking method to improve the detection performance by using not only positive correlation but also negative correlation. Also we present a statistical analysis for the detection performance with taking into account the false positive probability and prove the effectiveness of the proposed method. By using some experimental results, we verify the statistical analysis and show this method serves to improve the robustness against some attacks.