This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.

The main interest of this paper is the theoretical analysis of a recursive periodically time varying digital filter. The generalized transfer function of a recursive periodically time varying digital filter was obtained from its difference equation. It was proved that by making use of the generalized transfer function, we can not only derive the input and output relationship of a recursive periodically time varying digital filter easily but also obtain its equivalent structure effectively. An interesting property of a recursive periodically time varying digital filter was also derived by making use of its generalized transfer function. Moreover, it was completed in this paper the investigation of the generalized transfer functions and impulse responses of other periodically time varying models, including an input sampling polyphase model and an output sampling polyphase model. Meanwhile, the multirate Quadrature Mirror Filter bank system was proved by the authors to be a periodically time varying system. Several examples were also provided to illustrate the effectiveness of using the generalized transfer function to obtain the equivalent structure of a recursive periodically time varying digital filter.

In this paper we propose a method to aid a visually impaired person in the operation of a computer running a graphical user interface (GUI). It is based on image processing techniques, using images taken by a color camera placed over a Braille display. The shape of the user's hand is extracted from the image by analyzing the hue and saturation histograms. The orientation of the hand, given by an angle θ with the vertical axis, is calculated based on central moments. The image of the hand is then rotated to a normalized position. The number of pixels in each column of the normalized image is counted, and the result is put in a histogram. By analyzing the coefficient of asymmetry of this histogram, it can be determined whether the thumb is positioned along the pointing finger, or whether it is far from the other fingers. These two positions define two states that correspond to a mouse button up or down. In this way, by rotating the hand and moving the thumb, we can emulate the acts of moving a scroll bar and depressing a mouse button, respectively. These operations can be used to perform tasks in a GUI, such as cut-and-paste, for example. Experimental results show that this method is fast and efficient for the proposed application.

An approximate scheme for decomposing and reconstructing a continuous-time signal as a linear combination of the B-splines is studied. It is an oversampling discrete-time implementation derived by substituting the multifold RRS functions for the B-splines. The RRS functions are multifold discrete convolution of the sampled rectangular functions. Analysis of the scheme yields conditions for the circuit parameters to assure stability and required precision. A design example is presented that makes the error less than 1% in the supremal norm by the oversampling ratio of 512. Its numerical simulation is also presented.

The relationship between a multirate quadrature mirror filters (QMF) system and an output sampling polyphase model of a periodically time varying digital filter is examined. It is proved that a polyphase model of a periodically time varying digital filter is equivalent to a specified multirate QMF system. Using the derived relationship, another type of polyphase model of a periodically time varying digital filter which is called an input sampling polyphase model is proposed and analyzed. Furthermore, the equivalence of two types of polyphase models, i.e., the conventional output sampling polyphase model and the proposed input sampling polyphase model, is discussed and conditions for their equivalence are obtained.

This paper proposes a human interface where a novel input method is used to substitute conventional input devices. It overcomes the deficiencies of physical devices, as it is based on image processing techniques. The proposed interface is composed of three parts: extraction of a person's handshape from a digitized image, detection of its fingertip, and interpretation by a software application. First, images of a pointing hand are digitized to obtain a sequence of monochrome frames. In each frame the hand is isolated from the background by means of gray-level slicing; with threshold values calculated dynamically by the combination of movement detection and histogram analysis. The advantage of this approach is that the system adapts itself to any user and compensates any changes in the illumination, while in conventional methods the threshold values are previously defined or markers have to be attached to the hand in order to give reference points. Second, once the hand is isolated, fingertip coordinates are extracted by scanning the image. Third, the coordinates are inputted to an application interface. Overall, as the algorithms are simple and only monochrome images are used, the amount of processing is kept low, making this system suitable to real-time processing without needing expensive hardware.

This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.

This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals. This algorithm is based on a combination of FIR and IIR filters which enables a fast decomposition and reconstruction of a signal. When complex values are selected for the parameters of the exponentials, complex trigonometric functions are obtained. Only the real part of these functions are used for the interpolation of real signals, leading less bandlimited signals when they are compared with the polynomial B-spline counterparts. These characteristics were verified with 1-D and 2-D examples. This paper also discusses the effectiveness of exponential B-splines, when they are applied to image processing.

It is important to obtain a low coefficient sensitivity digital filter. This paper presents a new low coefficient sensitivity network structure that consists of a second order digital filter and a feedback path. This network structure is based on the effectiveness of the feedback path in an analog system. The coefficient sensitivity of the proposed digital filter can be control with the coefficient of the feedback path. Using this property, the digital filter with the low coefficient sensitivity is obtained. To add the feedback path makes the frequency response deviate from the characteristic of the original second order digital filter, but the deviation can be compensated with the other coefficients. A nonlinear optimization technique is employed to determine the coefficients of the digital filter. The proposed method is not effective only to narrow-band low-pass but wide-band low-pass filters.

This paper presents a new method for implementing modem by using a periodically time varying digital filter. Firstly, we present that a modulation and a demodulation are realized by using a periodically time varying digital filter (abbreviated to a PTV filter). Next, we present that these functions of a modem can be implemented in one PTV filter. Generally, it is very complicated to search the shifted carrier frequency of a transfered modulated signal. Since only a PTV filter are used in the proposed system, we do not need to search the shifted carrier frequency in modem. So, the proposed method is better than the conventional method in this point.