In this paper, some properties of Boolean functions via the unitary transform and c-correlation functions are presented. Based on the unitary transform, we present two classes of secondary constructions for c-bent4 functions. Also, by using the c-correlation functions, a direct link between c-autocorrelation function and the unitary transform of Boolean functions is provided, and the relationship among c-crosscorrelation functions of arbitrary four Boolean functions can be obtained.

In this paper, we consider the crosscorrelation of two interleaved sequences of period 4N constructed by Gong and Tang which has been proved to possess optimal autocorrelation. Results show that the interleaved sequences achieve the largest crosscorrelation value 4.

Binary maximal-length sequences (or m-sequences) are sequences of period 2m-1 generated by a linear recursion of degree m. Decimating an m-sequence {st} by an integer d relatively prime to 2m-1 leads to another m-sequence {sdt} of the same period. The crosscorrelation of m-sequences has many applications in communication systems and has been an important and well studied problem during more than 40 years. This paper presents an updated survey on the crosscorrelation between binary m-sequences with at most five-valued crosscorrelation and shows some of the many recent connections of this problem to several areas of mathematics such as exponential sums and Dickson polynomials.

A new construction method for polyphase sequences with two-valued periodic auto- and crosscorrelation functions is proposed. This method gives L families of polyphase sequences for each prime length L which is bigger than three. For each family of sequences, the out-of-phase auto- and crosscorrelation functions are proved to be constant and asymptotically reach the Sarwate bound. Furthermore, it is shown that sequences of each family are mutually orthogonal.

Binary sequences with good autocorrelation and crosscorrelation properties are widely used in signal processing. If the autocorrelation properties are optimum, then the sequences are called perfect. In this paper we show, that the calculation of the crosscorrelation between Gordon-Mills-Welch sequences and Dillon-Dobbertin sequences is related to the crosscorrelation of m-sequences and their decimations. Furthermore, we give an upper bound for the maximum crosscorrelation coefficient (in absolute value) for certain perfect sequences.

This paper describes subband-crosscorrelation analysis (SBXCOR) using two input channel signals. SBXCOR is an extended signal processing technique of subband-autocorrelation analysis (SBCOR) that extracts periodicities associated with the inverse of center frequencies present in speech signals. In addition, to extract more periodicity information associated with the inverse of center frequencies, the multi-delay weighting (MDW) processing is applied to SBXCOR. In experiments, the noise robustness of SBXCOR is evaluated using a DTW word recognizer under (1) a simulated acoustic condition with white noise and (2) a real acoustic condition in a sound proof room with human speech-like noise. As the results, under the simulated acoustic condition, it is shown that SBXCOR is more robust than the conventional one-channel SBCOR, but less robust than SBCOR extracted from the two-channel-summed signal. Furthermore, by applying MDW processing, the performance of SBXCOR improved about 2% at SNR 0 dB. The resultant performance of SBXCOR with MDW processing was much better than those of smoothed group delay spectrum (SGDS) and mel-filterbank cepstral coefficient (MFCC) below SNR 10 dB. The results under the real acoustic condition were almost the same as the simulated acoustic condition.

One serious problem affecting the rest and active state images obtained during a functional MRI (fMRI) study is that of involuntary subject movements inside the magnet while the imaging protocol is being carried out. The small signal intensity rise and small activation areas observed in the fMRI results, such as the statistical maps indicating the significance of the observed signal intensity difference between the rest and active states for each pixel, are greatly affected even by head displacements of less than one pixel. Near perfect alignment in the subpixel level of each image with respect to a reference, then, is necessary if the results are to be considered meaningful, specially in a clinical setting. In this paper we report the brain displacements that take place during a fMRI study with an image alignment method based on a refined crosscorrelation function which obtains fast (non-iterative) and precise values for the inplane rotation and X and Y translation correction factors. The performance of the method was tested with phantom experiments and fMRI studies using normal subjects executing a finger-tapping motor task. In all cases, subpixel translations and rotations were detected. The rest and active phases of the time course plots obtained from pixels in the primary motor area were well differentiated after only one pass of the motion correction program, giving enhanced activation zones. Other related areas such as the supplementary motor area became visible only after correction, and the number of pixels showing false activation was reduced.

In this paper, we analyze the multiple access interference of a variable processing gain DS/CDMA system and define discrete partial crosscorrelation functions. We also evaluate the bit error rate of the system using Gaussian approximation and bounding technique. Three kinds of spreading codes (long, short, and random codes) are considered in the analysis of the system. It is shown that the bit error rate of a user is not relevant to the processing gain of interfering users: it is relevant only to the processing gain of the user, transmitted powers, PN sequences, and spreading codes. The performance of short codes turns out to be better than that of long and random codes as in other systems.

In this study, we analyze the system which simultaneously transmits spread-spectrum signals with different processing gains. The main purpose of this study is to give an analytical framework that describes the influence of the interfering signals with different processing gains. For this purpose, we define a crosscorrelation function between the spreading sequences with different code lengths, and discuss the effects of interaction between the signals. As the results, we show that the power of the interference component after despreading procedure, the power ratio of the desired to undesired components, and thus the bit error rate are not constant but vary symbol by symbol.

A simple method is given for obtaining new families of pseudonoise (PN) sequences based on chaotic non-linear maps. Such families are worse than the Gold and the Kasami families in terms of maximum correlation values. Nevertheless, such a method has several advantages: the generation is easy, and various families with an arbitrary family size and sequence period can be obtained primarily because non-linear maps have several parameters to be secret keys for communications security. Hence these sequences are good candidates of spreading sequences for CDMA.