Efficient computation of the Discrete Fourier Transform (DFT) for signals with structured frequency support remains a significant challenge in signal processing. The traditional Fast Fourier Transform (FFT) algorithm achieves O(NlogN) complexity, but substantial improvements are possible for signals with known structured supports. In prior work, Pochimireddy et al. demonstrated that for signals with homogeneous supports and a length N that is a power of a prime, the DFT can be computed in O(klogk) time, where k is the size of the frequency support. However, this work was restricted signals with specific lengths. This paper extends these results by developing algorithms for signals of arbitrary lengths using circular convolution techniques to achieve the same computational efficiency. Our proposed methods enhance the theoretical framework and practical utility of structured DFT computation, extending the range of applicable signal lengths. Numerous examples demonstrate the effectiveness of our approach, paving the way for more efficient signal processing in various modern applications.

In this paper, we present a novel operator designed to handle the shifting of multiple periodic signals. By exploiting the unique properties of the companion matrix and the elegant structure of cyclotomic polynomials, we have developed an efficient and versatile tool for signal processing applications. The proposed operator can be further utilized to design an FIR filter for decomposition and separation of different period mixed signals.

In this paper, we investigate the intriguing connection between the Discrete Cosine Transform (DCT) and integral graphs, contributing to the field of signal processing on graphs. Throughout our investigation, we discover two types of novel integral graphs based on DCT. The first type emerges as a result of Ramanujan’s Sum, and interestingly, we establish its isomorphism with the DFT-based approach. The second type arises from fundamental properties of DCT, representing a unique and valuable contribution.

We investigate the reconstruction of a binary image from its sparse 2D discrete Fourier transform (2D-DFT) coefficients. Specifically, we focus on the case where the image height is equal to its width and is a prime number. We derive a lower bound on the number of coefficients required for perfect image recovery and propose a reconstruction algorithm. In our experiment, we demonstrate that the lower bound can be achieved when the height is less than 20. Consequently, we can efficiently reconstruct a 19×19 binary image using only 21 out of the total 361 2D-DFT coefficients, which accounts for approximately 5.81% of the coefficients..

Memory bandwidth has become the real-time bottleneck of current deep learning accelerators (DLAs), particularly for high definition (HD) object detection. Under resource constraints, this article proposes a low memory traffic DLA chip with joint hardware and software optimization. To maximize hardware utilization under memory bandwidth, we morph and fuse the object detection model into a group fusion-ready model to reduce intermediate data access. This reduces the YOLOv2’s feature memory traffic from 2.9 to 0.15 GB/s. To support group fusion, our previous DLA-based hardware employees a unified buffer with write-masking for simple layer-by-layer processing in a fusion group. When compared to our previous DLA with the same processing element (PE) numbers, the chip implemented in a 40-nm process supports$1280\times 720$at 30 frames per second (FPS) object detection and consumes$7.9\times $less external dynamic random access memory (DRAM) access energy, from 2607 to 327.6 mJ.

Hardware acceleration for dilated and transposed convolution enables real time execution of related tasks like segmentation, but current designs are specific for these convolutional types or suffer from complex control for reconfigurable designs. This paper presents a design that decomposes input or weight for dilated and transposed convolutions respectively to skip redundant computations and thus executes efficiently on existing dense CNN hardware as well. The proposed architecture can cut down 87.8% of the cycle counts to achieve 8.2X speedup over a naive execution for the ENet case.

In this article a low complexity and accurate frequency estimation method for 2D signals is proposed. It can be applied to antenna array signal processing and image processing. This method is very efficient because it only samples two 1D lines in first dimension. The corresponding frequency in the second dimension is estimated by phase difference and fine-tuned by sampling another line. Through experiments, we found it effective in noise removal. To conclude, the proposed method is suitable for 2D accurate frequency estimation and preprocessing.

Hardware accelerator for convolution neural network (CNNs) enables real time applications of artificial intelligence technology. However, most of the accelerators only support dense CNN computations or suffers complex control to support fine grained sparse networks. To solve above problem, this paper presents an efficient CNN accelerator with 1-D vector broadcasted input to support both dense network as well as vector sparse network with the same hardware and low overhead. The presented design achieves 1.93X speedup over the dense CNN computations.

A novel method is proposed to construct arbitrary length perfect integer sequences based on all-pass polynomial. It uses a fact that associative sequence of an all-pass polynomial is guaranteed to be perfect. In addition, geometric series method is our special case. Moreover, perfect Gaussian integer sequences can also be constructed. Furthermore, this approach can be applied to symmetric perfect sequences design. Finally, perfect sequence with low degree of freedom can be achieved by the difference set. Concrete examples are illustrated.

In this letter, a novel method is proposed to generate discrete approximations of continuous Hermite-Gaussian functions with noninteger shift and dilation. Moreover, the approximations preserve orthogonality. In addition, the discrete Hermite-Gaussian functions reach the minimum time-bandwidth product under discrete version of Gabor uncertainty principle. Two applications are demonstrated. In fractional delay application, the proposed method is compared with the windowing method and proved to have smaller delay error. Another one is the signal expansion based on the proposed complete orthogonal basis.

In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram-Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis. The relationship between the original basis and proposed basis is also clearly illustrated. Therefore, the original basis can be replaced easily.

A novel method to generate integer 2-D discrete Fourier transform (DFT) pairs and eigenvectors was proposed. Using projection slice theorem and Ramanujan's sum, the 2-D spatial signal is decomposed into 2-D gcd-delta functions which contain only zeroes and ones. The 2-D DFT of 2-D gcd-delta functions are also integers. The integer 2-D DFT pairs can be applied to obtain integer 2-D DFT eigenvectors and 2-D period detection. The connection between 2-D gcd-delta function and multidimensional Ramanujan's Sum is also illustrated with two numerical examples.

In this work, we describe some methods to generate zero autocorrelation Gauss integer sequences of arbitrary length. These methods can be combined with each other so that more choices can be made.

Recently, several Gaussian like image representations are proposed as an alternative of the bag-of-word representation over local features. These representations are proposed to overcome the quantization error problem faced in bag-of-word representation. They are shown to be effective in different applications, the Extended Hierarchical Gaussianization reached excellent performance using single feature in VOC2009, Vector of Locally Aggregated Descriptors and Fisher Kernel reached excellent performance using only signature like representation on Holiday dataset. Despite their success and similarity, no comparative study about these representations has been made. In this paper, we perform a systematic comparison about three emerging different gaussian like representations: Extended Hierarchical Gaussianization, Fisher Kernel and Vector of Locally Aggregated Descriptors. We evaluate the performance and the influence of feature and parameters of these representations on Holiday and CC_Web_Video datasets, and several important properties about these representations have been observed during our investigation. This study provides better understanding about these gaussian like image representations that are believed to be promising in various applications.

We propose a novel model for landmark discovery that locates region-based landmarks on map in contrast to the traditional point-based landmarks. The proposed method preserves more information and automatically identifies candidate regions on map by crowdsourcing geo-referenced photos. Gaussian kernel convolution is applied to remove noises and generate detected region. We adopt F1 measure to evaluate discovered landmarks and manually check the association between tags and regions. The experiment results show that more than 90% of attractions in the selected city can be correctly located by this method.

Object of Interest (OOI) detection has been widely used in many recent works in video analysis, especially in video similarity and video retrieval. In this paper, we describe a generic video classification algorithm using object of interest detection. We use online user-submitted videos and aim to categorize the videos into six broad categories hot star, news, anime, pets, sports and commercials. We show through our experiments that, detecting and describing the object of interest improves the video classification accuracy by about 10 percentage points.

This paper provides a novel method to obtain the eigenvectors of discrete Fourier transform (DFT), which are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). The proposed method uses a generating matrix and an initial eigenvector. By multiplying the initial eigenvector with the generating matrix, we can derive a new eigenvector. Repeating this procedure we can acquire all the eigenvectors. Compare with the conventional O(N3) commutative matrix method, this new method can generate all the DFT eigenvectors with complexity reduced to O(N2logN). The generating matrix can be further used to intensify the conventional commuting matrix. The simulation result shows that the Hermite-Gaussian like (HGL) eigenvectors of the strengthened commuting matrix outperform those of Santhanam's.

A special class of odd-symmetric length-4N periodic signals is studied, and it is shown how the odd Ramanujan sums are used as weighting coefficients to compute their pure imaginary discrete Fourier transform (DFT) integer-valued coefficients. The odd Ramanujan sum, being the sums of complex roots of unity, can be calculated either using closed-form formulas or computed recursively through the impulse response of a derived infinite impulse response (IIR) filter. This special class of odd-symmetric signals and odd Ramanujan sums can be combined together with the previous even-symmetric special class signals and the well-known even Ramanujan sums as a useful tool for signal processing

A new type of touch sensor for detecting contact pressure at human fingertips is presented. A fingernail is instrumented with miniature LEDs and photodetectors in order to measure changes in the nail color pattern when the fingertip is pressed against a surface. Unlike traditional electronic gloves, in which sensor pads are placed between the fingers and the environment surface, this new sensor allows the fingers to directly contact the environment without obstructing the human's natural haptic senses. The finger touch force is detected by measuring changes in the nail color, hence the sensor is mounted on the fingernail rather than on the fingertip. Photo-reflective plethysmography is used to measure the nail color. Haemodynamic modeling is used to investigate the dynamics of the change in blood volume under the fingernail. The model is simulated and then evaluated by comparison with the experimental dynamic response of the sensor. Applications to human-machine interaction are discussed.