Time--frequency feature representation using energy concentration: An overview of recent advances

The fractional Fourier transform (FRFT) is a potent tool to analyze the chirp signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the short-time fractional Fourier domain (STFRFD). Two aspects of its performance are considered: the 2-D resolution and the STFRFD support. The time-FRFD-bandwidth product (TFBP) is defined to measure the resolvable area and the STFRFD support. The optimal STFRFT is obtained with the criteria that maximize the 2-D resolution and minimize the STFRFD support. Its inverse transform, properties and computational complexity are presented. Two applications are discussed: the estimations of the time-of-arrival (TOA) and pulsewidth (PW) of chirp signals, and the STFRFD filtering. Simulations verify the validity of the proposed algorithms.

Short-Time Fractional Fourier Transform and Its Applications

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.

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Short-time Fourier transform: two fundamental properties and an optimal implementation

This paper proposes a novel representation, known as Lv's distribution (LVD), of linear frequency modulated (LFM) signals. It has been well known that a monocomponent LFM signal can be uniquely determined by two important physical quantities, centroid frequency and chirp rate (CFCR). The basic reason for expressing a LFM signal in the CFCR domain is that these two quantities may not be apparent in the time or time-frequency (TF) domain. The goal of the LVD is to naturally and accurately represent a mono- or multicomponent LFM in the CFCR domain. The proposed LVD is simple and only requires a two-dimensional (2-D) Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function. It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The computational complexity, properties, detection performance and representation errors are analyzed for this new distribution. Comparisons with three other popular methods, Radon-Wigner transform (RWT), Radon-Ambiguity transform (RAT), and fractional Fourier transform (FRFT) are performed. With several numerical examples, our distribution is demonstrated to be a CFCR representation that is computed without using any searching operation. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. One of the most important applications of the LVD is to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.

Lv's Distribution: Principle, Implementation, Properties, and Performance

Texture is an important visual attribute used to describe the pixel organization in an image. As well as it being easily identified by humans, its analysis process demands a high level of sophistic...

Plant leaf identification based on volumetric fractal dimension

This paper presents fast algorithms for type-II, type-III, and type-IV generalized discrete Hartley transform. In particular, new odd-factor algorithms are derived to support transforms whose sequence length contains multiple odd factors. By jointly using the odd-factor and radix-2 algorithms, fast computation for arbitrarily composite sequence length can be achieved. Compared to other reported algorithms, the proposed ones have a regular computational structure, achieve a substantial reduction of computational complexity, and support a wider range of choices on the sequence length.

https://ieeexplore.ieee.org/iel5/82/18803/00868457.pdf

Fast algorithms for generalized discrete Hartley transform of composite sequence lengths

This correspondence presents an improved split-radix algo- rithm that can flexibly compute the discrete Hartley transforms (DHT) of length- where is an odd integer. Comparisons with previously reported algorithms show that savings on the number of arithmetic operations can be made. Furthermore, a wider range of choices on different DHT lengths is naturally provided.

http://ieeexplore.ieee.org/iel4/82/15063/00686687.pdf

Fast DFT Algorithms for Length

The fractal dimension has been studied as a feature for texture analysis. It has been found that the fractal dimension is not an effective image texture measure but little is known about the reasons for the fractal dimension failing to be effective for texture analysis. This paper investigates into the underlying causes why the fractal dimension is not an effective image texture feature. Four mathematical properties have been identified which are responsible for the fractal dimension's ineffectiveness. The experimental results show that while the fractal dimension itself is hardly an effective feature for texture classification, it can considerably enhance other feature sets.

On texture classification using fractal dimension

A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than the short time Fourier transform (STFT) and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representations. The proposed method rotates the base tone and harmonics in time-frequency domain. After the rotation, base tone and harmonics become in parallel to the time axis in time-frequency domain so that a high concentration can be achieved.

Adaptive harmonic fractional Fourier transform

The harmonic transform is designed for harmonic signals, which are composed of a base tone and some harmonics (e.g., voiced speech). As a generalization of the Fourier transform, the harmonic transform represents signals by the sum of a base tone and some harmonics, which may give more concise results for harmonic signals than the Fourier transform. Some experiments of speech signals are used to demonstrate the advantages of the harmonic transform on harmonic signal processing.

http://ieeexplore.ieee.org/iel5/7486/20359/00940605.pdf

Yan Qiu Chen

Papers

Fast algorithms for generalized discrete Hartley transform of composite sequence lengths

Fast DFT Algorithms for Length

On texture classification using fractal dimension

Adaptive harmonic fractional Fourier transform

Harmonic transform