A parallel, pipelined architecture for calculating the fast Hartley transform (FHT) is discussed. Hardware implementation of the FHT introduces two challenges: retrograde indexing and data scaling. A novel addressing scheme that permits the fast computation of FHT butterflies is proposed, and a hardware implementation of conditional block floating point scaling that reduces error due to data growth with little extra cost is described. Simulations reveal a processor capable of transforming a 1 K-point sequence in 170 mu s using a 15.4 MHz clock. >

Calculating the FHT in hardware

A new class of real-valued linear code obtained by using the discrete Hartley transform (DHT) is defined. The authors have derived the limitation on the choice of parity frequencies so as to define DHT codes with the cyclic-shift property. Then, by introducing the well-established encoding/decoding algorithm for cyclic codes in error control coding, they have constructed the encoder/decoder for the DHT cyclic codes. >

Discrete Hartley transform in error control coding

For state-of-the-art digital signal processors (DSPs) alternative ways to implement FIR (finite impulse response) filters are compared with respect to the necessary number of instruction cycles per tap. Also, the accuracy attainable both with fixed-point and floating-point arithmetic is discussed. Besides direct form filtering and fast convolution algorithms using FFTs (fast Fourier transforms), radix FIR filter structures are also considered. The latter are very interesting for most DSP architectures, offering speed improvements of up to 25% compared to the direct form. >

Convolution algorithms on DSP processors

Time-frequency localization with the Hartley S-transform

Distributed Denial-of-Service (DDoS) attack has been a serious threat to the availability feature of cloud computing. As traditional DDoS attacks are implemented using a huge volume of malicious traffic, the detection of such attacks becomes a naive task. To evade this detection, attackers are moving towards the Low-Rate DDoS (LRDDoS) attacks. The stealthy behavior of LRDDoS attack makes it difficult to get detected due to its low volume traffic. The existing frequency-domain approaches for LRDDoS detection are not feasible in terms of computational and storage requirements. This paper aims to propose a lightweight, accurate, and adaptive approach for the detection of LRDDoS attacks in frequency-domain. In this paper, the LRDDoS attack is detected by analyzing the power spectral distribution. The novelty of the proposed approach is to calculate the power spectral density using Fast Hartley Transform (FHT). The FHT processes real-valued input data, and has low computational and storage complexities. The approach is implemented on OpenStack cloud platform, and the aggregate network traffic (external and internal) is captured and analyzed. Experimental results show that the computational and storage complexities involved in FHT are lower than other transformation algorithms’ complexities. Thus, the approach provides faster response with an average detection time of 60.16 s. The average true negative and true positive rates obtained by the proposed approach are 99.83% and 99.46% respectively, which are competitive.

Detection of Low-Rate Cloud DDoS Attacks in Frequency Domain Using Fast Hartley Transform

The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware. They describe the modifications required to convert existing fast Fourier transform (FFT) programs to execute FHTs, showing the ease with which these modifications can be implemented. They compare execution time and memory storage requirements of both transforms and present power spectrum calculation and convolution as illustrative examples to compare the performances of the two transform techniques. They also give a comparative survey of the performances of various microprocessors and digital signal processors in FFT and FHT computation. >

M.T. Vo

Papers

Implementation and performance of the fast Hartley transform