K.M.M. Prabhu

The fractional Fourier transform: theory, implementation and error analysis

Abstract The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications demand the implementation of the discrete fractional Fourier transform on a digital signal processor (DSP). The details of the implementation of the discrete fractional Fourier transform on ADSP-2192 are provided. The effect of finite register length on implementation of discrete fractional Fourier transform matrix is discussed in some detail. This is followed by the details of the implementation and a theoretical model for the fixed-point errors involved in the implementation of this algorithm. It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.

Fast Adaptive Algorithms for Active Control of Nonlinear Noise Processes

This correspondence attempts to derive the exact implementation of two nonlinear active noise control (ANC) algorithms, viz. FSLMS and VFXLMS. The concept of reutilizing a part of the computations performed for the first sample while computing the next sample, for a block length of two samples, is exploited here to implement the fast and exact versions of the FSLMS and VFXLMS algorithms which are computationally efficient. Detailed computational complexity analysis for both addition and multiplication requirements is presented to show the advantage of the proposed algorithms. Appropriate simulation experiments are carried out to compare the performance equivalence of the proposed fast algorithms with their original versions.

Fast communication: Fast exact multichannel FSLMS algorithm for active noise control

In this paper, we derive the fast and exact implementation of multichannel filtered-S LMS (FSLMS) algorithm. By removing redundancy in the governing equations of the standard FSLMS algorithm, we can obtain a significant reduction in the complexity of the controller. This has been achieved by rearranging the equations of FSLMS algorithm. We have carried out a detailed computational complexity analysis. Simulation experiments have been carried out to show the performance equivalence of the proposed fast algorithm with its standard version.

Fast communication: A substitution-by-interpolation algorithm for watermarking audio

Interpolation of a sample set from a signal gives a close mathematical, and hence, a perceptually similar approximation to the original samples. In this paper, an audio watermarking technique in the temporal domain using spline interpolation is proposed. Test results for imperceptibility of the watermark and its robustness against MP3 compression and resampling attacks are presented. The simulation study shows that the watermark performance is satisfactory against the two forms of attacks mentioned above.

Fast Hartley transform pruning

The discrete Hartley transform (DHT) is discussed as a tool for the processing of real signals. Fast Hartley transform (FHT) algorithms which compute the DHT in a time proportional to N log/sub 2/ N exist. In many applications, such as interpolation and convolution of signals, a significant number of zeros are padded to the nonzero valued samples before the transform is computed. It is shown that for such situations, significant savings in the number of additions and multiplications can be obtained by pruning the FHT algorithm. The modifications in the FHT algorithm as a result of pruning are developed and implemented in an FHT subroutine. The amount of savings in the operation is determined. >

Poisson image denoising using fast discrete curvelet transform and wave atom

In this paper, we propose a strategy to combine fast discrete curvelet transform (FDCT) and wave atom (WA) with multiscale variance stabilizing transform (MS-VST); our objective is to develop algorithms for Poisson noise removal from images. Applying variance stabilizing transform (VST) on a Poisson noisy image results in a nearly Gaussian distributed image. The noise removal can be subsequently done assuming a Gaussian noise model. MS-VST has been recently proposed in the literature (i) to improve the denoising performance of Anscombes VST at low intensity regions of the image and (ii) to facilitate the use of multiscale-multidirectional transforms like the curvelet transform for Poisson image denoising. Since the MS-VST has been implemented in the space-domain, it is not clear how it can be extended to FDCT and WA, which are incidentally implemented in the frequency-domain. We propose a simple strategy to achieve this without increasing the computational complexity. We also extend our approach to handle the recently developed mirror-extended versions of FDCT and WA. We have carried out simulations to validate the performance of the proposed approach. The results demonstrate that the MS-VST combined with FDCT and WA are promising candidates for Poisson denoising.

Estimation of frequency offset using warped discrete-Fourier transform

In this paper, the problem of estimating a small frequency offset in a signal with a large carrier frequency is addressed. The warped discrete-Fourier transform (WDFT) [A. Makur, S.K. Mitra, IEEE Trans. Circuits Systems--I: Fundam. Theory Appl. 6 (9) (September 2001) 1086-1093] is used and the accuracy of estimation and computational complexity of this technique is compared with the conventional discrete-Fourier transform (DFT) and the nonuniform discrete-Fourier transform (NDFT). A numerical example is provided to illustrate the comparison.

Space-frequency block coding in OFDM systems

An effective technique to improve wireless communication performance is transmit diversity. In this work, transmitter diversity using a new combination of space-time block codes (STBCs) concatenated with orthogonal frequency division multiplexing (OFDM) system in high-speed wireless data communication is investigated. Simulation results demonstrate that this scheme can achieve a significant performance increase for efficient data transmission over slow and fast fading environments, compared to conventional OFDM. Performance of proposed scheme has been compared to an STBC-OFDM scheme and it is evident that SFBC is more robust than STBC-OFDM system in a fast fading environment.

An improved LMS adaptive algorithm for narrowband interference suppression in direct sequence spread spectrum

In 1990 Vijayan and Poor proposed nonlinear predictive methods for suppressing narrowband interference in spread spectrum (SS) systems with a significant increase in signal-to-noise ratio (SNR) improvement. The main drawback of their adaptive nonlinear filter is its slow convergence rate. A new adaptive least mean squares (LMS) algorithm to increase the slow convergence of their nonlinear adaptive filter is described. Computer simulation results are presented to support the advantages of the new filter. >

Variable parameter window families for digital spectral analysis

Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered. Closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered. The results are compared to those obtained by J.F. Kaiser and R.W. Schafer (1980) in the case of zeroth-order Bessel (I/sub 0/-sinh) family. >