Multiple-Clock-Cycle Architecture for the VLSI Design of a System for Time-Frequency Analysis
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Multiple-Clock-Cycle Architecture for the VLSI Design of a System for Time-Frequency Analysis Veselin N. Ivanovi´c, Radovan Stojanovi´c, and LJubiˇsa Stankovi´c Department of Electrical Engineering, University of Montenegro, 81000 Podgorica, Montenegro, Yugoslavia Received 29 September 2004; Revised 17 March 2005; Accepted 25 May 2005 Multiple-clock-cycle implementation (MCI) of a flexible system for time-frequency (TF) signal analysis is presented. Some very important and frequently used time-frequency distributions (TFDs) can be realized by using the proposed architecture: (i) the spectrogram (SPEC) and the pseudo-Wigner distribution (WD), as the oldest and the most important tools used in TF signal analysis; (ii) the S-method (SM) with various convolution window widths, as intensively used reduced interference TFD. This architecture is based on the short-time Fourier transformation (STFT) realization in the first clock cycle. It allows the mentioned TFDs to take different numbers of clock cycles and to share functional units within their execution. These abilities represent the major advantages of multicycle design and they help reduce both hardware complexity and cost. The designed hardware is suitable for a wide range of applications, because it allows sharing in simultaneous realizations of the higher-order TFDs. Also, it can be accommodated for the implementation of the SM with signal-dependent convolution window width. In order to verify the results on real devices, proposed architecture has been implemented with a field programmable gate array (FPGA) chips. Also, at the implementation (silicon) level, it has been compared with the single-cycle implementation (SCI) architecture. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
1.
INTRODUCTION AND PROBLEM FORMULATION
The most important and commonly used methods in TF signal analysis, the SPEC and the WD, show serious drawbacks: low concentration in the TF plane and generation of crossterms in the case of multicomponent signal analysis, respectively, [1–3]. In order to alleviate (or in some cases completely solve) the above problems, the SM for TF analysis is proposed in [4]. Recently, the SM has been intesively used, [5–8]. Its definition is [4, 9, 10] SM(n, k) =
Ld (n,k)
∗
P(n,k) (i) STFT(n, k + i) STFT (n, k − i),
i=−Ld (n,k)
(1)
− j(2π/N)ik where STFT(n, k) = N/2 reprei=−N/2+1 f (n + i)w(i)e sents the STFT of the analyzed signal f (n), 2Ld (n, k) + 1 is the width of a finite frequency domain (convolution) rectangular window P(n,k) (i) (P(n,k) (i) = 0, for |i| > Ld (n, k)), and the signal’s duration is N = 2m . The SM produces, as its marginal cases, the WD and the SPEC with maximal (Ld (n, k) = N/2), and minimal (Ld (n, k) = 0) convolution window width, respectively. In the case of a multicomponent
signal with nonoverlapping components, by an appropriate convolution window width selection, the SM can produce a sum of the WDs of individual signal components, avoiding cross-terms [4, 10, 11]: P(n,k) (i) should be wide enough t
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