VLSI Architecture of DCT-Based Harmonic Wavelet Transform for Time–Frequency Analysis | IEEE Journals & Magazine | IEEE Xplore

VLSI Architecture of DCT-Based Harmonic Wavelet Transform for Time–Frequency Analysis


Abstract:

The complex harmonic wavelet (CHW) is being used to directly compute frequency content with respect to time by employing discrete Fourier transform (DFT) and inverse DFT ...Show More

Abstract:

The complex harmonic wavelet (CHW) is being used to directly compute frequency content with respect to time by employing discrete Fourier transform (DFT) and inverse DFT (IDFT). However, DFT coefficients suffer severe leakage of energy from one band to another band of frequency. The leakage between bands is minimized by employing discrete cosine transform (DCT) in the harmonic wavelet transform (HWT), which leads to a better representation of the time–frequency spectrum. This article introduces a new VLSI architecture for DCT -based harmonic wavelet for hardware implementation and prototyped on a commercially available virtex5 field-programmable gate array (FPGA) (xc5vlx110t). To validate the proposed implementation, its real-time captured results in the logic analyzer are verified with simulation results. The maximum operating frequency targeting the FPGA mentioned above device is reported as 114.34 MHz. The total ON-chip power of the above implementation is 1.102 W, out of which 68 mW is the dynamic power dissipation at a toggle rate of 12%. Finally, for the area utilization of the above implementation, its resource utilization targeting the above FPGA device is reported.
Article Sequence Number: 6502108
Date of Publication: 03 April 2023

ISSN Information:


I. Introduction

Awavelet transform is the popular time–frequency analysis technique that is being used in various applications, such as power electronics [1], power system engineering [2], biomedical signal processing [3], seismic data analysis [4], [5], [6], radar application [7], [8], communication engineering [9], and vibration signals modal analysis [10]. However, the wavelet transform decomposes the signal as the summation of the weights of the different scales and translation of the mother wavelet producing the spectrum of amplitude versus time scale, which is called scalogram. The complex harmonic wavelet (CHW) in [11] is such a wavelet transform that decomposes the signal in direct amplitude versus time–frequency called spectrogram, and its coefficients are computed using discrete Fourier transform (DFT) and inverse DFT (IDFT). However, in the case of DFT coefficients, the energy of each spectral component is spread over the whole frequency axis leading to a severe leakage from one band to another band [12], [13]. Therefore, the processing of coefficients of individual subbands in the case of CHW is ineffective, as the energy of one band has leaked to another [14]. Therefore, the application of CHW transform is limited due to its spectral leakage between its subbands.

References

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