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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
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Application of 1-D discrete wavelet transform based compressed sensing matrices for speech compression.

Yuvraj V Parkale1, Sanjay L Nalbalwar1

  • 1Department of Electronics and Telecommunication Engineering, Dr. Babasaheb Ambedkar Technological University, Lonere, Maharashtra India.

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Summary

This study introduces discrete wavelet transform (DWT) based sensing matrices for speech signal compression. The sym9 wavelet matrix offers superior performance and speech quality compared to other DWT and state-of-the-art sensing matrices.

Keywords:
Compressed sensing (CS)Discrete wavelet transform (DWT)Mean opinion score (MOS)Perceptual evaluation of speech quality (PESQ)Speech compression

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Area of Science:

  • Signal Processing
  • Data Compression
  • Wavelet Theory

Background:

  • Compressed sensing enables signal compression during acquisition, reducing storage needs by requiring fewer observations than traditional methods.
  • This research focuses on applying 1-D discrete wavelet transform (DWT) based sensing matrices for efficient speech signal compression.

Purpose of the Study:

  • To investigate and compare the performance of various DWT-based sensing matrices for speech signal compression.
  • To identify the optimal DWT wavelet family and specific matrix for speech signal compression applications.

Main Methods:

  • Development and evaluation of DWT-based sensing matrices using Daubechies, Coiflets, Symlets, Battle, Beylkin, and Vaidyanathan wavelet families.
  • Performance analysis of proposed matrices against each other and against state-of-the-art random and deterministic sensing matrices.
  • Speech quality assessment using Mean Opinion Score (MOS), Perceptual Evaluation of Speech Quality (PESQ), and information-based measures.

Main Results:

  • The sym9 wavelet-based sensing matrix demonstrated superior performance, characterized by reduced reconstruction time and lower relative error.
  • Among Daubechies, Coiflets, and Symlets families, db10, coif5, and sym9 showed the best performance, respectively.
  • The Beylkin wavelet matrix also exhibited good performance with low reconstruction time and error compared to Battle and Vaidyanathan families.

Conclusions:

  • The sym9 wavelet-based sensing matrix significantly outperforms existing state-of-the-art sensing matrices in speech signal compression.
  • The proposed sym9 wavelet matrix achieves high speech quality, as confirmed by excellent MOS and PESQ scores.