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Related Concept Videos

Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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Properties of the z-Transform I01:17

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The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
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Related Experiment Video

Updated: Jul 7, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

A new class of biorthogonal wavelet systems for image transform coding.

D Wei1, J Tian, R R Wells

  • 1Dept. of Electr. and Comput. Eng., Rice Univ., Houston, TX 77251-1892, USA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 16, 2008
PubMed
Summary

New biorthogonal Coifman wavelet systems offer competitive compression and lower computational complexity. These systems provide an improved tradeoff for wavelet transform coding applications.

Related Experiment Videos

Last Updated: Jul 7, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Area of Science:

  • Signal Processing
  • Applied Mathematics
  • Image Compression

Background:

  • Biorthogonal wavelets are crucial for signal and image compression.
  • Existing wavelet systems like the 9-7 tap filterbank have limitations in computational complexity.
  • The need for efficient and effective wavelet transforms persists in various applications.

Purpose of the Study:

  • To introduce a novel class of biorthogonal Coifman wavelet systems.
  • To develop a time-domain design method for these systems.
  • To evaluate their compression potential and computational efficiency.

Main Methods:

  • Construction of general biorthogonal Coifman wavelet systems with distributed vanishing moments.
  • Derivation of closed-form expressions for dual filter impulse and frequency responses.
  • Analysis of filter coefficients for multiplication-free discrete wavelet transform realization.

Main Results:

  • The proposed systems feature dyadic fraction filter coefficients, enabling multiplication-free transforms.
  • Even-ordered systems exhibit symmetry, resulting in linear-phase dual filters.
  • Three specific filterbanks demonstrate compression potential comparable to the 9-7 tap system.

Conclusions:

  • The new biorthogonal Coifman wavelet systems offer a superior tradeoff between compression performance and computational complexity.
  • Their design facilitates efficient implementation in discrete wavelet transform.
  • These systems represent a promising advancement for wavelet transform coding.