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Related Concept Videos

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

531
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
531
Properties of the z-Transform II01:16

Properties of the z-Transform II

277
The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
277
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

628
The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the...
628
Properties of the z-Transform I01:17

Properties of the z-Transform I

458
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...
458
Complex Zeros01:29

Complex Zeros

63
Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...
63
Definition of z-Transform01:26

Definition of z-Transform

1.2K
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
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Updated: Nov 23, 2025

Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
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New compression method for full-complex holograms using the modified zerotree algorithm with the adaptive discrete

Jin-Kyum Kim, Kyung-Jin Kim, Ji-Won Kang

    Optics Express
    |December 31, 2020
    PubMed
    Summary
    This summary is machine-generated.

    We developed a new compression method for random phase holograms. This technique, using an adaptive discrete wavelet transform (aDWT) and modified zerotree algorithm (mZTA), offers superior image compression and quality compared to existing methods.

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    Area of Science:

    • Digital holography
    • Image processing
    • Data compression

    Background:

    • Random phase holograms possess unique spatial and frequency characteristics.
    • Existing compression methods are not optimized for these unique hologram properties.

    Purpose of the Study:

    • To develop an efficient compression method for full complex holograms with random phase.
    • To improve the quality of reconstructed holographic images after compression.

    Main Methods:

    • Analysis of frequency characteristics of random phase holograms.
    • Proposal of a new adaptive discrete wavelet transform (aDWT).
    • Development of a new modified zerotree algorithm (mZTA) tailored for aDWT subbands.

    Main Results:

    • The proposed method demonstrates higher compression efficiency than previous techniques.
    • Reconstructed images from the compressed holograms exhibit visually superior quality.

    Conclusions:

    • The novel aDWT and mZTA provide an effective solution for random phase hologram compression.
    • This approach enhances both the efficiency of hologram data storage and the fidelity of image reconstruction.