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Related Concept Videos

Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Downsampling01:20

Downsampling

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.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Scalar Product (Dot Product)01:11

Scalar Product (Dot Product)

The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
The scalar product of two vectors is obtained by multiplying...

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Updated: May 8, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

2-Step scalar deadzone quantization for bitplane image coding.

Francesc Auli-Llinas

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |August 20, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a 2-step scalar deadzone quantization (2SDQ) scheme for image coding. 2SDQ offers the same performance as uniform scalar deadzone quantization (USDQ) but with reduced computational costs and fewer symbols.

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    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

    Published on: December 3, 2013

    Area of Science:

    • Digital image processing
    • Signal compression
    • Information theory

    Background:

    • Modern lossy image coding relies on quality progressive codestreams for efficient image representation.
    • Uniform scalar deadzone quantization (USDQ) with bitplane coding is standard for achieving quality progressivity.

    Purpose of the Study:

    • To introduce a novel 2-step scalar deadzone quantization (2SDQ) scheme.
    • To enhance coding efficiency and reduce computational complexity in image codecs.
    • To enable efficient coding of high dynamic range images.

    Main Methods:

    • Developed a 2SDQ scheme using two quantization step sizes based on wavelet coefficient density.
    • Implemented a rate-distortion optimization technique for adjusting distortion decreases.
    • Integrated the 2SDQ scheme into the JPEG2000 framework.

    Main Results:

    • Achieved equivalent coding performance to USDQ.
    • Reduced the number of coding passes and emitted symbols.
    • Demonstrated straightforward integration and efficiency within JPEG2000.

    Conclusions:

    • 2SDQ offers a computationally efficient alternative to USDQ for image coding.
    • The scheme effectively reduces complexity and is suitable for high dynamic range imaging.
    • 2SDQ is a practical advancement for current image compression standards.