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Transformations of Functions III01:20

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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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Traveling Waves: Lossless Lines01:27

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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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...
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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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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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End-to-End Optimized Versatile Image Compression With Wavelet-Like Transform.

Haichuan Ma, Dong Liu, Ning Yan

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    iWave++ introduces a versatile image compression method using a trained wavelet-like transform. This approach achieves state-of-the-art lossless and lossy compression with arbitrary compression ratios, outperforming existing deep learning techniques.

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Machine Learning

    Background:

    • Deep networks have advanced end-to-end image compression.
    • Conventional auto-encoders involve information loss during feature conversion and quantization.
    • Achieving arbitrary compression ratios with existing methods is challenging.

    Purpose of the Study:

    • To propose iWave++, a novel end-to-end optimized image compression scheme.
    • To enable versatile compression supporting both lossless and lossy modes.
    • To achieve arbitrary compression ratios with a single model.

    Main Methods:

    • Utilizing iWave, a trained wavelet-like transform, for lossless image-to-coefficient conversion.
    • Implementing optional coefficient quantization and entropy coding for compression.
    • Developing a de-quantization module for lossy compression.

    Main Results:

    • Lossy iWave++ demonstrates state-of-the-art compression efficiency, achieving 17.34% bit savings over BPG on the Kodak dataset.
    • Lossless iWave++ shows comparable or superior performance to FLIF.
    • The iWave++ model supports versatile compression by adjusting quantization scales.

    Conclusions:

    • iWave++ offers a versatile and efficient solution for both lossless and lossy image compression.
    • The trained wavelet-like transform and progressive entropy coding contribute to superior compression performance.
    • The proposed method achieves arbitrary compression ratios, setting a new benchmark in image compression technology.