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Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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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.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
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The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
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Convolution Properties I01:20

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Convolution computations can be simplified by utilizing their inherent properties.
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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
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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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Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
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Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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DiCENet: Dimension-Wise Convolutions for Efficient Networks.

Sachin Mehta, Hannaneh Hajishirzi, Mohammad Rastegari

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |December 2, 2020
    PubMed
    Summary
    This summary is machine-generated.

    We developed the DiCE unit, a novel convolutional block using dimension-wise convolutions and fusion. This efficient design significantly boosts performance in computer vision tasks like image classification and object detection.

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    Area of Science:

    • Computer Vision
    • Deep Learning Architectures

    Background:

    • Convolutional Neural Networks (CNNs) are fundamental to computer vision.
    • Efficient CNN architectures are crucial for resource-constrained devices.
    • Existing efficient convolution methods like depth-wise separable convolutions have limitations.

    Purpose of the Study:

    • Introduce a novel and generic convolutional unit, the DiCE unit.
    • Enhance the efficiency and performance of deep learning models.
    • Improve spatial and channel-wise information encoding.

    Main Methods:

    • The DiCE unit employs dimension-wise convolutions for light-weight filtering across input tensor dimensions.
    • Dimension-wise fusion efficiently combines these representations.
    • DiCE units are integrated into the DiCENet model architecture.

    Main Results:

    • DiCE units demonstrate significant improvements over depth-wise separable convolutions across various architectures.
    • The DiCENet model achieves state-of-the-art results in image classification, object detection, and semantic segmentation.
    • DiCENet shows 2-4% higher accuracy on ImageNet compared to models like MobileNetv2 and ShuffleNetv2.
    • DiCENet exhibits superior generalization for resource-constrained tasks, outperforming efficient networks like MobileNetv3 and MixNet.

    Conclusions:

    • The DiCE unit offers a simple yet effective method to enhance CNNs.
    • DiCENet provides a highly efficient and performant architecture for diverse computer vision applications.
    • The proposed approach is suitable for real-world applications on devices with limited computational resources.