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相关概念视频

Fast Fourier Transform01:10

Fast Fourier Transform

340
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
340
Discrete Fourier Transform01:15

Discrete Fourier Transform

295
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
295
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

264
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...
264
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

92
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....
92
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

83
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
83
Properties of DTFT II01:24

Properties of DTFT II

202
In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
202

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相关实验视频

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Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
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一个低延迟的DNN加速器,通过DFT-based Convolution Execution在横条数组内实现.

Hasita Veluri, Umesh Chand, Chun-Kuei Chen

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    |November 29, 2023
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    概括
    此摘要是机器生成的。

    这项研究介绍了一种基于DFT的新离散里埃转换方法,用于模拟电阻随机访问存储器 (RRAM),以加速神经网络训练和推理. 这种方法显著降低了硬件加速器的延迟和功耗.

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    科学领域:

    • 材料科学 材料科学 材料科学
    • 计算机工程 计算机工程
    • 人工智能的人工智能

    背景情况:

    • 模拟电阻随机访问存储器 (RRAM) 实现了神经网络的高效内存计算,克服了·诺伊曼架构的局限性.
    • 然而,RRAM导电状态的高调时间在实时训练中引入了延迟.
    • 现有的方法在平衡性能,功率和记忆耐久性方面面临挑战.

    研究的目的:

    • 为模拟RRAM开发基于离散里叶变换 (DFT) 的内存卷积方法.
    • 为了减少神经网络加速器中的系统延迟和输入再生.
    • 为了最大限度地减少RRAM电导更新,从而提高训练速度和设备耐用性.

    主要方法:

    • 在模拟RRAM阵列中存储静态DFT/反向DFT (IDFT) 系数.
    • 在里埃域中执行卷积,以最大限度地减少数字计算.
    • 利用DFT/IDFT特性,如对称性和线性,进行优化.

    主要成果:

    • 通过最小化连接重量更新,显著加快神经网络训练和推断.
    • 与传统方法相比,卷积操作的功耗降低.
    • 在设计的硬件加速器中提高了峰值功率效率和面积效率.

    结论:

    • 开发的基于 DFT 的 RRAM 方法为超高速,低功耗和紧的硬件加速器提供了一条途径.
    • 将RRAM导电性更新频率降至最低,可以减轻耐力限制.
    • 这种方法可以有效地部署深度神经网络的边缘部署,降低延迟和能源消耗.