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相关概念视频

Downsampling01:20

Downsampling

147
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...
147
Upsampling01:22

Upsampling

222
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...
222
Bandpass Sampling01:17

Bandpass Sampling

170
In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
170
Sampling Theorem01:15

Sampling Theorem

321
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
321
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

202
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...
202
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

187
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
187

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相关实验视频

Updated: Jun 20, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
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混合式梯度方法,基于带宽的步骤大小,用于有限和优化.

Yuqing Liang1, Yang Yang1, Jinlan Liu2

  • 1Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China.

Neural networks : the official journal of the International Neural Network Society
|July 18, 2024
PubMed
概括
此摘要是机器生成的。

这项研究增强了机器学习优化混合式梯度方法. 它提供了统一的收保证,并改善了有限和问题的收率.

关键词:
基于带宽的步骤大小以带宽为基础.最后一次代的收趋同.不凸的目标是指非凸的目标.条件 PL PL 条件混类型的梯度算法.

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科学领域:

  • 机器学习 机器学习
  • 优化算法 优化算法

背景情况:

  • 混类型的梯度方法对于有限和优化非常受欢迎.
  • 现有的方法对客观函数和梯度有限制性假设.

研究的目的:

  • 探索和统一混合型梯度方法的收性质.
  • 放宽现有的假设,改善趋同保障.

主要方法:

  • 采用基于带宽的步骤大小策略来实现统一的融合.
  • 取代目标函数下限与损失函数假设.
  • 分析非凸的目标和Polyak-Łojasiewicz (PL) 条件下的趋同.

主要成果:

  • 混合式梯度方法的统一收保证.
  • 消除对随机梯度变化和二次动量的实际限制.
  • 改善了有限和优化问题的收率.
  • 通过数值实验验证理论结果的验证.

结论:

  • 这项研究提供了对混合型梯度方法的更深入的理解.
  • 提供了优化机器学习中有限和问题的实用见解.
  • 证明了拟议方法的效率及其理论基础.