图形时间卷积神经网络:架构和理论分析.

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...

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...

Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

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.
The area property asserts that the area under the...

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...