signal processing part folder strucutre change
PinkR1ver
@ -20,7 +20,7 @@ $$
|
||||
H(\mu)(t) = \frac{1}{\pi} \text{p.v.} \int_{\infty}^{\infty} \frac{\mu(t)}{t-\tau}d\tau
|
||||
$$
|
||||
|
||||
|
||||
|
||||
|
||||
```MATLAB
|
||||
analytical = hilbert(signal)
|
||||
|
||||
@ -10,4 +10,4 @@ date: 2024-03-18
|
||||
# Method
|
||||
|
||||
* [DTW(Dynamic Time Warping)](computer_sci/deep_learning_and_machine_learning/Trick/DTW.md)
|
||||
* [Manhattan Distance](signal_processing/curve_similarity/manhattan_distance.md)
|
||||
* [Manhattan Distance](signal_processing/algorithm/curve_similarity/manhattan_distance.md)
|
||||
|
Before Width: | Height: | Size: 148 KiB After Width: | Height: | Size: 148 KiB |
|
Before Width: | Height: | Size: 21 KiB After Width: | Height: | Size: 21 KiB |
|
Before Width: | Height: | Size: 593 KiB After Width: | Height: | Size: 593 KiB |
@ -9,7 +9,7 @@ date: 2024-01-12
|
||||
|
||||
# Introduction
|
||||
|
||||
|
||||
|
||||
|
||||
# Envelope Explanation
|
||||
## Envelope and Fine Structure
|
||||
@ -36,7 +36,7 @@ date: 2024-01-12
|
||||
|
||||
早期关于包络和瞬时相位的研究都是基于笛卡尔坐标系x-y
|
||||
|
||||
|
||||
|
||||
|
||||
有关系：
|
||||
$$
|
||||
@ -73,7 +73,7 @@ $$
|
||||
H(\mu)(t) = \frac{1}{\pi} \text{p.v.} \int_{\infty}^{\infty} \frac{\mu(t)}{t-\tau}d\tau
|
||||
$$
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
The Hilbert transform is given by the [Cauchy principal value](math/real_analysis/cauchy_principal_value.md) of the convolution with the function $1/(\pi t)$.
|
||||
|
Before Width: | Height: | Size: 164 KiB After Width: | Height: | Size: 164 KiB |
|
Before Width: | Height: | Size: 120 KiB After Width: | Height: | Size: 120 KiB |
@ -54,7 +54,7 @@ T_{n+1}(x) & = 2xT_n(x)-T_{n-1}(x)
|
||||
\end{split}
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
|
||||
#### 第二类切比雪夫多项式
|
||||
|
||||
$$
|
||||
@ -67,7 +67,7 @@ U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
|
||||
|
||||
|
||||
### 正交性
|
||||
|
||||
@ -7,13 +7,13 @@ date: 2023-11-30
|
||||
---
|
||||
# Almost Fourier Transform
|
||||
|
||||
|
||||
|
||||
|
||||
It is important to see there are 2 different frequencies here:
|
||||
1. The frequency of the original signal
|
||||
2. The frequency with which the **little rotating vector winds around the circle**
|
||||
|
||||
|
||||
|
||||
|
||||
Different patterns appear as we wind up this graph, but it is clear that the x-coordinate for the center of mass is important when the winding frequency is 3; The same number as the original signal
|
||||
|
||||
@ -28,7 +28,7 @@ $$
|
||||
因为在Fourier transform中，convention way是顺时针旋转，所以使用$e^{-2\pi ift}$，那如何衡量center of mass呢，如下图：
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$
|
||||
@ -43,7 +43,7 @@ $$
|
||||
|
||||
这个就是Almost Fourier Transform, 但是实际情况上，Fourier transform倾向于得到scaled center mass，越长的time，旋转越多圈，其Fourier transform也会成倍放大
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
# Fourier Transform (FT)
|
||||
@ -118,7 +118,7 @@ $$
|
||||
|
||||
## 复数形式推导
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
## 三角函数推导
|
||||
@ -184,7 +184,7 @@ $$
|
||||
|
||||
**For $X[k]$, it means a $\cos$ wine like this:**
|
||||
|
||||
|
||||
|
||||
|
||||
# Fast Fourier transform(FFT)
|
||||
|
||||
|
||||
|
Before Width: | Height: | Size: 1.1 MiB After Width: | Height: | Size: 1.1 MiB |
|
Before Width: | Height: | Size: 790 KiB After Width: | Height: | Size: 790 KiB |
|
Before Width: | Height: | Size: 481 KiB After Width: | Height: | Size: 481 KiB |
|
Before Width: | Height: | Size: 132 KiB After Width: | Height: | Size: 132 KiB |
|
Before Width: | Height: | Size: 1.9 MiB After Width: | Height: | Size: 1.9 MiB |
|
Before Width: | Height: | Size: 368 KiB After Width: | Height: | Size: 368 KiB |
|
Before Width: | Height: | Size: 314 KiB After Width: | Height: | Size: 314 KiB |
@ -70,7 +70,7 @@ $$
|
||||
|
||||
对于拥有Ergodicity的信号，可以用时间平均代替集合平均，即
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$
|
||||
|
||||
@ -3,7 +3,7 @@ title: Oscilloscope basic knowledge
|
||||
tags:
|
||||
- signal-processing
|
||||
- devices
|
||||
date: 2024-11-04
|
||||
date: 2024-04-11
|
||||
---
|
||||
# Classification
|
||||
|
||||
|
||||
@ -9,7 +9,7 @@ date: 2024-03-18
|
||||
|
||||
* [Random Signal Basic](signal_processing/basic_knowledge/random_signal_basic.md)
|
||||
* [Fourier Transform](signal_processing/basic_knowledge/FT/fourier_transform.md)
|
||||
* [Power spectral density estimation](signal_processing/PSD_estimation/PSD_estimation.md)
|
||||
* [Power spectral density estimation](signal_processing/algorithm/PSD_estimation/PSD_estimation.md)
|
||||
* [FBW - Fractional Band Width](signal_processing/basic_knowledge/concept/FBW.md)
|
||||
|
||||
## Fourier Transform
|
||||
@ -27,25 +27,30 @@ date: 2024-03-18
|
||||
|
||||
## Envelope
|
||||
|
||||
* [Hilbert Transform - Envelope](signal_processing/envelope/hilbert_transform.md)
|
||||
* [Hilbert Transform - Envelope](signal_processing/algorithm/envelope/hilbert_transform.md)
|
||||
|
||||
## Curve similarity
|
||||
|
||||
* [Curve Similarity - MOC](signal_processing/curve_similarity/curve_similarity.md)
|
||||
* [Curve Similarity - MOC](signal_processing/algorithm/curve_similarity/curve_similarity.md)
|
||||
|
||||
## Filter
|
||||
|
||||
* [Chebyshev Filter](signal_processing/filter/chebyshev_filter.md)
|
||||
* [Chebyshev Filter](signal_processing/algorithm/filter/chebyshev_filter.md)
|
||||
|
||||
## Generating Impulse
|
||||
|
||||
* [Gaussian Impulse Generating](signal_processing/impulse_generating/gaussian_impulse.md)
|
||||
|
||||
* [Gaussian Impulse Generating](signal_processing/algorithm/impulse_generating/gaussian_impulse.md)
|
||||
|
||||
## Autocorrelation
|
||||
|
||||
* [Autocorrelation in Signal Processing](signal_processing/advanced_statistic/autocorrelation/autocorrelation.md)
|
||||
* [Period Detection by Autocorrelation](signal_processing/advanced_statistic/autocorrelation/period_detection.md)
|
||||
|
||||
|
||||
## Empirical Mode Decomposition
|
||||
|
||||
|
||||
|
||||
# Software
|
||||
|
||||
## CST MWS
|
||||
|
||||