Discrete Fourier Transform in Python

 Discrete Fourier Transform in Python

2022/03/17

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◎ 說明：

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Q1：試舉例說明離散傅立葉轉換？

A1：參考圖一與代碼一。

「If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.」

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Fig. 1. 時域與頻域。

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Fig. 2. 時域與頻域的分解圖。

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Fig. 3. 時域與頻域的 3D 分解圖 [8], [9]。

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Fig. 4. 時域與頻域的 3D 分解圖 [8] - [10]。

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A1：參考圖一到圖四。

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◎ 參考資料：

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References

[1] Discrete Fourier Transform (DFT) — Python Numerical Methods

https://pythonnumericalmethods.berkeley.edu/notebooks/chapter24.02-Discrete-Fourier-Transform.html

[2] Wave - 演算法筆記

https://web.ntnu.edu.tw/~algo/Wave.html

[3] 從傅立葉級數到快速傅立葉轉換

https://blog.yeshuanova.com/2019/04/fft_intro/

[4] 離散傅立葉轉換 | 線代啟示錄

https://ccjou.wordpress.com/2012/04/19/%E9%9B%A2%E6%95%A3%E5%82%85%E7%AB%8B%E8%91%89%E8%BD%89%E6%8F%9B/

# 二維陣列

[5] 如何在 Python 中建立二維陣列 | D棧 - Delft Stack

https://www.delftstack.com/zh-tw/howto/python/how-to-initiate-2-d-array-in-python/

# 二維陣列

[6] python - How to define a two-dimensional array? - Stack Overflow

https://stackoverflow.com/questions/6667201/how-to-define-a-two-dimensional-array

# plt.stem(x, y, use_line_collection=True)

[7] matplotlib.pyplot.stem — Matplotlib 3.1.0 documentation

https://matplotlib.org/3.1.0/api/_as_gen/matplotlib.pyplot.stem.html

# 3D 圖

[8] [筆記]離散餘弦變換、傅立葉變換、快速傅立葉變換 - iT 邦幫忙::一起幫忙解決難題，拯救 IT 人的一天

https://ithelp.ithome.com.tw/articles/10231357?sc=pt

# 3D 圖

[9] Machine Learning with Signal Processing Techniques – ML Fundamentals

https://ataspinar.com/2018/04/04/machine-learning-with-signal-processing-techniques/

# stem

[10] The Glowing Python: 3D stem plot

https://glowingpython.blogspot.com/2012/12/3d-stem-plot.html

# arrange reshape

[11] NumPy 陣列重塑形狀和調整大小 | D棧 - Delft Stack

https://www.delftstack.com/zh-tw/tutorial/python-numpy/numpy-array-reshape-and-resize/

# np.dot

[12] numpy.dot — NumPy v1.22 Manual

https://numpy.org/doc/stable/reference/generated/numpy.dot.html

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