From 6ab26f2b0a684082ee087ad904a1ec70d2ee86ff Mon Sep 17 00:00:00 2001 From: fly6516 Date: Fri, 25 Apr 2025 15:19:24 +0800 Subject: [PATCH] =?UTF-8?q?feat:=20=E6=B7=BB=E5=8A=A0=20FFT=20=E5=92=8C=20?= =?UTF-8?q?IFFT=E5=8A=9F=E8=83=BD?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - 实现了一维和二维 FFT 和 IFFT 函数- 添加了图像填充函数,以支持非 2 的整数次幂大小的图像 - 编写了主程序,演示了 FFT 和 IFFT 的使用方法 - 使用 Matplotlib 可视化了原始图像、频谱图和恢复后的图像 --- FFT-IFFT.png | Bin 0 -> 232974 bytes FFT.py | 87 +++++++++++++++++++++++++++++++++++++++++++++++++++ image.jpg | Bin 0 -> 361001 bytes 3 files changed, 87 insertions(+) create mode 100644 FFT-IFFT.png create mode 100644 FFT.py create mode 100644 image.jpg diff --git a/FFT-IFFT.png b/FFT-IFFT.png new file mode 100644 index 0000000000000000000000000000000000000000..89b94e4b08dff2cf244680890189da690ac57777 GIT binary patch literal 232974 zcmc$FWmuF^*Yz-fGK117UD6=}(j^Qj-Hm{Bhja;wG)jolNY@ZEbP9q)OM}u#clUSW 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z=^e_K#CTLF5k!p<==}mL8^2?=q?A=-ogO_ZrVBEMiW_W&y|yNVm}2;0rSG<@w~<$Z zo^JU}&kN+%h?g0rw(cWghGIkf`o33)Od8&|q;ae60MY^1$&BvA@dthky!)4|j^jp>xV0hoj6MP*j=}m%B$1y{_29o{?N9aYpRaI_;r|DE+b`|y=Q}X)e^u09it5jIP{99c hp}+O@|AVfI;469?neSn*Xds}SI&Sk<@ll`H{{cHF^^yPp literal 0 HcmV?d00001 diff --git a/FFT.py b/FFT.py new file mode 100644 index 0000000..0308ca2 --- /dev/null +++ b/FFT.py @@ -0,0 +1,87 @@ +# -*- coding: utf-8 -*- +import numpy as np # 导入NumPy库,用于数值计算 +import math # 导入math库,用于数学运算 +import cv2 # 导入OpenCV库,用于图像处理 +import matplotlib.pyplot as plt # 导入matplotlib库,用于绘图 + +# 一维FFT实现(递归 Cooley-Tukey) +def fft_1d(x): + N = len(x) # 获取输入序列的长度 + if N <= 1: # 如果序列长度小于等于1,直接返回序列 + return x + even = fft_1d(x[::2]) # 递归计算偶数索引位置的FFT + odd = fft_1d(x[1::2]) # 递归计算奇数索引位置的FFT + T = [np.exp(-2j * np.pi * k / N) * odd[k] for k in range(N // 2)] # 计算旋转因子 + return [even[k] + T[k] for k in range(N // 2)] + \ + [even[k] - T[k] for k in range(N // 2)] # 合并结果 + +# 一维IFFT实现 +def ifft_1d(x): + N = len(x) # 获取输入序列的长度 + x_conj = [np.conj(xi) for xi in x] # 对输入序列取共轭 + y = fft_1d(x_conj) # 对共轭序列进行FFT + return [np.conj(yi) / N for yi in y] # 对结果取共轭并除以N,得到IFFT结果 + +# 二维FFT +def fft_2d(image): + image = image.astype(float) # 将图像转换为浮点型 + rows, cols = image.shape # 获取图像的行数和列数 + # 对每行进行FFT + fft_rows = [fft_1d(list(image[i, :])) for i in range(rows)] + # 对每列进行FFT + fft_cols = [fft_1d([fft_rows[i][j] for i in range(rows)]) for j in range(cols)] + return np.array(fft_cols).T # 返回转置后的结果 + +# 二维IFFT +def ifft_2d(freq_domain): + rows, cols = freq_domain.shape # 获取频域图像的行数和列数 + # 对每列进行IFFT + ifft_cols = [ifft_1d([freq_domain[i][j] for i in range(rows)]) for j in range(cols)] + # 对每行进行IFFT + ifft_rows = [ifft_1d([ifft_cols[j][i] for j in range(cols)]) for i in range(rows)] + return np.array(ifft_rows) # 返回IFFT结果 + +# 填充图像为2的整数次幂大小 +def pad_image(image): + h, w = image.shape # 获取图像的高度和宽度 + h2 = 1 << (h - 1).bit_length() # 计算最接近且大于等于h的2的整数次幂 + w2 = 1 << (w - 1).bit_length() # 计算最接近且大于等于w的2的整数次幂 + padded = np.zeros((h2, w2)) # 创建填充后的零矩阵 + padded[:h, :w] = image # 将原图像放入填充矩阵的左上角 + return padded # 返回填充后的图像 + +# 主程序 +def main(): + # 读取图像 + image = cv2.imread("image.jpg", cv2.IMREAD_GRAYSCALE) # 以灰度模式读取图像 + if image is None: # 如果图像读取失败,输出错误信息并返回 + print("图像读取失败,请确认 image.jpg 文件存在于当前目录。") + return + + # 填充图像 + padded_image = pad_image(image) # 对图像进行填充 + + # 执行FFT和IFFT + freq = fft_2d(padded_image) # 对填充后的图像进行二维FFT + restored = ifft_2d(freq).real # 对频域图像进行二维IFFT,并取实部 + + # 可视化结果 + plt.figure(figsize=(12, 4)) # 创建绘图窗口 + + plt.subplot(1, 3, 1) # 创建第一个子图 + plt.title("Original") # 设置子图标题 + plt.imshow(image, cmap="gray") # 显示原始图像 + + plt.subplot(1, 3, 2) # 创建第二个子图 + plt.title("FFT Spectrum") # 设置子图标题 + plt.imshow(np.log(np.abs(freq) + 1), cmap="gray") # 显示FFT频谱 + + plt.subplot(1, 3, 3) # 创建第三个子图 + plt.title("Restored") # 设置子图标题 + plt.imshow(restored, cmap="gray") # 显示恢复后的图像 + + plt.tight_layout() # 调整子图布局 + plt.show() # 显示绘图窗口 + +if __name__ == "__main__": + main() # 运行主程序 \ No newline at end of file diff --git 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