{"id":23,"date":"2014-07-24T09:25:59","date_gmt":"2014-07-24T09:25:59","guid":{"rendered":"http:\/\/themes.tielabs.com\/sahifa5\/?p=23"},"modified":"2025-07-25T18:03:12","modified_gmt":"2025-07-25T14:33:12","slug":"time-sensitive-5-ways-to-reduce-your-taxes","status":"publish","type":"post","link":"https:\/\/ilk.ir\/sahifa\/fashion\/time-sensitive-5-ways-to-reduce-your-taxes\/","title":{"rendered":"Fast Fourier Transform (FFT) \u06cc\u0627 “\u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0633\u0631\u06cc\u0639” \u06cc\u0639\u0646\u06cc \u0686\u0647\u061f"},"content":{"rendered":"
\n

Fast Fourier Transform (FFT) \u06cc\u0627 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0633\u0631\u06cc\u0639\u060c \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0648 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u067e\u0631\u062f\u0627\u0632\u0634 \u0633\u06cc\u06af\u0646\u0627\u0644\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u062a\u0635\u0648\u06cc\u0631\u060c \u0648 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u0639\u0644\u0645\u06cc \u0648 \u0645\u0647\u0646\u062f\u0633\u06cc \u0627\u0633\u062a. \u062f\u0631 \u0648\u0627\u0642\u0639\u060c FFT \u06cc\u06a9 \u0631\u0648\u0634 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06af\u0633\u0633\u062a\u0647 (DFT)<\/b> \u0648 \u0645\u0639\u06a9\u0648\u0633 \u0622\u0646 (IDFT) \u0627\u0633\u062a.<\/p>\n

\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 FFT \u0631\u0627 \u0628\u0647 \u062e\u0648\u0628\u06cc \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0627\u06cc\u062f \u0645\u0641\u0647\u0648\u0645 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647<\/b> \u0648 \u0633\u067e\u0633 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06af\u0633\u0633\u062a\u0647 (DFT)<\/b> \u0631\u0627 \u0628\u062f\u0627\u0646\u06cc\u0645.<\/p>\n

1. \u0645\u0641\u0647\u0648\u0645 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 (Fourier Transform)<\/h3>\n

\u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0634\u0645\u0627 \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u067e\u06cc\u0686\u06cc\u062f\u0647 \u062f\u0627\u0631\u06cc\u062f\u060c \u0645\u062b\u0644\u0627\u064b \u06cc\u06a9 \u0642\u0637\u0639\u0647 \u0645\u0648\u0633\u06cc\u0642\u06cc. \u06af\u0648\u0634 \u0627\u0646\u0633\u0627\u0646 \u0627\u06cc\u0646 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0635\u062f\u0627\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 (\u0628\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627 \u0648 \u0634\u062f\u062a\u200c\u0647\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a) \u062f\u0631\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u062f\u0642\u06cc\u0642\u0627\u064b \u0647\u0645\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0631\u06cc\u0627\u0636\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n

\u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0631\u0627 \u0627\u0632 “\u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646” (Time Domain) \u0628\u0647 “\u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633” (Frequency Domain) \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/b><\/p>\n

    \n
  • \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646:<\/b> \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0648\u0632\u0647\u060c \u0645\u0627 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u062f\u0627\u0645\u0646\u0647 \u0622\u0646 (\u0645\u062b\u0644\u0627\u064b \u0648\u0644\u062a\u0627\u0698 \u06cc\u0627 \u0641\u0634\u0627\u0631 \u0647\u0648\u0627) \u0628\u0631 \u062d\u0633\u0628 \u0632\u0645\u0627\u0646 \u0645\u0634\u0627\u0647\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0646\u0645\u0648\u062f\u0627\u0631\u06cc \u06a9\u0647 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0635\u0648\u062a\u06cc \u0631\u0627 \u062f\u0631 \u0637\u0648\u0644 \u0632\u0645\u0627\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f\u060c \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646 \u0627\u0633\u062a.<\/li>\n
  • \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633:<\/b> \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0648\u0632\u0647\u060c \u0633\u06cc\u06af\u0646\u0627\u0644 \u0628\u0647 \u0627\u062c\u0632\u0627\u06cc \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u062a\u0634\u06a9\u06cc\u0644\u200c\u062f\u0647\u0646\u062f\u0647\u200c\u0627\u0634 \u062a\u062c\u0632\u06cc\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u06cc\u0639\u0646\u06cc\u060c \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0628\u0647 \u0645\u0627 \u0645\u06cc\u200c\u06af\u0648\u06cc\u062f \u06a9\u0647 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0627\u0635\u0644\u06cc \u0627\u0632 \u0686\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc\u06cc (\u0645\u062b\u0644\u0627\u064b 100 \u0647\u0631\u062a\u0632\u060c 1 \u06a9\u06cc\u0644\u0648\u0647\u0631\u062a\u0632\u060c 5 \u06a9\u06cc\u0644\u0648\u0647\u0631\u062a\u0632) \u0648 \u0628\u0627 \u0686\u0647 \u0634\u062f\u062a\u200c\u0647\u0627\u06cc\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0646\u0645\u0648\u062f\u0627\u0631 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u06cc\u06a9 \u0637\u06cc\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u062d\u0648\u0631 \u0627\u0641\u0642\u06cc \u0641\u0631\u06a9\u0627\u0646\u0633 \u0648 \u0645\u062d\u0648\u0631 \u0639\u0645\u0648\u062f\u06cc \u062f\u0627\u0645\u0646\u0647 (\u06cc\u0627 \u062a\u0648\u0627\u0646) \u0622\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/li>\n<\/ul>\n

    \u0628\u0647 \u0632\u0628\u0627\u0646 \u0633\u0627\u062f\u0647\u060c \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0631\u0627 \u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u0645\u0648\u062c\u200c\u0647\u0627\u06cc \u0633\u06cc\u0646\u0648\u0633\u06cc \u0633\u0627\u062f\u0647 \u0628\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627 \u0648 \u062f\u0627\u0645\u0646\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062a\u062c\u0632\u06cc\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n

    \u0641\u0631\u0645\u0648\u0644 \u06a9\u0644\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u067e\u06cc\u0648\u0633\u062a\u0647 (\u0628\u0631\u0627\u06cc \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0622\u0646\u0627\u0644\u0648\u06af):<\/p>\n

    \n
    \"\u0641\u0631\u0645\u0648\u0644
    \u0641\u0631\u0645\u0648\u0644 \u06a9\u0644\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u067e\u06cc\u0648\u0633\u062a\u0647 (\u0628\u0631\u0627\u06cc \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0622\u0646\u0627\u0644\u0648\u06af)<\/figcaption><\/figure>\n<\/div>\n

    \u06a9\u0647 x(t) \u0633\u06cc\u06af\u0646\u0627\u0644 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646 \u0648 X(\u03c9) \u0633\u06cc\u06af\u0646\u0627\u0644 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 (\u0637\u06cc\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc) \u0627\u0633\u062a.<\/p>\n

    2. \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06af\u0633\u0633\u062a\u0647 (DFT)<\/h3>\n

    \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u062f\u06cc\u062c\u06cc\u062a\u0627\u0644\u060c \u0645\u0627 \u0628\u0627 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u067e\u06cc\u0648\u0633\u062a\u0647 \u0633\u0631\u0648\u06a9\u0627\u0631 \u0646\u062f\u0627\u0631\u06cc\u0645\u060c \u0628\u0644\u06a9\u0647 \u0628\u0627 \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc \u06af\u0633\u0633\u062a\u0647 (sampled) \u0627\u0632 \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645. \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0648\u0642\u062a\u06cc \u06cc\u06a9 \u0645\u06cc\u06a9\u0631\u0648\u0641\u0648\u0646 \u0635\u062f\u0627 \u0631\u0627 \u0636\u0628\u0637 \u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u062f\u0631 \u0641\u0648\u0627\u0635\u0644 \u0632\u0645\u0627\u0646\u06cc \u0645\u0634\u062e\u0635\u06cc \u0627\u0632 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0646\u0645\u0648\u0646\u0647\u200c\u0628\u0631\u062f\u0627\u0631\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631 \u0628\u0627 \u0627\u06cc\u0646 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u06af\u0633\u0633\u062a\u0647\u060c \u0628\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06af\u0633\u0633\u062a\u0647 (DFT) \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.<\/p>\n

    DFT\u060c \u0647\u0645\u0627\u0646\u0646\u062f \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u067e\u06cc\u0648\u0633\u062a\u0647\u060c \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u06af\u0633\u0633\u062a\u0647 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646 \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0633\u06cc\u06af\u0646\u0627\u0644 \u06af\u0633\u0633\u062a\u0647 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n

    \u0641\u0631\u0645\u0648\u0644 DFT:<\/p>\n

    \"\u0641\u0631\u0645\u0648\u0644<\/div>\n

    \u06a9\u0647:<\/p>\n

      \n
    • x<\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: n<\/span><\/span><\/span><\/span><\/span>-\u0627\u064f\u0645\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0627\u0632 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0648\u0631\u0648\u062f\u06cc \u062f\u0631 \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646 (\u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0627\u064b N<\/span><\/span><\/span><\/span><\/span> \u0646\u0645\u0648\u0646\u0647 \u062f\u0627\u0631\u06cc\u0645).<\/li>\n
    • X<\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: k<\/span><\/span><\/span><\/span><\/span>-\u0627\u064f\u0645\u06cc\u0646 \u0645\u0624\u0644\u0641\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u062f\u0631 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633.<\/li>\n
    • N<\/span><\/span><\/span><\/span><\/span>: \u062a\u0639\u062f\u0627\u062f \u06a9\u0644 \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc \u0633\u06cc\u06af\u0646\u0627\u0644.<\/li>\n
    • k<\/span><\/span><\/span><\/span><\/span>: \u0627\u0646\u062f\u06cc\u0633 \u0641\u0631\u06a9\u0627\u0646\u0633 (\u0627\u0632 0 \u062a\u0627 N<\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>).<\/li>\n<\/ul>\n

      \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 DFT \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0641\u0631\u0645\u0648\u0644\u060c \u0646\u06cc\u0627\u0632 \u0628\u0647 N<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u0639\u0645\u0644\u06cc\u0627\u062a \u0636\u0631\u0628 \u0648 \u062c\u0645\u0639 (\u06a9\u0647 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0647\u0633\u062a\u0646\u062f) \u062f\u0627\u0631\u062f. \u0628\u0631\u0627\u06cc \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0637\u0648\u0644\u0627\u0646\u06cc (\u0628\u0627 N \u0628\u0627\u0644\u0627)\u060c \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0633\u06cc\u0627\u0631 \u0632\u0645\u0627\u0646\u200c\u0628\u0631 \u0648 \u067e\u0631\u0647\u0632\u06cc\u0646\u0647 \u0628\u0627\u0634\u062f.<\/p>\n

      3. \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0633\u0631\u06cc\u0639 (FFT)<\/h3>\n

      \u0627\u06cc\u0646\u062c\u0627\u0633\u062a \u06a9\u0647 FFT \u0648\u0627\u0631\u062f \u0639\u0645\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f!<\/p>\n

      FFT (Fast Fourier Transform) \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 DFT \u0627\u0633\u062a \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/b><\/p>\n

      \u0628\u0647 \u062c\u0627\u06cc N<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u0639\u0645\u0644\u06cc\u0627\u062a\u060c FFT \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b N<\/span>log2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>N<\/span>)<\/span><\/span><\/span><\/span><\/span> \u0639\u0645\u0644\u06cc\u0627\u062a \u062f\u0627\u0631\u062f. \u0627\u06cc\u0646 \u06a9\u0627\u0647\u0634 \u062f\u0631 \u0633\u0631\u0639\u062a \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u060c \u0628\u0647 \u062e\u0635\u0648\u0635 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0632\u0631\u06af N (\u0645\u062b\u0644\u0627\u064b \u0647\u0632\u0627\u0631\u0627\u0646 \u06cc\u0627 \u0645\u06cc\u0644\u06cc\u0648\u0646\u200c\u0647\u0627 \u0646\u0645\u0648\u0646\u0647)\u060c \u0628\u0633\u06cc\u0627\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631 \u0627\u0633\u062a \u0648 \u0628\u0627\u0639\u062b \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 DFT \u0627\u0632 \u0646\u0638\u0631 \u0639\u0645\u0644\u06cc \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0628\u0627\u0634\u062f.<\/p>\n

      \u0686\u06af\u0648\u0646\u0647 FFT \u0633\u0631\u0639\u062a \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u062f\u0647\u062f\u061f<\/b><\/p>\n

      \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc FFT \u0645\u062e\u062a\u0644\u0641\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0627\u0645\u0627 \u0645\u062d\u0628\u0648\u0628\u200c\u062a\u0631\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0627\u06cc\u062f\u0647 “\u062a\u0642\u0633\u06cc\u0645 \u0648 \u062d\u0644” (Divide and Conquer) \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f. \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Cooley-Tukey (\u06a9\u0647 \u0631\u0627\u06cc\u062c\u200c\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 FFT \u0627\u0633\u062a) \u0628\u0627 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f\u0646 \u06cc\u06a9 DFT \u0628\u0632\u0631\u06af \u0628\u0647 \u0686\u0646\u062f\u06cc\u0646 DFT \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631 \u0648 \u0633\u067e\u0633 \u062a\u0631\u06a9\u06cc\u0628 \u0646\u062a\u0627\u06cc\u062c \u0622\u0646\u0647\u0627\u060c \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0631\u0627 \u0628\u0647\u06cc\u0646\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0627\u0633\u062a \u0648 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0647 DFT\u0647\u0627\u06cc \u062f\u0648 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc (\u06a9\u0647 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0642\u0627\u0628\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0633\u062a\u0646\u062f) \u0628\u0631\u0633\u06cc\u0645\u060c \u0627\u062f\u0627\u0645\u0647 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n

      \u0645\u062b\u0627\u0644: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0631\u0639\u062a DFT \u0648 FFT<\/b><\/p>\n

      \u0627\u06af\u0631 N<\/span>=<\/span><\/span>1024<\/span><\/span><\/span><\/span><\/span> (\u062a\u0639\u062f\u0627\u062f \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627):<\/p>\n

        \n
      • DFT: 102<\/span>42<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span>,<\/span>048<\/span>,<\/span>576<\/span><\/span><\/span><\/span><\/span> \u0639\u0645\u0644\u06cc\u0627\u062a<\/li>\n
      • FFT: 1024<\/span>\u00d7<\/span><\/span>log2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>1024<\/span>)<\/span>=<\/span><\/span>1024<\/span>\u00d7<\/span><\/span>10<\/span>=<\/span><\/span>10<\/span>,<\/span>240<\/span><\/span><\/span><\/span><\/span> \u0639\u0645\u0644\u06cc\u0627\u062a<\/li>\n<\/ul>\n

        \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc\u200c\u0628\u06cc\u0646\u06cc\u062f\u060c FFT \u062f\u0647\u200c\u0647\u0627 \u062a\u0627 \u0635\u062f\u0647\u0627 \u0628\u0631\u0627\u0628\u0631 \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0627\u0632 DFT \u0645\u0633\u062a\u0642\u06cc\u0645 \u0627\u0633\u062a.<\/p>\n

        4. \u062e\u0631\u0648\u062c\u06cc FFT<\/h3>\n

        \u062e\u0631\u0648\u062c\u06cc FFT \u06cc\u06a9 \u0633\u0631\u06cc \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u0645\u062e\u062a\u0644\u0637 \u0627\u0633\u062a. \u0647\u0631 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0634\u0627\u0645\u0644 \u06cc\u06a9 \u0642\u0633\u0645\u062a \u062d\u0642\u06cc\u0642\u06cc \u0648 \u06cc\u06a9 \u0642\u0633\u0645\u062a \u0645\u0648\u0647\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0645\u0641\u06cc\u062f \u0645\u0627\u0646\u0646\u062f \u062f\u0627\u0645\u0646\u0647 (\u0634\u062f\u062a) \u0647\u0631 \u0641\u0631\u06a9\u0627\u0646\u0633\u060c \u0628\u0627\u06cc\u062f \u0642\u062f\u0631 \u0645\u0637\u0644\u0642 (magnitude) \u0627\u06cc\u0646 \u0627\u0639\u062f\u0627\u062f \u0645\u062e\u062a\u0644\u0637 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n

        Amplitude<\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>(<\/span>Real\u00a0Part<\/span>k<\/span><\/span><\/span>\u200b<\/span><\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span>+<\/span>(<\/span>Imaginary\u00a0Part<\/span>k<\/span><\/span><\/span>\u200b<\/span><\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n

        \u0627\u06cc\u0646 \u062f\u0627\u0645\u0646\u0647\u060c \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0645\u06cc\u0632\u0627\u0646 \u062d\u0636\u0648\u0631 \u0622\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633 \u062e\u0627\u0635 \u062f\u0631 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0627\u0635\u0644\u06cc \u0627\u0633\u062a.<\/p>\n

        5. \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc FFT:<\/h3>\n

        FFT \u062f\u0631 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u06af\u0633\u062a\u0631\u062f\u0647\u200c\u0627\u06cc \u062f\u0627\u0631\u062f\u060c \u0627\u0632 \u062c\u0645\u0644\u0647:<\/p>\n

          \n
        • \u067e\u0631\u062f\u0627\u0632\u0634 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0635\u0648\u062a\u06cc:<\/b>\n
            \n
          • \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0637\u06cc\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0645\u0648\u0633\u06cc\u0642\u06cc \u0648 \u06af\u0641\u062a\u0627\u0631.<\/li>\n
          • \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u0646\u0648\u06cc\u0632 (\u0628\u0627 \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u0641\u0631\u06a9\u0627\u0646\u0633 \u0646\u0648\u06cc\u0632 \u0648 \u062d\u0630\u0641 \u0622\u0646).<\/li>\n
          • \u0641\u0634\u0631\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0635\u062f\u0627 (\u0645\u062b\u0644 MP3) \u0628\u0627 \u062d\u0630\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u06a9\u0645\u062a\u0631 \u0634\u0646\u06cc\u062f\u0647 \u0634\u062f\u0647.<\/li>\n
          • \u062a\u0634\u062e\u06cc\u0635 \u0627\u0644\u06af\u0648\u0647\u0627\u06cc \u0635\u0648\u062a\u06cc \u0648 \u06af\u0641\u062a\u0627\u0631\u06cc.<\/li>\n
          • \u0627\u06a9\u0648\u0644\u0627\u06cc\u0632\u0631\u0647\u0627 (\u0645\u0627\u0646\u0646\u062f \u062a\u0631\u0627\u0634\u0647 MSGEQ7 \u06a9\u0647 \u0628\u0647 \u0622\u0646 \u0627\u0634\u0627\u0631\u0647 \u06a9\u0631\u062f\u06cc\u062f\u060c \u062f\u0631 \u0648\u0627\u0642\u0639 \u06cc\u06a9 \u0646\u0633\u062e\u0647 \u0633\u062e\u062a\u200c\u0627\u0641\u0632\u0627\u0631\u06cc \u0633\u0627\u062f\u0647 \u0627\u0632 \u062a\u062d\u0644\u06cc\u0644 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0627\u0633\u062a\u060c \u0627\u0645\u0627 DFT\/FFT \u062a\u062c\u0632\u06cc\u0647 \u0628\u0633\u06cc\u0627\u0631 \u062f\u0642\u06cc\u0642\u200c\u062a\u0631 \u0648 \u062c\u0632\u0626\u06cc\u200c\u062a\u0631\u06cc \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f).<\/li>\n<\/ul>\n<\/li>\n
          • \u067e\u0631\u062f\u0627\u0632\u0634 \u062a\u0635\u0648\u06cc\u0631:<\/b>\n
              \n
            • \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u062a\u0635\u0627\u0648\u06cc\u0631 (\u0645\u062b\u0644\u0627\u064b \u0634\u0627\u0631\u067e \u06a9\u0631\u062f\u0646 \u06cc\u0627 \u062a\u0627\u0631 \u06a9\u0631\u062f\u0646 \u062a\u0635\u0627\u0648\u06cc\u0631).<\/li>\n
            • \u0641\u0634\u0631\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u062a\u0635\u0627\u0648\u06cc\u0631 (\u0645\u062b\u0644 JPEG) \u0628\u0627 \u062a\u0628\u062f\u06cc\u0644 \u062a\u0635\u0648\u06cc\u0631 \u0628\u0647 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0648 \u062d\u0630\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u0628\u0627\u0644\u0627 \u06a9\u0647 \u062c\u0632\u0626\u06cc\u0627\u062a \u06a9\u0645\u062a\u0631 \u0645\u0647\u0645 \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f.<\/li>\n
            • \u062a\u0634\u062e\u06cc\u0635 \u0644\u0628\u0647\u200c\u0647\u0627 \u0648 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627.<\/li>\n<\/ul>\n<\/li>\n
            • \u062a\u062d\u0644\u06cc\u0644 \u0627\u0631\u062a\u0639\u0627\u0634\u0627\u062a \u0648 \u0645\u0627\u0634\u06cc\u0646\u200c\u0622\u0644\u0627\u062a:<\/b>\n
                \n
              • \u062a\u0634\u062e\u06cc\u0635 \u0639\u06cc\u0648\u0628 \u062f\u0631 \u0645\u0648\u062a\u0648\u0631\u0647\u0627\u060c \u0628\u0644\u0628\u0631\u06cc\u0646\u06af\u200c\u0647\u0627 \u0648 \u0633\u0627\u06cc\u0631 \u0645\u0627\u0634\u06cc\u0646\u200c\u0622\u0644\u0627\u062a \u0628\u0627 \u062a\u062d\u0644\u06cc\u0644 \u0637\u06cc\u0641 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0627\u0631\u062a\u0639\u0627\u0634\u0627\u062a \u0622\u0646\u0647\u0627.<\/li>\n<\/ul>\n<\/li>\n
              • \u0645\u062e\u0627\u0628\u0631\u0627\u062a:<\/b>\n
                  \n
                • \u0645\u062f\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0648 \u062f\u0645\u062f\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627.<\/li>\n
                • \u0637\u0631\u0627\u062d\u06cc \u0641\u06cc\u0644\u062a\u0631\u0647\u0627.<\/li>\n<\/ul>\n<\/li>\n
                • \u0639\u0644\u0648\u0645 \u067e\u0632\u0634\u06a9\u06cc:<\/b>\n
                    \n
                  • \u0622\u0646\u0627\u0644\u06cc\u0632 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0645\u063a\u0632\u06cc (EEG) \u0648 \u0642\u0644\u0628\u06cc (ECG).<\/li>\n<\/ul>\n<\/li>\n
                  • \u0646\u062c\u0648\u0645:<\/b>\n
                      \n
                    • \u062a\u062d\u0644\u06cc\u0644 \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627\u06cc \u0631\u0627\u062f\u06cc\u0648\u06cc\u06cc \u0627\u0632 \u0641\u0636\u0627.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                      6. \u0645\u062d\u062f\u0648\u062f\u06cc\u062a\u200c\u0647\u0627 \u0648 \u0645\u0644\u0627\u062d\u0638\u0627\u062a FFT:<\/h3>\n
                        \n
                      • \u067e\u0646\u062c\u0631\u0647\u200c\u0628\u0646\u062f\u06cc (Windowing):<\/b> FFT \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0648\u0631\u0648\u062f\u06cc \u062a\u0646\u0627\u0648\u0628\u06cc \u0627\u0633\u062a \u0648 \u062f\u0642\u06cc\u0642\u0627 \u062f\u0631 \u0627\u0646\u062a\u0647\u0627\u06cc \u067e\u0646\u062c\u0631\u0647 \u0632\u0645\u0627\u0646\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06af\u0631 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0648\u0631\u0648\u062f\u06cc \u0627\u06cc\u0646 \u062e\u0627\u0635\u06cc\u062a \u0631\u0627 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c “\u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0637\u06cc\u0641\u06cc” (Spectral Leakage) \u0631\u062e \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0628\u0627\u0639\u062b \u0645\u06cc\u200c\u0634\u0648\u062f \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0646\u0634\u0648\u0646\u062f. \u0628\u0631\u0627\u06cc \u06a9\u0627\u0647\u0634 \u0627\u06cc\u0646 \u0627\u062b\u0631\u060c \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u067e\u0646\u062c\u0631\u0647\u200c\u0627\u06cc (\u0645\u0627\u0646\u0646\u062f Hanning, Hamming, Blackman) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0628\u0647 \u062a\u062f\u0631\u06cc\u062c \u0633\u06cc\u06af\u0646\u0627\u0644 \u0631\u0627 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0648 \u0627\u0646\u062a\u0647\u0627\u06cc \u067e\u0646\u062c\u0631\u0647 \u0628\u0647 \u0635\u0641\u0631 \u0645\u06cc\u200c\u0631\u0633\u0627\u0646\u0646\u062f.<\/li>\n
                      • \u0631\u0632\u0648\u0644\u0648\u0634\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc:<\/b> \u0631\u0632\u0648\u0644\u0648\u0634\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc (\u062f\u0642\u062a \u062f\u0631 \u062a\u0634\u062e\u06cc\u0635 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0647\u0645) \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc N \u0648 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0646\u0645\u0648\u0646\u0647\u200c\u0628\u0631\u062f\u0627\u0631\u06cc (Sampling Frequency) \u0628\u0633\u062a\u06af\u06cc \u062f\u0627\u0631\u062f. \u0647\u0631\u0686\u0647 N \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u0631\u0632\u0648\u0644\u0648\u0634\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0628\u0627\u0644\u0627\u062a\u0631 \u0627\u0633\u062a.<\/li>\n
                      • \u0641\u0631\u06a9\u0627\u0646\u0633 \u0646\u0627\u06cc\u06a9\u0648\u0626\u06cc\u0633\u062a (Nyquist Frequency):<\/b> \u0628\u0631\u0627\u06cc \u062c\u0644\u0648\u06af\u06cc\u0631\u06cc \u0627\u0632 \u067e\u062f\u06cc\u062f\u0647 “\u0622\u0644\u06cc\u0627\u0633\u06cc\u0646\u06af” (Aliasing) \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u0628\u0627\u0644\u0627 \u0628\u0647 \u0627\u0634\u062a\u0628\u0627\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u067e\u0627\u06cc\u06cc\u0646\u200c\u062a\u0631 \u0638\u0627\u0647\u0631 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u0641\u0631\u06a9\u0627\u0646\u0633 \u0646\u0645\u0648\u0646\u0647\u200c\u0628\u0631\u062f\u0627\u0631\u06cc \u0628\u0627\u06cc\u062f \u062d\u062f\u0627\u0642\u0644 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0628\u0627\u0634\u062f (\u0642\u0636\u06cc\u0647 \u0646\u0627\u06cc\u06a9\u0648\u0626\u06cc\u0633\u062a).<\/li>\n
                      • \u0642\u062f\u0631\u062a 2 \u0628\u0648\u062f\u0646 N:<\/b> \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc FFT \u0628\u0647\u06cc\u0646\u0647\u200c\u062a\u0631 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0627\u06af\u0631 \u062a\u0639\u062f\u0627\u062f \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc N \u062a\u0648\u0627\u0646\u06cc \u0627\u0632 2 \u0628\u0627\u0634\u062f (\u0645\u062b\u0644\u0627\u064b 256, 512, 1024, 2048). \u0627\u06af\u0631 N \u062a\u0648\u0627\u0646\u06cc \u0627\u0632 2 \u0646\u0628\u0627\u0634\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc\u06cc \u0645\u0627\u0646\u0646\u062f “\u067e\u062f\u06cc\u0646\u06af \u0635\u0641\u0631” (Zero Padding) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u06a9\u0647 \u0628\u0647 \u0627\u0646\u062a\u0647\u0627\u06cc \u0633\u06cc\u06af\u0646\u0627\u0644 \u0635\u0641\u0631 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u062a\u0627 \u0637\u0648\u0644 \u0622\u0646 \u0628\u0647 \u06cc\u06a9 \u062a\u0648\u0627\u0646 \u0627\u0632 2 \u0628\u0631\u0633\u062f.<\/li>\n<\/ul>\n

                        \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc:<\/b><\/p>\n

                        FFT \u06cc\u06a9 \u0627\u0628\u0632\u0627\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0642\u062f\u0631\u062a\u0645\u0646\u062f \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0645\u0627 \u0627\u0645\u06a9\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u0633\u06cc\u06af\u0646\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u0627\u0632 \u062d\u0648\u0632\u0647 \u0632\u0645\u0627\u0646 \u0628\u0647 \u062d\u0648\u0632\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u0647 \u0648 \u0633\u0627\u062e\u062a\u0627\u0631 \u0641\u0631\u06a9\u0627\u0646\u0633\u06cc \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u0645. \u0627\u06cc\u0646 \u0642\u0627\u0628\u0644\u06cc\u062a \u062f\u0631 \u062a\u062d\u0644\u06cc\u0644\u060c \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646\u060c \u0641\u0634\u0631\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0648 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u062f\u06cc\u062c\u06cc\u062a\u0627\u0644 \u0648 \u0645\u0647\u0646\u062f\u0633\u06cc \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a. \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 MSGEQ7 \u06a9\u0647 \u06cc\u06a9 \u062a\u062d\u0644\u06cc\u0644\u06af\u0631 \u0628\u0627\u0646\u062f-\u067e\u0627\u0633 \u0622\u0646\u0627\u0644\u0648\u06af \u0633\u0627\u062f\u0647 \u0627\u0633\u062a\u060c FFT \u06cc\u06a9 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0642\u06cc\u0642 \u0648 \u062c\u0632\u0626\u06cc \u0627\u0632 \u062a\u0645\u0627\u0645 \u0641\u0631\u06a9\u0627\u0646\u0633\u200c\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0633\u06cc\u06af\u0646\u0627\u0644 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f \u0648 \u0627\u0646\u0639\u0637\u0627\u0641\u200c\u067e\u0630\u06cc\u0631\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u06cc\u0634\u062a\u0631\u06cc \u062f\u0627\u0631\u062f.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

                        Fast Fourier Transform (FFT) \u06cc\u0627 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0633\u0631\u06cc\u0639\u060c \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0648 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u067e\u0631\u062f\u0627\u0632\u0634 \u0633\u06cc\u06af\u0646\u0627\u0644\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u062a\u0635\u0648\u06cc\u0631\u060c \u0648 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u0639\u0644\u0645\u06cc \u0648 \u0645\u0647\u0646\u062f\u0633\u06cc \u0627\u0633\u062a. \u062f\u0631 \u0648\u0627\u0642\u0639\u060c FFT \u06cc\u06a9 \u0631\u0648\u0634 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u06af\u0633\u0633\u062a\u0647 (DFT) \u0648 \u0645\u0639\u06a9\u0648\u0633 \u0622\u0646 (IDFT) \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 FFT \u0631\u0627 \u0628\u0647 \u062e\u0648\u0628\u06cc \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0627\u06cc\u062f \u0645\u0641\u0647\u0648\u0645 …<\/p>\n","protected":false},"author":1,"featured_media":119,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,3,4,6],"tags":[17,16,27,32],"class_list":["post-23","post","type-post","status-publish","format-standard","has-post-thumbnail","","category-beauty","category-fashion","category-hair","category-life-love","tag-lm358","tag-lmv358","tag-post","tag-video"],"_links":{"self":[{"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/posts\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/comments?post=23"}],"version-history":[{"count":2,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/posts\/23\/revisions"}],"predecessor-version":[{"id":761,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/posts\/23\/revisions\/761"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/media\/119"}],"wp:attachment":[{"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/media?parent=23"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/categories?post=23"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ilk.ir\/sahifa\/wp-json\/wp\/v2\/tags?post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}