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Matlab - Fourier Analysis

Matlab - Fourier Analysis. 主講人：林麗娟 主講部分： FFT & 例題. Fourier Transform. 連續時間 下的 Fourier Transform 定義：. 離散時間 下的 Fourier Transform 定義﹝ DTFT﹞：. Fourier Transform. 無限 的 Discrete Fourier transform 定義﹝ DTFT﹞：. 有限 的 Discrete Fourier Transform 定義﹝ DFT﹞：. Compare DTFT & DFT.

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Matlab - Fourier Analysis

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  1. Matlab - Fourier Analysis 主講人：林麗娟 主講部分：FFT & 例題

  2. Fourier Transform 連續時間下的Fourier Transform定義： 離散時間下的Fourier Transform定義﹝DTFT﹞：

  3. Fourier Transform 無限的DiscreteFourier transform定義﹝DTFT﹞： 有限的Discrete Fourier Transform定義﹝DFT﹞：

  4. Compare DTFT & DFT DFT→可以將信號由時間領域轉換到頻率領域 IDFT→可以將信號由頻率領域轉換回時間領域

  5. FFT & IFFT 將 代入 然後修改k、n的範圍，就會得到下面的FFT和IFFT的公式

  6. 波函式經FFT後的純量和相位 % Ex-1 % Prupose : Gnerate a 20 Hz sinnsoid samples at 128 Hz clear; N = 64; T = 1/128; k = 0:N-1; x = sin(2*pi*20*k*T); X = fft(x); magX = abs(X); hertz = k*(1/(N*T)); →將先前的變數和函數從記憶體中清除 →取樣數目 →週期 →數據資料的長度 →sin(w*t) = sin(2πf*t) = sin(2πf*kT) = sin(2*pi*20*k*T) →做FFT →算出純量的絕對值

  7. figure; subplot(311) ; plot(0:T:T*(N-1),x) , ylabel('x(kT)') , grid on subplot(312) ; stem(k(1:N),magX(1:N)) , ylabel('|X(k)|') , grid on subplot(313);stem(hertz(1:N),magX(1:N)),ylabel('|X(k)|'),grid on →產生一個新的圖形視窗 將數個小圖畫於同一個視窗中 Y軸的標籤 繪製一維曲線的基本函數 顯示網格線 繪製針狀圖

  8. % Ex-2 clear; n = 63; L = 2; t = -L:2*L/n:L; y = sin(13*pi*t/L); z = fft(y); p1 = angle(z); p2 = unwrap(angle(y)); figure; subplot(411);plot(t,y),ylabel('y=fft(t)'),grid on subplot(412);plot(0:n,abs(z)),ylabel('Abs'),grid on subplot(413);plot(0:n,p1),ylabel('phase'),grid on subplot(414);plot(0:n,p2),ylabel('phase'),grid on →sin(w*t0 ) = sin(2πf*t0 ) = sin(2πf*t/2L) = sin(πf*t/L) = sin(13*pi*t/L) →算出複數z的相位角 使相位在180度不會產生不連續點

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