engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Discrete Fourier Transform (DFT) and Discrete Fourier Series (DFS) Definition of Discrete Fourier Transform (DFT)
For a vector x̅ = [x[0], x[1],......x[7]] the 8-point discrete Fourier transform (DFT) is denoted by X̅ = DFT (x̅) = X[0], X[1], ...., X[7]], where
\(\rm X[k]=\sum_{n=0}^{7}x[n]\ exp\left(-j\frac{2\pi}{8}nk\right) \space \)
Here j = √-1, if X̅ = [1, 0, 0, 0, 2, 0, 0, 0] and y̅ = (DFT (x̅)), then the value of y[0] is ________ (rounded off to one decimal place).
Enter numerical value using the virtual keypad. Round off where necessary.