hw5-2 - ECE130B February 3 2010 Home Work 5 Due date...

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ECE130B February 3, 2010 Home Work 5 Due date : February 8, 2010 by 5p.m. at the home work box. Exercise 1. Inverse FFT . In Home Work 4 you wrote code to rapidly compute the Fourier series coeffi- cients of a discrete signal (FFT). Write a similar code to rapidly compute a discrete signal from its Fourier series coefficients. Hint : The code is pretty much the same. You probably have to switch the sign of j in two places and remember to divide by N . Please submit your derivation of the algorithm along with a printed copy of the working code. Energy in a band . Let x [ n ] be a discrete signal of length N with a k as its Fourier series coefficients. Let k 1 and k 2 be two integers such that 0 lessorequalslant k 1 <k 2 <N . We call the expression summationdisplay k = k 1 k 2 | a k | 2 radicaltp radicalvertex radicalvertex radicalbt , as the energy of the signal in the band [ k 1 , k 2 ] . The larger the energy of the signal in a particular band, the more dominant are oscillations at that frequency in the signal. The energy in the band [0 , N - 1] is called the total energy of the signal.
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