Please individually complete the following prior to your first lab. Bring a printed copy to lab, including your results AND your MATLAB code. 1. Write a short code which can perform the FFT on a signal of arbitrary length. Please use MATLAB's FFT function, but do not just copy and paste the complete FFT example code found in MATLAB's 'Help' resources. To validate your code, provide an input sinusoid with frequency 5 Hz and an amplitude 3, using a time vector with final time 10 seconds and a time step of 0.01 s: x(t) = A sin (2nf t) A-3,f-5 Hz t = 0:0.01: 10 . What do you expect the frequency spectrum to look like? How many peaks do you expect, and what do you anticipate their amplitudes to be? What happens if you vary the sampling rate dt and the length of the signal, N? (whereessefrequencyspectrumrelatetotheNyquistfrequency,AUh5% where fs is the sampling frequency:f 1/dt)