(a) Find the spectrum of this waveform:  x = [ exp( -[0:1:49]/10), exp(-[50:-1:1]/10)]. Subplot only the magnitude by using the spectrum program from the class notes.

(b) Using this information from the 100-point DFT, re-create the waveform by summing the sinusoidal contributions from all the DFT coefficients as done in lecture. Show both the waveform x and its re-creation xhat on another subplot. (The waveforms might merge into one figure so the mean square error is effectively zero in this case.)

(d)  Using MATLAB, find the index n0 at which the spectral magnitude falls below 0.05 of its maximum (which is a point beyond which there is little energy left in the higher frequencies.)

(e)   Using only the first n0 DFT coefficients, generate the waveform and plot in Matlab by using the symmetry properties of the transform. Plot xhat over the actual signal and annotate the plot to indicate the value of the calculated mse. Title and label the axes. Submit plot and code.