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ECE 513 - DIGITAL SIGNAL PROCESSINGCranos M. WilliamsSAMPLE EXAM 2:NAME:STUDENT ID:1.Spectral Estimation: (20 Pts)Consider the following signal:x(n) = cos(ω0(n−n0))(1)USEFUL DTFT PROPERTIES:h(n)ejωon⇔H(ω−ωo),Frequency Shifting Propertyh(n−n0)⇔H(ω)e-jωn0,Time Shifting Property(a) Draw the magnitude response ofX(ω) for−π≤ω≤π(b) The signalx(n) is windowed by two windows, one of lengthL1and one of lengthL2. The main lobe of the magnitude response of window 1 is 4π/Land the mainlobe of the magnitude response of window 2 is 8π/L. The main lobe of the twowindowed sequencesx1(n) andx2(n), however, are the the same width.Statewhich of the following is true:•L1> L2•L1< L2•L1=L21