Where A = 22 and B = 25

Problem Statement The aim of this complex problem is to enable students to understand how a mathematical algorithm can be implemented in a computationally efficient manner. The problem has been divided into the following steps and each step has been clearly explained in detail. 1. Derive mathematically the 16-point radix-2 butterfly FFT using decimation-in-time and draw the final structure. You have to write the complete derivation as well as draw the complete structure, showing all multiplications in the right places. 2. Repeat part 1 using decimation-in-frequency. 3. Write a MATLAB code for either part 1 OR part 2 (not both). The code should be optimized. This means that the code should not include 16 lines, each solving one equation to give an output. Instead, your code should use a recursion that efficiently performs each decimation step itself until it reaches only 2 points and performs 2 point DFT and then recursively solves the 16-point FFT. 4. Verify that your code works properly by performing the convolution of the following signals using FFT. This means that you should take 16-point FFT of each signal using your FFT code, then multiply the two FFT signals and then take the inverse FFT. Perform convolution of the two signals using the built-in convolution function and verify that the two output signals are exactly the same. The marks in this step depend on the verification of the two output signals. Without verification no marks will be awarded. *[n]=]} {[m]-u[n10} *.-G----(1-71 B where A is the sum of the numbers in the student ID of group member 1 and B is the sum of the numbers in the student ID of group member 2