[Optional] A faster DFT for a real sequence Exercises 3 & 4 suggest that we might be able to perform a single real N-point DFT using only one N/2 point DFT. This is possible by noting the following: a) Your solution to part 3 can calculate a real N-point DFT using two real N/2 DFTs b) and your solution to part 4 allows you to calculate two real N/2 DFTs using one complex N/2- point DFT. Hence create a MATLAB function, realFFT (x) that can calculate a real N-point DFT using a single fft command applied to an N/2-point sequence. Test the function on a known sequence. [Optional] A faster DFT for a real sequence Exercises 3 & 4 suggest that we might be able to perform a single real N-point DFT using only one N/2 point DFT. This is possible by noting the following: a) Your solution to part 3 can calculate a real N-point DFT using two real N/2 DFTs b) and your solution to part 4 allows you to calculate two real N/2 DFTs using one complex N/2- point DFT. Hence create a MATLAB function, realFFT (x) that can calculate a real N-point DFT using a single fft command applied to an N/2-point sequence. Test the function on a known sequence