Consider an 8 point DFT: 1. Obtain DFT matrix for an 8-point DFT using paper and pencil method. 2. Prove the efficiency of the FFT algorithm and simplification on matrix elements discussed in class to prove the efficiency of FFT algorithm. Show how symmetry helps simplifying the matrix. 3. Draw the butterfly diagram for an 8 point FFT. 4. Show the repeating pattern of the coefficients on unit circle. Consider an 8 point DFT: 1. Obtain DFT matrix for an 8-point DFT using paper and pencil method. 2. Prove the efficiency of the FFT algorithm and simplification on matrix elements discussed in class to prove the efficiency of FFT algorithm. Show how symmetry helps simplifying the matrix. 3. Draw the butterfly diagram for an 8 point FFT. 4. Show the repeating pattern of the coefficients on unit circle