2. (6 points) The FFT can also be performed using modular arithmetic and integers rather than complex numbers. This problem will guide you along this path. Note that all calculations should be done modulo 7. .( pt) Find a number w such that wo,w1,2,3. u4, and us are all different modulo 7 (i.e. these powers modulo 7 give some permutation of 1,2,3,4,5,6). The value of "n" will be 6 (I pt) Write the Fourier Matrix for this w (see slide 12 of the FFT slides). (2 pts) Use your Fourier Matrix to transform the sequence a = (0, 1, 2, 1,5,2) into the corre- (2 pts) Finally, write down the inverse FFT matrix (Gn on slide 19 of the FFT slides) and com- Note that in mod 7 group, the value is that number z such that z1 (mod 7), and don't sponding y sequence. pute the inverse FFT transform Gn y to recover the original sequence a. forget the 1 in the definition of Gn