This project will emphasize the practical aspects of the use of the DFT and the FFT in digital signal processing.
Exercises Write a matlab function that implements a DFT using the direct summation formula.
Note that you can eliminate one loop by using an inner product of a vector to implement the summation. Take the DFT of a random sequence 503 points long using your function. Use cputime to time this operation. Compare this to the time required for a 503-point FFT using fft . The FFT defaults to a DFT implementation because 503 points is a prime number and incapable of being decomposed into smaller FFT's.