Compression of Data Using the Fft

In this experiment we are asked to compress discrete time data by storing only the most significant points of the data's FFT. If every point in the FFT is stored, it is possible to recover the original signal exactly. But by effectively zeroing out less significant points in the FFT, we elect to introduce some error into the reconstructed signal in order to reduce the amount of storage space. The plot below shows the FFT of a given data signal—the sum of three complex sinusoids. Both the data and the FFT have 64 points. Each sinusoid has magnitude A = 1 and the following frequencies: ω 1 = 2π(2.3438 × 10-2) radians/sec ω 2 = 2π(8.6458 × 10-2) radians/sec ω 3 = 2π(1.3409 × 10-1) radians/sec Noting that most of the signal's energy is in the low frequency region of the FFT, we arbitrarily decide to keep only the first 15 points. (The remaining points are assumed to be zero.) Taking the IFFT, the estimated signal is found to be a fairly close approximation of the original data signal. See the plots on the following page. Figure 1: FFT magnitude of the original data signal, d[n].