Learning Experience: Discrete Fourier Transform

Experiment Performed: 

We used C codes to mathematically compute the DFT of a four point spectrum, of an 8 point spectrum, of a zero padded signal and of an expanded signal. We created functions that performed real and complex computations separately and concatenated the output upon display on the hyper terminal. We added variables to keep a count of the number of computations computations being performed during experiments.

Conclusions Inferred: 

We learnt that discrete fourier transform always produces periodic results. The frequency spacing is given by 

W= 2πk/N where k=0,1,2...N-1.

We plotted the magnitude and phase spectrum of the signals and realized that as the signal length increases, the frequency spacing decreases. Therefore, we have learnt that an expanded signal in the time domain would give a compressed, more resolved signal in the frequency domain. The increased resolution is good for the analytical applications because it reduces the error in the approximated signal.

We verified the number of computations and inferred that DFT is computationally slow.