A DFT was implemented on a 128Hz sinusoid sampled at 2048Hz and the phase of the DFT was calculated. A DFT was then applied to a 220 Hz sinusoid to demonstrate spectral leakage and the signal was reconstructed by taking an inverse DFT, showing the complex conjugate property of the DFT. Next, we created a 512-length sequence of the sinusoid to get rid of spectral leakage. In the second part of the lab, we explored downsampling by decimation and looked at the spectrogram of a speech signal. It was found that decimation destroys the high frequency information of the signal, creating aliasing. Low pass filtering was used to counter this problem.