A simple audio processing to review the concepts of Fourier transform, correlation and spectral density
This project is designed for reviewing the concepts of Fourier transform, correlation and spectral density. The following steps are completed in this project:
- The Fourier transform of an audio signal is calculated and plotted.
- Frequency response of a time-delay system is plotted.
- The audio signal goes through an echo attachment system and the result is calculated in frequency domain.
- The result of the same system is calculated in the time domain and it is conspicuous that the resultant signals of steps 3 and 4 are equal.
- Cross correlation of the original signal (step 1) and the echoed signal (step 3 or 4) is calculated. A second peak appears in the cross correlation which is indicative of the echo.
- Spectral density of the signals are plotted and the accuracy of below formulas is observed:
- Ryx = Rx * h
- Gy = Gx . |H|^2
- A second echo is added to the signal.
NOTE: I designed this project as the first computer assignment of the Communications I course held by Professor M. Sabbaghian in the fall of 2020 at the University of Tehran.