Fourier analysis is a method of defining periodic waveforms in terms of trigonometric functions. In this project, the goal is to analyze and calculate the Fourier coefficients. This project consists of different parts such as Fourier analysis, Audio signal analysis, and image analysis in the frequency domain.
1. Fourier analysis
The following steps have been taken:
- calculated Fourier coefficients for 4 different signals
- displayed the plot of each Fourier signal
- calculated Fourier transform of the above-mentioned signals
- analyzed the difference between the Fourier transform of each signal, when various changes occur in its arguments
- The principle of Signal Sampling
2. Audio signals analysis
In this part of the project, the analog sound of each number in a telephone has been given. Using these sounds, the audio related to each number is stored in a particular matrix. after that, various functions such as the FFT function have been applied to the matrix to take the data in the frequency domain.
In the end, using the array of zeros, the audio of the sounds of the desired phone number has been created and saved in audio format. Here is the audio:
3. Image analysis
In the last part of the project, two different images have been taken to the frequency domain, Using the FFT function in MATLAB.
The full research project is available via the following link: