Ziad-Maged/Python-PIANO-Project

Python-PIANO-Project

This project was divided on two Milestones. The Idea for Milestone One: You are the PIANIST, you should mix and match frequencies to generate your own song using the numpy, matplotlib.pyplot, and sounddevice libraries in Python. The Idea For Milestone Two: Noise Cancellation and Frequency Domain

Background For Milestone One:

Each pressed piano key/note number 𝑖, corresponds to a single tone with frequency 𝑓𝑖 generated for a certain period of time 𝑇𝑖starting from time 𝑡𝑖 over a defined time range 𝑡.

𝑥𝑖(𝑡) = sin(2 * 𝜋 * 𝑓𝑖 * 𝑡) * [𝑢(𝑡 − 𝑡𝑖) − 𝑢(𝑡 − 𝑡𝑖 − 𝑇𝑖)]

Where the unit step functions defines the playing interval.

Example: Assume that we started pressing the middle C key (𝑓1 = 261.63 𝐻𝑧), at time 𝑡1 = 0 for a duration of 𝑇1 = 1.5 seconds, the resultant signal is:

𝑥1(𝑡) = sin(2 * 261.63𝜋 * 𝑡) [𝑢(𝑡) − 𝑢(𝑡 − 0.5)]

Background For Milestone Two:

Assume that additional noise is generated by a child who kept pressing the same 2 random piano keys during your song playing interval such that the noise is represented as follows, 𝑛(𝑡) = sin(2 * 𝑓𝑛1 * 𝜋 * 𝑡) + sin(2 * 𝑓𝑛2 * 𝜋 * t)

Where, 𝑓𝑛1 and 𝑓𝑛2 are two frequencies selected randomly from the 3rd and 4th octaves frequencies list respectively. Your final song after the noise becomes, 𝑥𝑛(𝑡) = 𝑥(𝑡) + 𝑛(𝑡)

Goal: Noise Cancelation: using frequency domain conversion