Write a MATLAB program to implement the STFT with 50% overlapping and a second program to implement its inverse. Verify numerically that the inverse program reconstructs a test signal. Find another window satisfying the perfect reconstruction condition for 50% overlapping, use it with your STFT program, and verify that it reconstructs a test signal. Find the perfect reconstruction (PR) condition for an STFT with 2/3 overlapping. Find a window that satisfies your PR condition. Write a MATLAB program to implement the STFT and its inverse with 2/3 overlapping and verify the reconstruction of a test signal. Write a MATLAB program to implement the STFT with 50% overlapping and a second program to implement its inverse. Verify numerically that the inverse program reconstructs a test signal. Find another window satisfying the perfect reconstruction condition for 50% overlapping, use it with your STFT program, and verify that it reconstructs a test signal. Find the perfect reconstruction (PR) condition for an STFT with 2/3 overlapping. Find a window that satisfies your PR condition. Write a MATLAB program to implement the STFT and its inverse with 2/3 overlapping and verify the reconstruction of a test signal