New efficient window function, replacement for the Hamming window

A new simple window function is presented, which for the same window order (M), has a main-lobe width less than or equal to that of the Hamming window, while offering about 2–4.5 dB smaller peak side-lobe amplitude. Furthermore, just like the Hamming window, it is computationally efficient for signal spectrum analysis; this is because of the fact that, the sum of window coefficients with its shifted version by M/2 samples (i.e. 50% overlap) is constant for the overlapped region. The new window is obtained by adding the third harmonic of the cosine function to the Hamming window, and finding the appropriate amplitudes of DC term, cosine function, and its third harmonic to minimise the peak side-lobe amplitude. A comparison with the Kaiser and Dolph–Chebyshev windows is also performed. Finite impulse response filters designed by windowing method show the efficiency of the new window.