The Nuttall window coefficients are given by the following formula
where N is the length of the filter and k = 0, 1, …, N – 1.
Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the Nuttall window.
The magnitude response of the same filter is shown on the graph below.
Measures for the Nuttall window
The following is a comparison of the discrete Fourier transform of the Nuttall window and the rectangular window.
The Nuttall window measures are as follows.
|Equivalent noise bandwidth||2.03|
|Processing gain||-3.06 dB|
|Scalloping loss||-0.81 dB|
|Worst case processing loss||-3.87 dB|
|Highest sidelobe level||-93.3 dB|
|Sidelobe falloff||-23.4 dB / octave, -77.6 dB / decade|
|Main lobe is -3 dB||1.92 bins|
|Main lobe is -6 dB||2.68 bins|
|Overlap correlation at 50% overlap||0.035|
|Amplitude flatness at 50% overlap||0.423|
|Overlap correlation at 75% overlap||0.452|
|Amplitude flatness at 75% overlap||1.000|