The spectral features of window functions include the main lobe width, side lobe level, transition width, passband ripple, and stopband attenuation. The main lobe width refers to the width of the central peak of the spectral response, which determines the frequency resolution of a windowed signal. The side lobe level is the magnitude of the energy in the spectral response outside of the main lobe, and it determines how much [[spectral leakage]] occurs in adjacent frequency bands. Window functions with narrower main lobes and lower side lobe levels are preferred for applications that require high-frequency resolution and low noise leakage The transition width refers to the frequency range over which the spectral response of a window function transitions from the main lobe to the side lobes. The passband ripple refers to the variation in amplitude of the spectral response within the main lobe of a window function. It is typically measured as the maximum deviation from the average amplitude in the passband, expressed as a percentage of the average amplitude. The stop band attenuation refers to the amount of attenuation applied to frequency components outside of the passband of a window function. It is typically measured as the ratio of the energy in the stop band to the energy in the passband, expressed in decibels (dB). Stop band attenuation is important for applications that require suppression of unwanted frequency components, such as in signal filtering or noise reduction. |Type of Window|Side Lobe Amplitude|Width of Main Lobe|Transition Width|Passband Ripple|Stopband Attenuation| |---|---|---|---|---|---| |Rectangular|$-13dB$| $4\pi/M$|$0.9/(MT)$|$0.7416dB$|gt;21dB$| |Hann|$-31dB$|$8\pi/M$|$3.1/(MT)$|$0.0546dB$|gt;44dB$| |Hamming|$-41dB$|$8\pi/M$|$3.3/(MT)$|$0.0194dB$|gt;53dB$| |Blackman|$-74dB$|$12\pi/M$|$5.5/(MT)$|$0.0274dB$|gt;74dB$| ![[Window_function_and_frequency_response_-_Rectangular.svg]] ![[Window_function_and_its_Fourier_transform_–_Hann_(n_=_0...N).svg]] ![[Window_function_and_frequency_response_-_Hamming_(alpha_=_0.53836,_n_=_0...N).svg]] ![[Window_function_and_its_Fourier_transform_–_Blackman_(n_=_0...N).svg]]