Digital Signal Processing - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 53

Figure 2.7. Graphical representation of indices (rectangular window)

Band at
-3 dB

Band equivalent
to noise

Stronger
secondary lobes

Decreasing
secondary lobes

Rectangular 0.89 1.00 -13.3 dB -6 dB/octave

Hamming 1.30 1.36 -43.0 dB -6 dB/octave

Hanning 1.44 1.50 -31.5 dB -18 dB/octave

Blackman 1.68 1.73 -58.0 dB -18 dB/octave

Bartlett 1.28 1.33 -26.5 dB -12 dB/octave

Table 2.4. Characteristics of continuous time windows

For digital processing, we record a signal x ( k ), k ∈ Z with only a finite number of
points N , that is x ( k ), 0 < k < N - 1. We approximate the Fourier transform x , i.e.:

+∞

= ∑

− j 2 π vk

() ()

xv ˆ xke

k =−∞