Digital Signal Processing - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 56

The equivalent noise bandwidth B en , in its reduced form, becomes:

1
2
1
2

+

2

∫

()

ˆ

wv dv

0, N − 1

−

BN =

en

0,

()

w ˆ 0

N − 1

N −

=

1

∑
∑

0,

()

wk

T

k 0

= N

2

N − 1

⎛ ⎞

()

wk

⎜ ⎟

0, N − 1

⎝

0

⎠

.

.

.

.

.

.

.

.

Figure 2.9. Blackman and Bartlett windows
and their frequency response (in dB)

The amplitude of the secondary lobe is defined in the same way as in continuous.
However, these indices that are independent of the length T of the continuous
window, depend on N in discrete. By considering the discrete time windows as a
sampling to the period N of the corresponding continuous time window, we can
consider the spectral aliasing phenomenon as negligible for quite large N ; the indices
defined in discrete thus tend towards their equivalent in continuous time for quite a
large N . Thus, Table 2.4 remains valid in discrete time, for quite large values of N
(and for lobes sufficiently spaced out of the reduced frequency 1/2 for the decreasing
index of secondary lobes).