Digital Signal Processing Reference
In-Depth Information
1.6
L = 55
L = 33
L = 54
L = 32
1.4
Upper Bound
1.2
1
0.8
0.6
0.4
0.2
0
0
0.25
0.5
0.75
1
1.25
Cut-off Frequency,
F
c
c
Figure 2.30
Noise propagation through low-pass filters with various cut-off frequencies. (Used by
permission of the Institute of Physics Publishing.)
2
2
in noise variance) for the ideal low-pass filter (i.e.,
/
), is given by
x
G
=
10
log
F
(dB) (2.36)
SNR
10
c
This is sometimes referred to as the processing gain of the filter.
2.10.2 Band-Pass and Band-Stop Filters
For band-pass filters, the output noise power is given by
2
2
(
F
F
)
(2.37)
x
c
off
c
on
whereas for band-stop filters, this becomes
2
2
(
+
F
F
)
(2.38)
x
c
off
c
on
Note that in the latter case,
F
c-off
is less than
F
c-on
.
2.10.3 Cascaded Filters
When two or more filters are cascaded, their spectra are multiplied in the
frequency space. This is a direct result of their convolution in the time domain. In
