Page 144 - Fundamentals of Radar Signal Processing

frequency responses are equal. This condition guarantees that given a white

noise input, both filters exhibit the same output noise power. Thus

FIGURE 2.24 Illustration of the concept of noise equivalent bandwidth of a
filter.

(2.78)

2
where the receiver power gain G is defined as the maximum gain of |H(F)| .
s
The total noise power N present at the output of the filter H(F) is then given by

(2.79)

White noise passed through a filter H(F) is no longer white, but instead has
2
the power spectrum |H(F)| . If |H(F)| is approximated as a rectangular filter of
2
two-sided bandwidth β Hz, the autocorrelation function of the noise at the filter
n
output is approximately a sinc function with its first zero at lag 1/β seconds.
n
However, it will be seen in Chap. 3 that the receiver output is normally sampled
at intervals of approximately 1/β seconds. Consequently, the noise component
n
of the successive receiver output samples are still uncorrelated with one
another.
The power spectral density of white noise at the output of any source or

circuit can be described as the product of Boltzmann’s constant and some
equivalent temperature T′, mimicking the simple formulation of Eq. (2.77).
Source noise power is usually referenced to the input of a system so that the
power gain G (or loss if G < 1) of the system must also be taken into account.
s
s
That is, if the observed output power spectral density (still assumed white over