B-24 Liberator in detail & scale Vol 64 by Bert Kinzey

By Bert Kinzey

B-24 Liberator intimately

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N0 S(w ) ∑ S H ) H(w G(w ) + Gn(w ) FIGURE 3-8 Signal Corrupted by Additive White Noise Alabaster-7200031 32 book ISBN : 9781891121524 CHAPTER 3 April 17, 2012 12:1 32 Pulsed Radar The output signal in the frequency domain is G(ω) = S(ω)H (ω) (3-10) where S(ω) is the target return, N0 is the peak noise voltage, H (ω) is the transfer function of the receiver filter, G(ω) is the target signal on the filter output, and G n (ω) is the noise signal on the filter output. The output signal in the time domain is the inverse transform 1 g(t) = 2π ∞ S(ω)H (ω)e jωt dω (3-11) −∞ The output noise power spectral density is N0 |H (ω)|2 2 G n (ω) = (3-12) The mean output noise power is then σn2 = 2 1 2π ∞ −∞ N0 |H (ω)|2 dω 2 (3-13) Integrating over all frequencies, the output signal-to-noise ratio is therefore 2 ∞ g 2 (t) = SNR = σn2 S (ω) H (ω)e −∞ N0 2 jωt dω (3-14) ∞ |H (ω)|2 dω −∞ One has to find H (ω) that maximizes this expression.

2 Ideal and Practical Matched Filtering A filter transfer function that is truly matched to the signal spectrum over an infinite bandwidth is very difficult to implement; however, a good practical approximation is a filter of bandwidth, B, given by 1 (3-19) τ This filter covers the central half of the main lobe of a pulsed spectrum, as illustrated in Figure 3-9, and therefore filters off high-order harmonics of the PRF lines. As a result, the signal on the matched filter output is distorted and is no longer a series of rectangular pulses.

Peak and Average Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulse Delay Ranging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low PRF Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectrum of Pulsed Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matched Reception . . . . . . . . . . . . . .

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