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Pulse compression is a signal processing technique commonly used by radar, sonar and echography to either increase the range resolution when pulse length is constrained or increase the signal to noise ratio when the peak power and the bandwidth (or equivalently range resolution) of the transmitted signal are constrained.
In Fourier analysis, the cepstrum (/ ˈ k ɛ p s t r ʌ m, ˈ s ɛ p-,-s t r ə m /; plural cepstra, adjective cepstral) is the result of computing the inverse Fourier transform (IFT) of the logarithm of the estimated signal spectrum.
The free spectral range of a diffraction grating is the largest wavelength range for a given order that does not overlap the same range in an adjacent order. If the ( m + 1)-th order of λ {\displaystyle \lambda } and m -th order of ( λ + Δ λ ) {\displaystyle (\lambda +\Delta \lambda )} lie at the same angle, then
An echo from a target will therefore be 'painted' on the display or integrated within the signal processor every time a new pulse is transmitted, reinforcing the return and making detection easier. The higher the PRF that is used, then the more the target is painted. However, with the higher PRF the range that the radar can "see" is reduced.
The χ 2 distribution given by Wilks' theorem converts the region's log-likelihood differences into the "confidence" that the population's "true" parameter set lies inside. The art of choosing the fixed log-likelihood difference is to make the confidence acceptably high while keeping the region acceptably small (narrow range of estimates).
The target range is determined by measuring elapsed time while the pulse travels to and returns from the target. Because two-way travel is involved, a total time of 12.35 microseconds per nautical mile will elapse between the start of the pulse from the antenna and its return to the antenna from a target in a range of 1 nautical mile.
The concepts of signal-to-noise ratio and dynamic range are closely related. Dynamic range measures the ratio between the strongest un-distorted signal on a channel and the minimum discernible signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level (not necessarily the most powerful signal ...
Electromagnetic (e.g. radio or light) waves are conceptually pure single frequency phenomena while pulses may be mathematically thought of as composed of a number of pure frequencies that sum and nullify in interactions that create a pulse train of the specific amplitudes, PRRs, base frequencies, phase characteristics, et cetera (See Fourier Analysis).