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In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of propagation delay and Doppler frequency, (,).It represents the distortion of a returned pulse due to the receiver matched filter [1] (commonly, but not exclusively, used in pulse compression radar) of the return from a moving target.
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.
Each of the spin-echo signal is a sinc function of time, which can be described by = Where = + ¯ Here ¯ is the gyromagnetic ratio constant, and is the basic resonance frequency of the spin. Due to the presence of the gradient G , the spatial information r is encoded onto the frequency ω {\displaystyle \omega } .
The smaller is, the smaller is the contribution of previous samples to the covariance matrix. This makes the filter more sensitive to recent samples, which means more fluctuations in the filter co-efficients.
The aim is either for the cell system to report the location of a cell phone placing an emergency call or to provide a service to tell the user of the cell phone where they are. Multiple receivers on a base station would calculate the AoA of the cell phone's signal, and this information would be combined to determine the phone's location.
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.
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).
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.