Constant amplitude zero autocorrelation waveform information
In signal processing, a Constant Amplitude Zero AutoCorrelation waveform (CAZAC) is a periodic complex-valued signal with modulus one and out-of-phase periodic (cyclic) autocorrelations equal to zero. CAZAC sequences find application in wireless communication systems, for example in 3GPP Long Term Evolution for synchronization of mobile phones with base stations. Zadoff–Chu sequences are well-known CAZAC sequences with special properties.
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Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all...
modelled by independent and identically distributed zero-mean Gaussian processes so that the amplitude of the response is the sum of two such processes....
amounts to assuming that the autocorrelation peak is centered at zero. This will not change the resolution and the amplitudes but will simplify the math:...
pulse is not a desirable waveform from a pulse compression standpoint, because the autocorrelation function is too short in amplitude, making it difficult...
function S ¯ x x ( f ) {\displaystyle {\bar {S}}_{xx}(f)} and the autocorrelation of x ( t ) {\displaystyle x(t)} form a Fourier transform pair, a result...
signals to instead take the Fourier transform of its autocorrelation function. The autocorrelation function R of a function f is defined by R f ( τ ) =...
equal to zero for all n {\displaystyle n} , i.e. E [ W ( n ) ] = 0 {\displaystyle \operatorname {E} [W(n)]=0} and if the autocorrelation function R...
both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal. Although it is common to refer...
systems if we replace R v {\displaystyle R_{v}} with the continuous-time autocorrelation function of the noise, assuming a continuous signal s ( t ) {\displaystyle...
frequency components are created. The existing ones are only modified (amplitude and/or phase). In other words, the output transform is the pointwise product...