The Wideband Arecibo Pulsar Processor Signal Processing Page 


WAPP  Signal Processing Page
IntroductionThe WAPP uses custom digital hardware to create estimates of
correlation functions from sampled data. The digital hardware used to estimate correlation function uses
quantization to represent input After creating an estimate of input correlation functions, the
WienerKhintchine Theorem is applied to create estimates of input Power
spectral density (PSD) and Stokes parameters In practice, the measured correlation function proudced by the digitial hardware is a biased^{1 }estimator of the actual correlation function. This is due to coarse quantization of the sampled data values. A correction to the raw correlation must be applied. Also, the raw correlation values written to disk by the WAPP have offset terms which must be removed. This discussion will outline these issues and discuss methods of dealing with their effects. ^{1} Baised in the sense that the measured correlation has a onetoone correspondence to the actual correlation function, but there relationship is not linear Raw CorrelationThe raw data produced by the WAPP are unsigned integers that represent estimates of correlation functions. This data requires Counter OffsetThe multiplication applied by the NAIC correlator chips produces only positive values {0,1,2}. This complication simplifies the postmultipication storage into simple ripple counters. The offset produces
Quantization Correction (Van Vleck Correction)The custom designed CMOS chip used to measure correlation fucntions uses a very coarse quantization of the input data and subsequent multipication. The standard mode of the chip uses only 3 levels (or 1.5 bits), while an special mode can combine produces from mutliple chip to create a 9 level respresentation of the input data. The resulting correlation function has some addtional noise due to quantization that reduces SNR, hower this effect is modest and deemed a worth tradeoff. However, the . SensitivityThe loss associated with 3level and 9level correlation is fairly modest. However, it is affected by the signal level relative to the threshold voltages. Consider the extreme case where the power level is much larger than the threshold levels. In this case, virtually the only values that will be produced by the sampler are the maximum and minimum level and the sampler approaches the performance of a 2 level (single bit) correlator. Conversely, if the level drops signficantly below the For the 3level, we correlator SNR of the measured correlation fucntion, as compared to a sampler with inifinite quantizition is 81%, but this value only holds when the power level is ideal. The full relationship is expressed by the following formula: Power EstimationThe total power in the input band is estimated using from the
autocorrelation function at delay =0 (zerolag). If the value
produced by the WAPP was a perfect measurement of input correlation, the
zerolag would be directly proportional to input power. However, like the
quantization correction discussed above, the zerolag must be manipulated to
produce a nonbiased estiamte of input power. Power SpectraThe FFTW subroutine library (available at http://www.fftw.org) was used to implement the fourier transfer to create power spectrum. In Snap, a Hamming window is applied as a matter of course. ExampleReferences[1]Weinreb, Sander, "A Digital Spectral Analysis Technique and its
Application to Radio Astronomy," MIT Technical Report #412, 1963 

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