The most prominent selection effect is the inverse square law, i.e. for a given intrinsic luminosity1, the observed flux density falls off as the inverse square of the distance. This results in the observed sample being dominated by nearby and/or high luminosity objects. Beyond distances of a few kpc from the Sun, the apparent flux density falls below the detection thresholds of most surveys. Following , we express this threshold as follows:
It follows from Equation (3) that the sensitivity decreases as and hence increases. Also note that if , the pulsed signal is smeared into the background emission and is no longer detectable, regardless of how luminous the source may be. The detected pulse width may be broader than the intrinsic value largely as a result of pulse dispersion and multipath scattering by free electrons in the interstellar medium. The dispersive smearing scales as , where is the observing frequency. This can largely be removed by dividing the pass-band into a number of channels and applying successively longer time delays to higher frequency channels before summing over all channels to produce a sharp profile. This process is known as incoherent dedispersion.
The smearing across the individual frequency channels, however, still remains and becomes significant at high dispersions when searching for short-period pulsars. Multipath scattering from electron density irregularities results in a one-sided broadening due to the delay in arrival times. A simple scattering model is shown in Figure 12 in which the scattering electrons are assumed to lie in a thin screen between the pulsar and the observer . The timescale of this effect varies roughly as , which can not be removed by instrumental means.
Standard pulsar searches use Fourier techniques  to search for a-priori unknown periodic signals and usually assume that the apparent pulse period remains constant throughout the observation. For searches with integration times much greater than a few minutes, this assumption is only valid for solitary pulsars or binary systems with orbital periods longer than about a day. For shorter-period binary systems, the Doppler-shifting of the period results in a spreading of the signal power over a number of frequency bins in the Fourier domain, leading to a reduction in S/N . An observer will perceive the frequency of a pulsar to shift by an amount , where is the (assumed constant) line-of-sight acceleration during the observation of length , is the (constant) pulsar period in its rest frame and is the speed of light. Given that the width of a frequency bin in the Fourier domain is , we see that the signal will drift into more than one spectral bin if . Survey sensitivities to rapidly-spinning pulsars in tight orbits are therefore significantly compromised when the integration times are large.
It is clearly desirable to employ a technique to recover the loss in sensitivity due to Doppler smearing. One such technique, the so-called “acceleration search” , assumes the pulsar has a constant acceleration during the observation. Each time series can then be re-sampled to refer it to the frame of an inertial observer using the Doppler formula to relate a time interval in the pulsar frame to that in the observed frame at time , as . Searching over a range of accelerations is desirable to find the time series for which the trial acceleration most closely matches the true value. In the ideal case, a time series is produced with a signal of constant period for which full sensitivity is recovered (see right panel of Figure 13). This technique was first used to find PSR B2127+11C , a double neutron star binary in M15 which has parameters similar to B1913+16. More recently, its application to 47 Tucanae  resulted in the discovery of nine binary millisecond pulsars, including one in a orbit around a low-mass () companion. This is currently the shortest binary period for any known radio pulsar.
For intermediate orbital periods, in the range -several hours, another promising technique is the dynamic power spectrum search. Here the time series is split into a number of smaller contiguous segments which are Fourier-transformed separately. The individual spectra are displayed as a two-dimensional (frequency versus time) image. Orbitally modulated pulsar signals appear as sinusoidal signals in this plane as shown in Figure 14.This technique has been used by various groups where spectra are inspected visually . Much of the human intervention can be removed using a hierarchical scheme for selecting significant events . This approach was recently applied to a search of the globular cluster M62 resulting in the discovery of three new pulsars. One of the new discoveries - M62F, a faint pulsar in a orbit - was detectable only using the dynamic power spectrum technique.
For the shortest orbital periods, the assumption of a constant acceleration during the observation clearly breaks down. In this case, a particularly efficient algorithm has been developed [262, 143, 263] which is optimised to finding binaries with periods so short that many orbits can take place during an observation. This “phase modulation” technique exploits the fact that the Fourier components are modulated by the orbit to create a family of periodic sidebands around the nominal spin frequency of the pulsar. While this technique has so far not resulted in any new discoveries, the existence of short period binaries in 47 Tucanae , Terzan 5  and the X-ray binary X1820303 in NGC 6624 , suggests that there may be more ultra-compact binary pulsars that await discovery.
© Max Planck Society and the author(s)