= Pulsar dedispersion
{title2=$t_{\rm corrected}=t-\Delta t(f)$}
<Pulsar dedispersion> aligns <radio wave> arrival times in separate <frequency> channels before combining them. For an original illustrative model choose
$$
\Delta t(f)=D\left[\left(\frac{f}{100\,\mathrm{MHz}}\right)^{-2}-\left(\frac{150\,\mathrm{MHz}}{100\,\mathrm{MHz}}\right)^{-2}\right],\qquad D=0.24\,\mathrm{s}.
$$
Both bracketed ratios are dimensionless, so $D$ supplies all the time units. The reference is $150\,\mathrm{MHz}$: delays are $0$ there, $0.13333\,\mathrm{s}$ at $100\,\mathrm{MHz}$, and $0.26833\,\mathrm{s}$ at $80\,\mathrm{MHz}$. These are chosen model values, not measurements of the first <pulsar>. Subtracting the delay aligns the peaks; summing channels first spreads a short pulse over a longer interval and reduces its peak. Finite channel width and incorrect delay parameters leave residual smearing.
\Image[/pulsar-dispersion-dedispersion.png]
{title=Correcting a chosen inverse-square frequency delay}
{id=pulsar-dispersion-dedispersion}
{description=Original noiseless synthetic pulses with a chosen 1.4 second period, 0.025 second Gaussian standard deviation and D=0.24 seconds. The curved arrival track straightens after channel shifts; the profiles compare equal-weight channel averages. This is a propagation model, not original observations or a recreation of a historical chart.}
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