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"In the dechirped SAR signal range spatial frequency is RF frequency scaled by $\frac{4\pi}{c} $. This quantity is has units of radians per unit length and is denoted by the symbol $K_R$. It varies from a minimum of $\frac{4\pi}{c} (F_c - B/2) $to a maximum of $\frac{4\pi}{c} (F_c - B/2) $ "

This is taken from Spotlight Synthetic Aperture Radar by Walter G Carrara

My question is related to this excerpt where it mentions the dechirped SAR signal has bandwidth and is centered about $F_c$. From what I understand dechirped signals only have a single frequency component. How do i make sense of this excerpt and implement the range migration algorithm?

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  • $\begingroup$ In the dechirped signal a single frequency will correspond to a target range. The frequency components will be determined by the ranges of the various target returns. Subsequent processing is assuming the Residual Video Phase (from deramping) has been corrected or can be ignored. $\endgroup$
    – David
    Nov 16, 2022 at 18:44

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From what I understand dechirped signals only have a single frequency component.

That's the problem – they don't. (if they had 0 bandwidth, they'd be bad in terms of autocorrelation – you want your signal to compress down to a pulse, not to a sinusoid).

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    $\begingroup$ I think you've assumed matched-filtering for pulse compression. If we're considering a nominal LFM chirp against a single point target and we're performing dechirping, the result is a single sinusoid with a frequency proportional to the target's range. $\endgroup$
    – Envidia
    Nov 17, 2022 at 3:57
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    $\begingroup$ That's true, I was considering an end-to-end view of a pulse compression system that included the mapping back into the range plane. Reading the question again, you're right, that doesn't apply. $\endgroup$ Nov 17, 2022 at 8:07
  • $\begingroup$ Giving it a few hours of grace time, then deleting this answer $\endgroup$ Nov 17, 2022 at 8:08
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    $\begingroup$ Funny, because at the end of the day the bandwidth put into the pulse determines the range resolution, no matter how you process it (correlation vs DFT-based range). This is barring the residual video phase (RVP) produced from homodyning, where it's critical for SAR applications but not so much for "simpler" range-Doppler systems. $\endgroup$
    – Envidia
    Nov 18, 2022 at 6:22
  • $\begingroup$ Don't delete the answer but just caveat it. $\endgroup$
    – Envidia
    Dec 5, 2022 at 6:20

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