Signal processing methods and apparatus

1. A signal processor for performing an input signal transform of a signal, the signal processor comprising:

a signal demodulator for demodulating said input signal by a first chirp signal having a first chirp rate to obtain a reduced bandwidth signal;

an all-pass quadratic phase filter for filtering the demodulated reduced bandwidth signal to introduce a delay proportional to a frequency of said demodulated reduced bandwidth signal, wherein a constant of proportionality is the reciprocal of the first chirp rate; and

a signal modulator for modulating said filtered signal from the all-pass quadratic phase filter by a second chirp signal having a second chirp rate to obtain an increased bandwidth chirped signal, the second chirp rate chosen to provide an output representing a time domain spectrum of said input signal,

wherein each of said first chirp signal and said second chirp signal is a complex signal representing a linear frequency modulated chirp.

2. The signal processor according to claim 1 , wherein said all-pass quadratic phase filter is configured to transform, via a Fourier transform, the demodulated reduced bandwidth signal into a frequency spectrum.

3. The signal processor according to claim 2 , wherein said all-pass quadratic phase filter further includes a further signal modulator for modulating said frequency spectrum and generating a further modulated output signal.

4. The signal processor according to claim 3 , wherein said all-pass quadratic phase filter is further configured to generate, via an inverse Fourier transform, an inverse Fourier transform of said further modulated output signal.

5. A radar system for acquiring a synthetic aperture image, said radar system comprising:

a receiver for receiving an input radar signal including a two-dimensional array of data comprising down-range data and along-track data, wherein said along-track data includes at least one along-track chirp signal;

a processor for processing said received radar signal, said processor includes a signal processor including

a signal demodulator for demodulating said input signal by a first chirp signal having a first chirp rate to obtain a reduced bandwidth signal;

an all-pass quadratic phase filter for filtering the demodulated reduced bandwidth signal to introduce a delay proportional to a frequency of said demodulated reduced bandwidth signal, wherein a constant of proportionality is the reciprocal of the first chirp rate; and

a signal modulator for modulating said filtered signal from the all-pass quadratic phase filter by a second chirp signal having a second chirp rate to obtain an increased bandwidth chirped signal, the second chirp rate chosen to provide an output representing a time domain spectrum of said input signal,

wherein each of said first chirp signal and said second chirp signal is a complex signal representing a linear frequency modulated chirp;

a signal bandwidth reduction reducer for reducing the bandwidths of said down-range frequency spectra data and said along-track frequency spectra data;

a Stolt interpolator for interpolating said reduced bandwidth frequency spectra data to generate interpolated data, and

wherein said processor is further operable to perform a two-dimensional inverse Fourier transformation of the interpolated data to generate an output image.

6. The radar system according to claim 5 , wherein said all-pass quadratic phase filter is configured to transform, via a Fourier transform, the demodulated reduced bandwidth signal into a frequency spectrum.

7. The radar system according to claim 5 , wherein said all-pass quadratic phase filter further includes a further signal modulator for modulating said frequency spectrum and generating a further modulated output signal.

8. The radar system according to claim 5 , wherein said all-pass quadratic phase filter is further configured to generate an inverse Fourier transform of said further modulated output signal.

9. The radar system according to claim 5 , wherein the Stolt interpolator is configured to interpolate said reduced bandwidth frequency spectra data to generate the interpolated data including down-range data and along-track data for the two-dimensional inverse Fourier transformation.

10. A method of performing a signal transform of an input signal, the method comprising:

demodulating, in a signal demodulator, said input signal by a first chirp signal having a first chirp rate to obtain a reduced bandwidth signal;

filtering the demodulated reduced bandwidth signal in an all-pass quadratic phase filter to introduce a delay proportional to a frequency of said demodulated signal, wherein a constant of proportionality is the reciprocal of the first chirp rate; and

modulating in a signal modulator said filtered signal received from the all-pass quadratic phase filter by a second chirp signal having a second chirp rate to obtain an increased bandwidth chirped signal, the second chirp rate chosen to provide an output representing a time domain spectrum of said input signal,

wherein each of said first chirp signal and said second chirp signal is a complex signal representing a linear frequency modulated chirp.

11. The method according to claim 10 , wherein said step of filtering includes performing a Fourier transform to transform the demodulated reduced bandwidth signal into a frequency spectrum.

12. The method according to claim 11 , wherein said step of filtering further includes modulating said frequency spectrum to generate a further modulated output signal.

13. The method according to claim 12 , wherein said step of filtering further includes performing an inverse Fourier transform to generating an inverse Fourier transform of said further modulated output signal.

14. A method of acquiring a synthetic aperture image, said method system comprising:

receiving an input radar signal including a two-dimensional array of data comprising down-range data and along-track data, wherein said along-track data includes at least one along-track chirp signal;

processing said received radar signal by:

demodulating, in a signal demodulator, said input signal by a first chirp signal having a first chirp rate to obtain a reduced bandwidth signal;

filtering the demodulated reduced bandwidth signal in an all-pass quadratic phase filter to introduce a delay proportional to a frequency of said demodulated signal, wherein a constant of proportionality is the reciprocal of the first chirp rate;

modulating in a signal modulator said filtered signal received from the all-pass quadratic phase filter by a second chirp signal having a second chirp rate to obtain an increased bandwidth chirped signal, the second chirp rate chosen to provide an output representing a time domain spectrum of said input signal; and

wherein each of said first chirp signal and said second chirp signal is a complex signal representing a linear frequency modulated chirp;

reducing the bandwidths of said down-range frequency spectra data and said along-track frequency spectra data;

interpolating said reduced bandwidth frequency spectra data to generate interpolated data; and

performing a two-dimensional inverse Fourier transformation of the interpolated data to generate an output image.

15. The method according to claim 14 , wherein said step of filtering includes performing a Fourier transform to transform the demodulated reduced bandwidth signal into a frequency spectrum.

16. The method according to claim 14 , wherein said step of filtering further includes modulating said frequency spectrum to generate a further modulated output signal.

17. The method according to claim 14 , wherein said step of filtering further includes performing an inverse Fourier transform to generate an inverse Fourier transform of said further modulated output signal.

18. The method according to claim 14 , wherein the interpolated data includes down-range data and along-track data for the two-dimensional inverse Fourier transformation.