Chirp (useful) signal shown in the background of radar noise clutter
Chirp on the instantaneous frequency plot
Here is where the chirp is (impossible to detect its presence on the signal plot or using FFT)
Radar transient signals are usually transient in time domain and wide-band in frequency domain. Since classical methods ( such as Fourier transform ) have difficulty to handle transient signal analysis, time-frequency or time-scale analysis is more suitable for preserving high-frequency contents of the information carried by transient signals. Comparing with the Fourier transform, the time-frequency/time-scale transform of a transient signal may detect and locate rapid changes of the signal better than Fourier transform. One of the important applications of time-frequency/time-scale transform is the detection and extraction of unknown radar signals in noise. The localization of the time and frequency by time-frequency/time-scale transform makes it possible for de-noising, signal detection and extraction in the time-frequency domain. Feature extraction in the time-frequency domain refers to the identification of specific feature attributes from the transform domain. To recover and isolate specific signal features, the transform pairs must be not only effective, but also computationally efficient.