Space/time/frequency methods in adaptive radar - New Jersey ...

19Figure 2.7 Computation of the short-time Fourier transform (STFT). To estimatethe frequency content of the signal s around time t o , the low-passwindow g is centered at to and the Fourier transform of s(τ)g*(τ - to )is calculated2.3.1.1 Time-frequency Resolution: The performance of the STFT is affectedby the choice of the window and the signal concentration. The fundamental tradeoffbetween time and frequency resolution may be understood by reviewing Equations2.8 and 2.9.Each constant-time slice of the STFT indicates the frequency content of theportion of the signal that lies within the window function at the selected time. Anarrow window g may be used to increase the time resolution of the STFT. However,as g narrows in time, the corresponding frequency window G widens, reducing thefrequency resolution. This demonstrates that it is impossible to have 'perfect' timeand frequency resolution simultaneously and is referred to as the time-frequencyuncertainty principle[33].This principle also illustrates that it may be useful to use different windowingfunctions for different applications. Narrow time windows are typically used when