Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 38

Sampling can be regarded as the preprocess of transforming a continuous or analog signal to a discrete or digital signal. When the signal analysis has to be done using digital computers via numerical evaluations, continuous signals need to be converted to the digital versions. This is achieved by applying the common procedure of sampling. Analog‐to‐digital (A/D) converters are common electronic devices to accomplish this process. The implementation of a typical sampling process is shown in Figure 1.9. A time signal s(t) is sampled at every T_s seconds such that the discrete signal, s[n], is generated via the following equation:

Figure 1.9 Sampling. (a) continuous time signal, (b) discrete‐time signal after the sampling.

(1.20)

Therefore, the sampling frequency f_s is equal to 1/T_s where T_s is called the sampling interval.

A sampled signal can also be regarded as the digitized version of the multiplication of the continuous signal, s(t) with the impulse comb waveform, c(t) as depicted in Figure 1.10.

According to the Nyquist–Shannon sampling theorem, the perfect reconstruction of the signal is only possible provided that the sampling frequency f_s is equal or larger than twice the maximum frequency content of the sampled signal (Shannon 1949). Otherwise, signal aliasing is unavoidable and only distorted version of the original signal can be reconstructed.

Figure 1.10 Impulse comb waveform composed of ideal impulses.