Dirac delta comb

In the Fourier domain, the spectra are convolved with the Dirac delta comb (Eq. 2.13), which means the spectrum will be infinitely repeated. To avoid aliasing, if the spectrum covers a bandwidth from 0 to v ax, the transformed Dirac delta comb must have a period of at least Iv ax, this is... 

FIGURE 3.22 Potential dirac delta ( comb ) function. 

Figure 3.4. (a) Dirac delta comb (or Shah fimction) of period l/rr (b) its Fourier transform, another Dirac comb of period x. 

Figure 4.13 Dirac delta comb and its Fourier transform, (a) LU (x) and (b) (1 /a)lU (v) (arbitrary height).

As described in Section 19.3.3.2, the strength of the electric field of the terahertz radiation is detected as a time-series signal thz(0- These signals are actually measured as / (t) signals that are proportional to LLI j(0 thz(0> where LU /0 indicates the Dirac delta comb (see Section D.3.3). thz(0 signals are converted to equivalent complex electric field (< ) values on the frequency axis as... 

The Dirac delta comb and its Fourier transform are referred to in Section 4.4.2. An infinite train of the Dirac delta functions at intervals of a on the x axis is called the Dirac delta comb and denoted by dJ (x). This function is defined as... 

Now we are in position to recognize the Poisson summation (the comb) formula (see Appendix A. 1.2) linking the exponential fluctuations with the delta Dirac point-contributions... 

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