Impulse excitation, time-domain response

To summarize, all of the information of the system is available from either means of exciting the resonance, driving it and sweeping the frequency, or hitting it with an impulse for its time response. The first experiment is performed in the frequency domain and the second in the time domain. The mathematical transformation of one representation into the other is the Fourier transform. The time domain response and the frequency domain response are called Fourier transform... 

Transient time-domain response to impulse excitation... 

In the previous section, we established a correspondence between the transient time-domain response (exponentially damped cosine wave) to a sudden "impulse" excitation and the steady-state frequency-domain response (Lorentzian absorption and dispersion spectra) to a continuous excitation. The Fourier transform may be thought of as the mathematical recipe for going from the time-domain to the frequency-domain. In this section, we shall introduce the mathematical forms of the transforms, along with pictorial examples of several of the most important signal shapes. 

The steady-state ESR absorption spectrum, A((u), is equivalent to the Fourier transform of the time-domain response, f(t), to an impulse excitation, if the magnetic resonance system is linear (i.e., absence of saturation). Since f(t) is causal (i.e., f(t) = 0 for t < 0), there is a simple mathematical relation between the absorption spectrum, A(w), and its corresponding dispersion spectrum, D(w) ... 

Figure 25a shows the response of the cyclic penta peptide introduced in Section IV.C after semi-impulsive excitation with an intense, ultrashort pump pulse, in the time domain. Pronounced beatings, originating from... 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

The objective of either time or frequence-domain fluorometry is to detemtine the decay law of the sample. For example, consider protein containing two tryptophan residues, and assume further that each residue has a single decay time. The impulse response of the sample is the decay which would be observed with an ideal instrument following excitation with a S-function light pulse. For our hypothetical protein we expect a doubly exponential decay of intensity. 

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