Practical Tips on Pulse Testing

Theoretically, the best possible input pulse would be an impulse or a Dirac function S, y. The Fourier transformation of is equal to unity at all frequencies. 

Therefore would be simply the Fourier transformation of the output function. No division by a small number would be required. 

Practically, however, we can never have an infinitely high pulse with zero width. In general, we need to keep the width of the pulse fairly small to keep its frequency content from becoming too small at higher frequencies. For 

When frequency co is equal to 2n/D, the FIT of the input pulse goes to zero. Since we are dividing by this term, the calculation of the transfer function becomes meaningless at frequencies near 2n/D. Therefore the smaller D can be made, the higher is the frequency to which C i ) can be accurately found. 

A good rule of thumb is to keep the width of the pulse less than about half the smallest time constant of interest. If the dynamics of the process are completely unknown, it takes a few trials to establish a reasonable pulse width. If the width of the pulse is too small, for a given pulse height, the system is disturbed very little, and it becomes dilTicult to separate the real output signal from noise and experimental error. The height of the pulse can be increased to kick the process more, but there is a limit here also. 

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