The determination of the modal characteristics of industrial and aerospace rotating machinery during its operation is not a common practice. This is because it is difficult to filter out the vibrations that occur naturally due to the machine's operation. It is shown how this problem can be solved even when the vibration level produced by the machine under investigation is very high and, in some cases, broadband. The method used involves time-averaging an exponentially windowed output cumulatively prior to Fourier transformation. The start of the window is triggered by the beginning of the modal impulse force, as supplied by an instrumented hammer or other impulse device.