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Introduction to DSP - frequency: short signals III

If we only measure the signal for a short time, the Fourier Transform works as is the data were periodic for all time.

Sometimes this assumption can be wrong:

The diagram shows what happens if we only measure a signal for a short time: the Fourier Transform works as if the data were periodic for all time.

In the case chosen it happens that the signal is periodic - but that not quite an integral number of cycles fit into the total duration of the measurement.

This means that when the Fourier Transform assumes the signal repeats, the end of one signal segment does not connect smoothly with the beginning of the next - the assumed signal is similar to the actual signal, but has little 'glitches' at regular intervals.

The assumed signal is not the same as the actual signal.

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