Küpfmüller's uncertainty principle

The küpfmüllersche indeterminacy or uncertainty principle of communication engineering is the statement of the System Theory ( Communications Engineering ), that the period of time or settling time and the bandwidth of a signal can not be simultaneously arbitrarily small. It provides a customized news to the conditions of technical systems and analogous to Heisenberg's uncertainty principle statement.

The küpfmüllersche uncertainty relation was first formulated in 1924 by Karl Küpfmüller. Then apply for the duration? T and the bandwidth of a signal? F always

K depending on the definition of bandwidth and time duration is equal to 1 or a value of 0.5.

On the uncertainty relation with respect to time and bandwidth are based, for example, well-known principles of measurement:

• To measure a signal of 100 ns, it takes an oscilloscope over 10 MHz bandwidth.
• To determine a frequency of 1 Hz, the signal of at least 1 s must be measured for.

Time -bandwidth product

Since the definition of a given bandwidth the following various specifications, and the time period of signals is not clear, there are a number of different definitions of time-bandwidth products. For example, in not time -limited signals the product on equal area rectangles around the maximum value of the signal is expressed in the origin:

With, the Fourier transform of. The bandwidth is analogous to set to:

The time-bandwidth product is stable at this time and setting the bandwidth to the value: