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In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a signal to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or is fuzzy by about some statistic of that noise floor. Due to the aliasing of that above bandlimit frequency noise into the spectrum (FFT result bins) of interest.

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a signal to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or is fuzzy by about some statistic of that noise floor, due to the aliasing of that above bandlimit frequency noise into the spectrum (FFT result bins) of interest.

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a signal to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or is fuzzy by about some statistic of that noise floor.

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a signal to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or is fuzzy by about some statistic of that noise floor. Due to the aliasing of that above bandlimit frequency noise into the spectrum (FFT result bins) of interest.

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a system to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or fuzzy by about some statistic of that noise floor.

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and arithmetic, etc., among other limitations, creating a noise floor.

So in practice, one considers a signal to be band limited if all the spectrum above the band limit frequency is thought to be below the desired or assumed noise floor. Or considers the portion of the spectrum above the band limit frequency to be noise contributing to the measurement and computational noise floor.

So you take your FFT by taking an FFT. But your FFT result becomes fuzzy by up to the maximum of that floor, or is fuzzy by about some statistic of that noise floor.