Bandwidth

Strictly Limited in Frequency/Time

A signal is strictly limited in frequency (also called strictly band limited) if outside a certain bandwidth, the Fourier Transform is exactly zero. If a Fourier transform is strictly limited in frequency, it’s time domain signal will trail on attaining nonzero values into infinity, even if the amplitude of the function goes to zero.

Similarly a signal is strictly limited in time if outside a time interval, the signal is exactly zero. If a signal is strictly limited in time, then its Fourier Transform will trail off indefinitely, meaning it will be comprised of infinite frequencies, even if the amplitude diminishes.

Therefore, a given signal and its Fourier transform cannot be both strictly time and frequency limited

Bandwidth

Low-pass Signal

If a signal’s most significant frequency is centered around .

Main lobe bounded bandwidth for low-pass signals: because only half is in the positive frequency range

Band-pass Signal

Significant frequency is centered around some

Null-to-Null bandwidth for band-pass signals:

3-dB Bandwidth

The distance between ( for low-pass signals), and the positive frequency at which the signal dips to of the peak value at . For oscillatory signals this may be the first time the signal dips below on the positive side, or the last time (the point at which all further frequencies are less than ) depending on what you want.