# Bandwidth

### Communications

The difference between the lowest and highest frequency components of a signal or device. The bandwidth of optical fibre is in the gigabit or billions of bits per second range, while ethernet coaxial cable is in the megabit or millions of bits per second range.

### Filter

The bandwidth of a filter is the separation between the lower and upper frequencies at which the amplitude of a sinusoidal signal is attenuated by a factor of 2 (half power points).

Bandwidth is defined as the width of the resonance curve at a specified point from the peak, normally at 3 dB down.

Note that for 3dB down from the peak, decibel calculations give this as the ½ power point, or 1/√2 which is 0.707 of the peak value.

### Mathematics

One further definition concerns the bandedness of a symmetric square matrix. The bandwidth of a matrix is defined as b = 2 m +1, where m is the number of terms past the diagonal beyond which all elements of the matrix equal to zero.

### Optics

Usually described in terms of transmission level, the bandwidth is the spectral range over which an interference filter transmits.

### Signal Processing

The resolution bandwidth in a digital frequency analysis is the separation between adjacent frequencies in the Fourier Series. The analysis bandwidth in a digital frequency analysis is the total frequency range over which Fourier components are obtained. (Usually 0 to half the sampling frequency).