# Analog Systems Bandwidth

For analog signals, which can be mathematically viewed as functions of time, bandwidth Δf is the width, measured in hertz, of the frequency range in which the signal's Fourier transform is nonzero. Because this range of non-zero amplitude may be very broad, this definition is often relaxed so that the bandwidth is defined as the range of frequencies where the signal's Fourier transform has a power above a certain amplitude threshold, commonly half the maximum value (half power approx -3 dB). Bandwidth of a signal is a measure of how rapidly its parameters (e.g. amplitude and phase) fluctuate with respect to time. Hence, the greater the bandwidth, the faster the variation in the signal parameters may be. The word bandwidth applies to signals as described above, but it could also apply to systems. In the latter case, to say that a system has a certain bandwidth means that the system can process signals of that bandwidth.

A baseband bandwidth is a specification of only the highest frequency limit of a signal. A non-baseband bandwidth is a difference between highest and lowest frequencies.

As an example, the (non-baseband) 3-dB bandwidth of the function depicted in the figure is Δf = f2 - f1, whereas other definitions of bandwidth would yield a different answer.

A commonly used quantity is fractional bandwidth. This is the bandwidth of a device divided by its center frequency. E.g., a device that has a bandwidth of 2 MHz with center frequency 10 MHz will have a fractional bandwidth of 2/10, or 20%.

The fact that real baseband systems have both negative and positive frequencies can lead to confusion about bandwidth, since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as B = 2W, where B is the total bandwidth, and W is the positive bandwidth. For instance, this signal would require a lowpass filter with cutoff frequency of at least W to stay intact.

The 3-dB bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at its peak, which is typically at or near its center frequency.

In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops to -3 dB.

In basic electric circuit theory when studying Band-pass and Band-reject filters the bandwidth represents the distance between the two points in the frequency domain where the signal is frac{1}{sqrt{2}} of the maximum signal amplitude (half power).

In photonics, the term bandwidth occurs in a variety of meanings: » the bandwidth of the output of some light source, e.g., an ASE source or a laser; the bandwidth of ultrashort optical pulses can be particularly large; » the width of the frequency range that can be transmitted by some element, e.g. an optical fiber; » the gain bandwidth of an optical amplifier; » the width of the range of some other phenomenon (e.g., a reflection, the phase matching of a nonlinear process, or some resonance); » the maximum modulation frequency (or range of modulation frequencies) of an optical modulator; » the range of frequencies in which some measurement apparatus (e.g., a powermeter) can operate; » the data rate (e.g., in Gbit/s) achieved in an optical communication system.