# Bandwidth of a system

This link says that the bandwidth is the frequency at which the magnitude of the frequency response is decreased by 3dB from the value of the initial horizontal asymptote.

But wikipedia says "In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak." So, should the bandwidth be calculated from the initial horizontal slope or from the peak value ?

It seems that you are speaking about the bandwidth of a lowpass system, right?

At first, you should realize that the bandwidth of a system is a parameter that needs DEFINITION. Hence, in some cases, you can define the bandwidth for your own purposes even at 1dB or 2dB points. But that it is not the core element of your question.

(1) Your graph shows a lowpass response according to a so called "Chebyshev behaviuor" (with gain peaking higher than the value at f=0). Indeed, for such a transfer function it makes sense to specify the bandwidth at that frequency where the magnitude crosses again the DC value (horizontal line).

(2) However, if the magnitude response does NOT exhibit such a peaking (lowpass response according to a "Butterworth" or "Bessel") it is commonly agreed to use the classical 3dB frequency (3 dB below the DC value).

Summary: The bandwidth of a lowpass system is a matter of definition. In general, it defines the end of the "passband" based on an acceptable "ripple" (magnitude variations) within this frequency band. If, for example, the gain peaking (in your figure) is w=1 dB it makes sense to specify that the ripple within the passband is 1 dB only. For another system without such peaking (typical example: Butterworth response) the magnitude variation (ripple) would be 3 dB.

Remarks: As you have made reference to a wikipedia contribution: Please note that the mentioning of "3 dB below peak" applies to a bandpass system only. And even this is a matter of definition - for some bandpass systerms it makes sense to require 1dB or 2dB break points. For lowpass responses the explanations/definitions apply as outlined above.

Please note that most filter design aids (tables, programs) are using bandwidth definitions in accordance with the above mentioned two cases.

• So, w0 is the bandwidth if definition 1 is applied ? Jan 15 '17 at 16:16
• Not exactly - the bandwidth is where the red curve and the horizontal line meet - slightly larger than wo.
– LvW
Jan 15 '17 at 16:37

Main Difference – Data Rate vs. Bandwidth Data rate and bandwidth are terms that are used often in the fields of communications and networking. Sometimes, there are differences in the usage of these words. In general, the main difference between data rate and bandwidth is that bandwidth refers to the range of component frequencies that a signal carries, whereas data rate refers to the number of bits that a signal carries per second.