Glossary term

Equivalent Noise Bandwidth

Engineering definition of equivalent noise bandwidth covering ENBW, filter shape, FFT windows, integrated noise floor, receiver sensitivity and validation.

Branch: Engineering Physics
Glossary type: metric
Content: Glossary term
Updated: Jun 26, 2026
Revision: v1.0.0 · reviewed

Definition

metric

Equivalent noise bandwidth is the rectangular bandwidth that would pass the same integrated white-noise power as the actual filter, detector or spectral window.

Equivalent noise bandwidth, often abbreviated ENBW, converts a non-rectangular frequency response into the bandwidth that should be used for white-noise integration. It matters in receiver sensitivity, spectrum analysis, lock-in measurements, FFT window correction, sensor noise budgets and any calculation where noise density is turned into RMS noise or total noise power.

Equivalent noise bandwidth, abbreviated ENBW, is the bandwidth of an ideal rectangular filter that would pass the same integrated white-noise power as the real filter, detector or spectral window. It is the bandwidth to use when a noise density must be converted into total noise power or RMS noise.

The term exists because nominal bandwidth is often not enough. A 100 Hz cutoff, a 100 Hz resolution-bandwidth setting and a 100 Hz FFT bin can pass different amounts of broadband noise depending on filter shape, windowing, detector implementation and calibration convention.

Filter Definition

For a filter with frequency response H(f), a common equivalent-noise-bandwidth definition is:

\displaystyle B_{ENBW}=\frac{\int |H(f)|^2 df}{|H(f_0)|^2}

where f_0 is the reference frequency, often DC for a low-pass filter or the center frequency for a band-pass response. The integration convention must match the noise-density convention: one-sided and two-sided bandwidths should not be mixed.

If white voltage noise density is:

e_n

the integrated RMS voltage noise is:

v_{n,rms}=e_n\sqrt{B_{ENBW}}

For thermal or receiver noise calculations, the same idea appears as:

N=-174+NF+10\log_{10}(B_{ENBW})

when the result is an input-referred RF noise floor in dBm.

First-Order Low-Pass Example

For a first-order low-pass filter with -3 dB cutoff frequency f_c, the one-sided equivalent noise bandwidth is:

\displaystyle B_{ENBW}=\frac{\pi}{2}f_c

A channel with cutoff:

f_c=100\ \text{Hz}

therefore has:

B_{ENBW}=1.571(100)=157.1\ \text{Hz}

If the input voltage noise density is:

e_n=8\ \text{nV}/\sqrt{\text{Hz}}

the integrated RMS noise is:

v_{n,rms}=8\sqrt{157.1}=100.3\ \text{nV}

Using 100 Hz directly would give:

v_{n,rms}=8\sqrt{100}=80.0\ \text{nV}

The shortcut underestimates the RMS noise by about:

\displaystyle 20\log_{10}\left(\frac{100.3}{80.0}\right)=2.0\ \text{dB}

That error can be enough to change a receiver sensitivity, SFDR or uncertainty decision.

FFT Window ENBW

In spectral analysis, window shape also changes noise per bin. For discrete window samples w_n, a common bin-width-normalized expression is:

\displaystyle B_{ENBW,bins}=N\frac{\sum w_n^2}{(\sum w_n)^2}

and the bandwidth in hertz is:

B_{ENBW,Hz}=B_{ENBW,bins}\Delta f

where Delta f is the FFT bin spacing. A rectangular window is about 1.0 bin. A Hann window is about 1.5 bins. That does not make the signal weaker; it changes how broadband noise is integrated and displayed.

Boundary With Bandwidth and Noise Floor

Bandwidth is the broader engineering idea. It may describe channel allocation, throughput, filter passband, control response or sampling limits. Equivalent noise bandwidth is narrower: it is the bandwidth that preserves integrated white-noise power.

Noise floor is the resulting level after the correct bandwidth, reference plane and detector are applied. ENBW is one input to that calculation. If the noise is not white across the band, if strong interference is present, or if the detector averages in a nonlinear way, ENBW alone is not enough.

This distinction matters during design reviews. A specification may list channel bandwidth because it describes the allowed signal, while the noise calculation needs the filter or detector bandwidth that shapes random noise. In a spectrum analyzer, the displayed trace may depend on resolution bandwidth, video bandwidth, detector type and window correction. In a digital receiver, the relevant ENBW may be set by matched filtering or decimation, not by the nominal occupied bandwidth.

Validation Evidence

A defensible ENBW statement includes the filter transfer function or instrument setting, cutoff or bin spacing, window type, resolution bandwidth, detector mode, averaging rule, one-sided or two-sided convention, reference plane, calibration state and whether the assumed noise density is actually flat over the relevant band.

For lock-in measurements, record time constant, filter order and settling policy. For RF receivers, record the receiver noise bandwidth used for sensitivity and SFDR. For FFT measurements, record sample rate, record length, window, bin spacing and amplitude/noise correction factors.

Common Mistakes

Common mistakes include using -3 dB cutoff as if it were always ENBW, mixing one-sided and two-sided noise densities, forgetting FFT window correction, comparing spectrum traces with different RBW settings, using ENBW for colored noise without checking the spectrum, and reporting an RMS noise value without the filter or window that produced it.

The practical rule is simple: when noise density becomes total noise, state the equivalent noise bandwidth, not just the nominal bandwidth.

REF

Disciplines