Window Shapefactor and Equivalent Noise Bandwidth

The following table shows a performance summary of the different types of windows supported by the 89600 VSA. Following the table is a section that describes the terms shapefactor and equivalent noise bandwidth.

Window Shapefactor & Equivalent Noise Bandwidth

Window shapefactor is a frequency ratio. It is the ratio of the frequency at -3dB to the frequency at -60dB. Window shapefactor is sometimes called window selectivity.

Equivalent noise bandwidth (ENBW) compares a window to an ideal, rectangular time-window. It is the bandwidth of the rectangular window's frequency-domain shape that passes the same amount of white noise energy as the frequency-domain shape defined by the other window.

In the table below, the ENBW has been normalized by the time-record length. To compute the ENBW for a given time-record length, divide the ENBW by the time-record length. For example, a Hanning window on a 0.5 second time record would have an ENBW of 3 Hz (1.5 Hz-sec/0.5 sec). Notice that the ENBW is slightly larger than the 3 dB bandwidth.

Window summary

Parameter	Uniform	Hanning	Gaussian Top	Flat Top
Leakage Performance	Poor	Relatively Good	Best	Good
Frequency Resolution: main length fixed	Poor**	Relatively Good	Good	Poor
Frequency Resolution: RBW Resolution Band Width (RBW or ResBW): specifies the minimum frequency bandwith that two separate frequency spectra can be resolved and viewed seperately. For FFT (digital) based VSA's the process is equivalent to passing a time-domain signal through a bank of bandpass filters, whose center frequencies correspond to the frequencies of the FFT bins. For a traditional swept-tuned (non-digital) spectrum analyzer, the resolution bandwidth is the bandwidth of the IF filter which determines the selectivity. fixed	Poor**	Good	Good	Best
Normalized Equivalent Noise BW	1.00 Hz-sec	1.50 Hz-sec	2.215 Hz-sec	3.8194 Hz-sec
3 dB BW	0.8844 Hz-sec	1.438 Hz-sec	2.091 Hz-sec	3.767 Hz-sec
Window ShapeFactor	716:1	9.1:1	4.0:1	2.45:1
Maximum Amplitude Error*	3.92 (dB)	1.42 (dB)	0.68 (dB)	< 0.01 (dB)
Highest Sidelobe	-13 (dB)	-31 (dB)	-125 (dB)	-95 (dB)
Sidelobe Fall Off	-20 dB / decade	-60 dB / decade	-20 dB / decade	-20 dB / decade

Parameter	Blackman-Harris	Kaiser-Bessel	Gaussian
Leakage Performance	Good	Good	Good
Frequency Resolution	Good	Good	Good
Normalized Equivalent Noise BW	2.0044 Hz-sec	2.0013 Hz-sec	2.0212 Hz-sec
Window ShapeFactor	3.79	3.78	4.45
Maximum Amplitude Error*	0.83 (dB)	0.83 (dB)	0.83 (dB)
Highest Sidelobe	-92 (dB)	-89 (dB)	-73 (dB)
Sidelobe Fall Off	-20 dB / decade	-20 dB / decade	-20 dB / decade

*	The maximum amplitude error occurs when a signal is halfway between frequency bins.
**	Frequency resolution is best for equal amplitude signals (for example, two closely spaced sine waves) but poor in general because of the large sidelobes.