Window Type

The VSA provides the following types of time data windows:

Window	Common Uses
Uniform	Transient and self-windowing data
Hanning	General purpose
Gaussian Top	High dynamic range
Flat Top	High amplitude accuracy
Blackman-Harris	Relatively high dynamic range
Kaiser-Bessel	Relatively high dynamic range
Gaussian	Special purpose only

Before transforming the time data into the frequency domain using a Fast Fourier Transform (FFT Fast Fourier Transform: A mathematical operation performed on a time-domain signal to yield the individual spectral components that constitute the signal. See Spectrum.), the 89600 VSA multiplies the time data by a window that is the same length as the time record.

One of the properties of the Fourier transform is that multiplying two time signals in the time domain is equivalent to convolving their frequency responses in the frequency domain. This is analogous to a swept spectrum analyzer where the frequency spectrum you see is really the true frequency spectrum of the input signal swept by the IF filter frequency response. The Discrete Fourier Transform (DFT discrete Fourier transform) takes a time record and produces the frequency spectrum for this time signal. However, the DFT assumes that the time record is one cycle of a periodic signal, meaning that when the time record is not periodic, there are effectively discontinuities at the beginning and end of the time record, which add unwanted frequency content to the spectrum.

To reduce the effect of the discontinuities, a time window is applied to the time record to make the time record appear as a section of a periodic signal. Choosing a time window affects the sharpness and amplitude accuracy of frequency components in the frequency domain.

The sharpness (frequency resolution) of the spectrum is affected by the main lobe width of the window's frequency response. Each type of window has a different main lobe width for the same time length. For better frequency resolution, you might want to choose a window like the Uniform or Hanning window.

The amplitude accuracy of each frequency point is affected by the alignment of the frequency component with respect to the FFT frequency bins. If a frequency component is aligned with a frequency point in the spectrum, there will be no attenuation in amplitude. However, if the frequency component is somewhere between frequency points, a window with a main lobe amplitude lower than -3 dB midway between frequency points will show an amplitude reading that is lower than the actual amplitude of the frequency component. Correspondingly, for a window with a main lobe that does not drop by at least 3 dB midway between frequency points, the amplitude reading for a frequency component will be higher than the actual amplitude of the frequency component.

Uniform Window

The uniform window (also called the rectangular window) is a time window with unity amplitude for all time samples and has the same effect as not applying a window.

Use this window when leakage is not a concern, such as observing an entire transient signal.

The uniform window has a rectangular shape and does not attenuate any portion of the time record. It weights all parts of the time record equally. Because the uniform window does not force the signal to appear periodic in the time record, it is generally used only with functions that are already periodic within a time record, such as transients and bursts.

The uniform window is sometimes called a transient or boxcar window.

For sine waves that are exactly periodic within a time record, using the uniform window allows you to measure the amplitude exactly (to within hardware specifications) from the Spectrum trace.

The normalized equivalent noise bandwidth of this window is 1 Hz-sec.

Hanning Window

The Hanning window attenuates the input signal at both ends of the time record to zero. This forces the signal to appear periodic. The Hanning window offers good frequency resolution at the expense of some amplitude accuracy.

This window is typically used for broadband signals such as random noise. This window should not be used for burst or chirp source types or other strictly periodic signals. The Hanning window is sometimes called the Hann window or random window.

The normalized equivalent noise bandwidth of this window is 1.5 Hz-sec.

Gaussian Top Window

The Gaussian Top (high dynamic range) window offers less amplitude accuracy, slightly higher frequency resolution, and much lower sidelobes than the Hanning window. The Gaussian Top window provides higher dynamic range than other windows because it has much lower sidelobes. It is used for general-purpose measurements and when high dynamic range is required (such as when time averaging).

The normalized equivalent noise bandwidth of this window is 2.21534968 Hz-sec.

Flat Top Window

The Flat Top window is the default window for FFT measurements. The Flat Top window provides better amplitude accuracy with a tradeoff in frequency resolution. Typically, this window is used for narrowband signals when you must measure the amplitude of a particular frequency component with great accuracy, for example, when using a fixed-sine source. This window should not be used for burst or chirp source types or other strictly periodic signals. The Flat Top window is sometimes called a sinusoidal window.

The normalized equivalent noise bandwidth of this window is 3.8193596 Hz-sec.

Blackman-Harris

This is the original "Minimum 4-sample Blackman-Harris" window, as given in the classic window paper by Fredric Harris "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform", Proceedings of the IEEE Institute of Electrical and Electronics Engineers. A US-based membership organisation that includes engineers, scientists, and students in electronics and related fields. The IEEE developed the 802 series wired and wireless LAN standards. Visit the IEEE at http://www.ieee.org, vol 66, no. 1, pp. 51-83, January 1978. The maximum side-lobe level is -92.00974072 dB.

The normalized equivalent noise bandwidth of this window is 2.004352938217 Hz-sec.

Kaiser-Bessel

This is a Kaiser-Bessel window with the parameter pi*alpha = 11.9. The maximum side-lobe level is around -89.09 dB.

The normalized ENBW varies slightly with window length, but converges on 2.00126601155359 Hz-sec for large window lengths.

This window is very similar to the Blackman-Harris window. The maximum side-lobe level is about 3 dB higher, but the subsequent side-lobes decay more quickly.

Gaussian

This is a Gaussian window with parameter alpha = 3.58, which has a standard deviation of σ = 1/(2 alpha) = 0.13966480446927374301. The maximum side-lobe level is around -73.49 dB.

The normalized ENBW varies slightly with the window length, but converges on 2.02118657238688 Hz-sec for large window lengths.

Note that this window is entirely different from the Gaussian Top window supported by the VSA.