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Scaled Time Domain Window (Not in Base Package)

Applies the selected window to the time-domain signal. Details  Example

Waveform is the time-domain signal.
window is the time-domain window to be used.

0Uniform
1Hanning
2Hamming
3Blackman-Harris
4Exact Blackman
5Blackman
6Flat Top
7Four Term Blackman-Harris
8Seven Term Blackman-Harris
9Low Sidelobe
Windowed Waveform is the time-domain signal, multiplied by the scaled window.
window constants contains the window constants for the selected window. The default values are set to those of the uniform window (no window).
eq noise BW is the equivalent noise bandwidth of the selected window. You can use this value to divide a sum of individual power spectra of the power spectrum or to compute the power in a given frequency span.
coherent gain is the inverse of the scaling factor applied to the window.

Scaled Time Domain Window Details

The Scaled Time Domain Window VI scales the result so that when the power or amplitude spectrum of the windowed waveform is computed, all windows provide the same level within the accuracy constraints of the window. The Scaled Time Domain Window VI also returns important window constants for the selected window. These constants are useful when you use VIs that perform computations on the power spectrum, such as the Power & Frequency Estimate VI and the Spectrum Unit Conversion VI.

Defining Equations

All cosine windows without scaling are defined by the following equation.

where , n is the number of elements in X, and m is the number of elements in the window coefficient array a[].

For this VI, the preceding equation is modified to include division by the coherent gain (cg), as shown in the following equation.

Coefficients and Window Parameters for the Different Window Types

This section provides information about the a coefficients and window parameters for each window type available in this VI. Each window type has the following window parameters:

  • coherent gain (cg)
  • equivalent noise bandwidth (enbw)
  • 6dB bandwidth (6dB BW)

Uniform

a[] is empty because no window is applied. The window equation is yi = xi
cg = 1
enbw = 1
6dB BW = 1.21

Hanning

a0 = 0.5cg = 0.5
a1 = 0.5enbw = 1.5
6dB BW = 2.0

Hamming

a0 = 0.54cg = 0.54
a1 = 0.46enbw = 1.362826
6dB BW = 1.82

Blackman-Harris

a0 = 0.42323cg = 0.42323
a1 = 0.49755enbw = 1.0708538
a2 = 0.079226dB BW = 2.27

Exact Blackman

a0 = 0.42659071367153911200cg = 0.42659071367
a1 = 0.49656061908856408100enbw = 1.693699
a2 = 0.076848667239896820106dB BW = 2.25

Blackman

a0 = 0.42cg = 0.42
a1 = 0.5enbw = 1.726757
a2 = 0.086dB BW = 2.3

Flat Top

a0 = 0.215578948cg = 0.215578948
a1 = 0.41663158enbw = 3.770246506303
a2 = 0.2772631586dB BW = 4.58
a3 = 0.083578947
a4 = 0.006947368

4 Term B-Harris

a0 = 0.35875cg = 0.35875
a1 = 0.48829enbw = 2.004353
a2 = 0.141286dB BW = 2.67
a3 = 0.01168

7 Term B-Harris

a0 = 0.27105140069342415cg = 0.27105140069342415
a1 = 0.43329793923448606enbw = 2.631905
a2 = 0.218122999543110626dB BW = 3.5
a3 = 0.065925446388030898
a4 = 0.010811742098372268
a5 = 7.7658482522509342E-4
a6 = 1.3887217350903198E-5

Low Sidelobe

a0 = 0.323215218cg = 0.323215218
a1 = 0.471492057enbw = 2.215350782519
a2 = 0.175534286dB BW = 2.95
a3 = 0.028497078
a4 = 0.001261367

Example

Refer to the Sound Card Simple Spectrum Analyzer VI in the labview\examples\sound\sound adv.llb directory for an example of using the Scaled Time Domain Window VI.

 


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