National Instruments 320571-01 用户手册
Chapter 1
NI-DSP Analysis VI Reference Overview
NI-DSP SRM for LabVIEW for Windows
1-7
Part 3: NI-DSP Function Reference
The simplest window is a rectangular window. Because this window requires no special effort it is commonly
referred to as the no window option. Remember, however, that a discrete signal and its spectrum is always affected
by a window. Let x[n] be a digitized time-domain waveform that has a finite length of n. w[n] is a window
sequence of n points. The windowed output is calculated as follows:
referred to as the no window option. Remember, however, that a discrete signal and its spectrum is always affected
by a window. Let x[n] be a digitized time-domain waveform that has a finite length of n. w[n] is a window
sequence of n points. The windowed output is calculated as follows:
y[i] = x[i] * w[i]
(1)
If X, Y, and W are the spectra of x, y, and w, respectively, the time-domain multiplication in formula 1 is equivalent
to the convolution shown as follows:
to the convolution shown as follows:
Y[k] = X[k]
Θ
W[k].
(2)
Convolving with the window spectrum always distorts the original signal spectrum in some way. A window
spectrum consists of a big mainlobe and several sidelobes.
spectrum consists of a big mainlobe and several sidelobes.
The mainlobe is the primary cause of lost frequency resolution. When two signal spectrum lines are too close to
each other, they may fall in the width of the mainlobe, causing the output of the windowed signal spectrum to have
only one spectrum line. Use a window with a narrower mainlobe to reduce the loss of frequency resolution. It has
been shown that a rectangular window has the narrowest mainlobe, so that it provides the best frequency resolution.
each other, they may fall in the width of the mainlobe, causing the output of the windowed signal spectrum to have
only one spectrum line. Use a window with a narrower mainlobe to reduce the loss of frequency resolution. It has
been shown that a rectangular window has the narrowest mainlobe, so that it provides the best frequency resolution.
The sidelobes of a window function affect frequency leakage. A signal spectrum line will leak into the adjacent
spectrum if the sidelobes are large. Once again, the leakage results from the convolution process. Select a window
with relatively smaller sidelobes to reduce spectral leakage. Unfortunately, a narrower mainlobe and smaller
sidelobes are mutually exclusive. For this reason, selecting a window function is application dependent. An
example of a windowed spectrum in the continuous case is shown in Figure 1-2.
spectrum if the sidelobes are large. Once again, the leakage results from the convolution process. Select a window
with relatively smaller sidelobes to reduce spectral leakage. Unfortunately, a narrower mainlobe and smaller
sidelobes are mutually exclusive. For this reason, selecting a window function is application dependent. An
example of a windowed spectrum in the continuous case is shown in Figure 1-2.
*
Signal Spectrum
Window Spectrum
Windowed Signal Spectrum
Figure 1-2. Spectral Leakage Demonstrated Using Convolution
The original signal spectrum is convolved with the window spectrum and the output is a smeared version of the
original signal spectrum. In this example, you can still see four distinctive peaks from the original signal, but each
peak is smeared and the frequency leakage effect is clear.
original signal spectrum. In this example, you can still see four distinctive peaks from the original signal, but each
peak is smeared and the frequency leakage effect is clear.