Digital Signal Processing Reference
In-Depth Information
2
2
1
1.5
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1000
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Time index n
Frequency (Hz)
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1
1.5
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Time index n
Frequency (Hz)
FIGURE 4.21
Comparison of a one-sided spectrum without using the window function and a one-sided spectrum using
a Hanning window with 150 samples in Example 4.11.
4.4
APPLICATION TO SIGNAL SPECTRAL ESTIMATION
The following plots compare amplitude spectra for speech data (we.dat) with 2,001 samples and
a sampling rate of 8,000 Hz using the rectangular window (no window) function and the
Hamming window function. As demonstrated in
Figure 4.22
(two-sided spectrum) and
Figure 4.23
(one-sided spectrum), there is little difference between the amplitude spectrum using the
Hamming window function and the spectrum without using the window function. This is due to
the fact that when the data length of the sequence (e.g., 2,001 samples) increases, the frequency
resolution will be improved and the spectral leakage will become less significant. However, when
data length is short, the reduction in spectral leakage using a window function will be more
prominent.
Next, we compute the one-sided spectrum for 32-bit seismic data sampled at 15 Hz (provided by
the US Geological Survey, Albuquerque Seismological Laboratory) with 6,700 data samples. The
computed spectral plots without using a window function and using the Hamming window are
displayed in
Figure 4.24
.
We can see that most of seismic signal components are below 3 Hz.
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