Digital Signal Processing Reference
In-Depth Information
1.2
BASIC DIGITAL SIGNAL PROCESSING EXAMPLES IN BLOCK DIAGRAMS
We first look at digital noise filtering and signal frequency analysis, using block diagrams.
1.2.1
Digital Filtering
Let us consider the situation shown in
Figure 1.2
,
depicting a digitized noisy signal obtained from
digitizing analog voltages (sensor output) containing a useful low-frequency signal and noise that
occupies all of the frequency range. After ADC, the digitized noisy signal
xðnÞ
, where
n
is the sample
number, can be enhanced using digital filtering.
Since our useful signal contains the low-frequency component, the high-frequency components
above that of our useful signal are considered noise, which can be removed by using a digital lowpass
filter. We set up the DSP block in
Figure 1.2
to operate as a simple digital lowpass filter. After pro-
cessing the digitized noisy signal
xðnÞ
, the digital lowpass filter produces a clean digital signal
yðnÞ
.
We can apply the cleaned signal
yðnÞ
to another DSP algorithm for a different application or convert it
to the analog signal via DAC and the reconstruction filter.
The digitized noisy signal and clean digital signal, respectively, are plotted in
Figure 1.3
,
where the
top plot shows the digitized noisy signal, while the bottom plot demonstrates the clean digital signal
obtained by applying the digital lowpass filter. Typical applications of noise filtering include acqui-
sition of clean digital audio and biomedical signals and enhancement of speech recording, among
others (Embree, 1995; Rabinar and Schafer, 1978; Webster, 1998).
yn
()
xn
()
DSP
Digital filtering
Digitized noisy input
Clean digital signal
FIGURE 1.2
The simple digital filtering block.
1.2.2
Signal Frequency (Spectrum) Analysis
As shown in
Figure 1.4
,
certain DSP applications often require that time domain information and
the frequency content of the signal be analyzed.
Figure 1.5
shows a digitized audio signal and its
calculated signal spectrum (frequency content), that is, the signal amplitude versus its corre-
sponding frequency for the time being, obtained from a DSP algorithm, called the
fast Fourier
transform
(FFT), which will be studied in Chapter 4. The plot in
Figure 1.5
(a) is a time domain
display of the recorded audio signal with a frequency of 1,000 Hz sampled at 16,000 samples per
second, while the frequency content display of plot (b) displays the calculated signal spectrum
versus frequency, in which the peak amplitude is clearly located at 1,000 Hz. Plot (c) shows a time
domain display of an audio signal consisting of one signal of 1,000 Hz and another of 3,000 Hz
sampled at 16,000 samples per second. The frequency content display shown in plot (d) gives two
locations (1,000 Hz and 3,000 Hz) where the peak amplitudes reside, hence the frequency content
display presents clear frequency information of the recorded audio signal.
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