Biomedical Engineering Reference
In-Depth Information
You can use the following Matlab command to look at the actual frequency shift and
distortion of the VCO signal sampled through the sound card:
specgram(y,512,Fs,kaiser(256,5),220)
If you are not a Matlab user, here is how you can write a program to determine the
instantaneous frequency (or phase) of the sampled VCO output:
1.
Transform the incoming signal to a complex data stream using a Hilbert transform.
3
This gives
I
(in-phase) and
Q
(quadrature-phase) data. A true Hilbert transform is
unrealizable, but you can get excellent approximations with FIR or IIR
filters. A thor-
ough description of how to implement the discrete Hilbert transform is available in
P. A. Regalia, Special Filter Designs, in S. K. Mitra and J. F. Kaiser (eds.),
Handbook
for Digital Signal Processing
, Wiley, New York, 1993.
2.
Pass these complex samples through a polar discriminator (i.e., multiply the new
complex sample by the conjugate of the old sample).
3.
The output is the phase di
fi
erence vector from the two samples.
4.
Compute arctan(
Q/I
) to get the phase angle of the vector. You can use an easy poly-
nomial
ff
fi
fit, Taylor series, or lookup table to estimate the arctan(
) function in order
to extract the phase angle.
cial ECG test sig-
nal was generated by an Agilent 33120A ARB. Note that the demodulated signal faithfully
reproduces the dc o
Figure 5.14 displays a signal acquired through this method. The arti
fi
set and low-frequency components of the ECG.
Since the VCO output is in the audible range, the modulated signal can be transmitted to
the sound card via a voice radio or telephonic link for remote data acquisition. This is the
principle of ECG transtelephonic monitoring, a common technique used to follow up pace-
maker patients using a transmitter such as that of Figure 5.15. To do so, however, the tone
frequencies produced by the VCO for a full-scale input must be limited within the bandpass
of the communications channel. For a plain telephone line, this range is 400 Hz to 3 kHz,
while a commercial FM audio link is speci
ff
ed to cover the audio bandwidth 30 Hz to
15 kHz. Another interesting possibility is to use a small 1 : 1 audio isolation transformer and
a
fi
floating power supply to turn the VCO into an isolated data acquisition front end.
It should be noted that the full bandwidth of a single sound card channel can be shared
by multiple VCOs occupying separate audio bands to convey various simultaneous low-
frequency signals to an array of software bandpass
fl
filters and demodulators. This is exactly
what FM telemetry systems do, and the U.S. Army's Inter-Range Instrumentation Group
of the Range Commanders Council (IRIG) has established a standard (IRIG-106-96) that
covers all aspects of frequency modulation (FM) and pulse code modulation (PCM) teleme-
try, including transmitters, receivers, and tape recorders. Owing to its success as a proven
standard and its wide support by telemetry equipment manufacturers, most commercial
data acquisition systems use the same IRIG standard channels.
The IRIG standard speci
fi
es ways of performing frequency-division multiplexing (FDM)
over a telemetry channel, that is, how to generate a composite signal consisting of a group
of subcarriers arranged so that their frequencies do not overlap or interfere with each other.
Various FM subcarrier and deviation schemes are available to accommodate di
fi
ff
erent
3
The
Hilbert transform
is a mathematical operation that decomposes a waveform into an instantaneous phase and
an instantaneous amplitude waveform. If the input is a pure sine wave, the output instantaneous amplitude wave-
form will have a constant value while the phase will increase linearly over time. If the sine wave were amplitude
modulated, the instantaneous amplitude waveform would show this modulation. Similarly, frequency modulation
will affect the instantaneous phase waveform.
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