Monthly Archives: May 2014

Decimation of a Band-Pass Signal and Its Inverse Operation

Decimation of a Band-Pass Signal. As was seen in the section entitled “Decimation,” if the input signal x(m) was low pass and band limited to [—n/M, n/M], the aliasing after decima­tion by a factor of M could be avoided [see Eq. (5)]. However, if a signal is split into M uniform frequency bands, at most one band will have its spectrum confined to [—n/M, n/M]. In fact, if a signal is split into M uniform real bands, one can say that band xk(n) will be confined to [—n(k + 1)/M, —nk/M] U [nk/M, n(k + 1)/M] [1] (see Fig. 11).

This implies that band k, k Ф 0 is not confined to [—n/M, n/M]. However, by examining Eq. (5) one can notice that aliasing is still avoided in this case. The only difference is that, after decimation, the spectrum contained in [—n(k + 1)/ M, —nk/M] is mapped to [0, n] if k is odd, and to [—n, 0] if k is even. Similarly, the spectrum contained in the interval [nk/M, n(k + 1)/M] is mapped to [—n, 0] if k is odd and to [0,

Critically Decimated М-Band Filter Banks. It is clear that if a signal x(m) is decomposed into M non-overlapping band­pass channels Bk, k = 0, . . ., and M — 1 such that UM=—o1 Bk = [—n, n], then it can be recovered from these M channels by just summing them up. However, as conjectured above, ex­act recovery of the original signal might not be possible if each channel is decimated by M. However, in the section enti­tled ‘‘Decimation of a Band-Pass Signal and Its Inverse Oper­ation,’’ we examined a way to recover the band-pass channel from its subsampled version. All that is needed are interpola­tion operations followed by filters with passband [—n(k + 1)/M, —nk/M] U [nk/M, n(k + 1)/M] (see Fig. 13). This process of decomposing a signal and restoring it from the frequency bands is depicted in Fig. 14. We often refer to it as an M-band filter bank. The frequency bands uk(n) are called sub-bands. If the input signal can be recovered exactly from its sub-bands, it is called an M-band perfect reconstruction filter bank. Figure 15 details a perfect reconstruction filter bank for the 2-band case.

However, the filters required for the M-band perfect recon­struction filter bank described above are not realizable [see Eqs. (6) and (10)], that is, at best they can be only approxi­mated (1). Therefore, in a first analysis, the original signal


j M


j M




1 M


j M




1 y(n)

HM – 1(z)




1 M

GM – 1(z)

History of Radar Tracking

Cursor position Range 026.7 km | Azimuth 042.8"

History of Radar Tracking

N Range ring

Fig. 1. PPI radar display showing targets and clutter.



In the early days of radar, range and angle-tracking functions were performed manually. Using a device such as a track ball, the operator could keep the cross-hairs positioned on the range and azimuth angle of a detected target viewed on a display such as a plan position indicator (PPI) display. The PPI display, such as that shown in Fig. 1, provides a two-dimensional display of range and azimuth angle for a radar with an azimuth-scanning antenna. Targets result in blips on the display where the brightness (and size) of the blips are related to
the amplitude of the target echoes at the receiver. The output of the track ball can provide readout of the target range and azimuth angle or provide the required range and angle information to weapons systems for targeting purposes. Although this was a satisfactory technique for tracking slow-moving targets such as ships, it is certainly a tedious process.

To aid in the tracking of ships and aircraft, a rate-aided device was added to some systems. With rate – aided tracking, the operator needed to make only fine adjustments to account for changes of the target range and angle rates with respect to the radar. With this configuration, the radar operators were better able to track faster-moving objects such as aircraft. Still, this tracking function required the constant attention of the radar operator.

Automated target tracking evolved as a necessary tool to allow the radar operator to perform the tracking function efficiently. After range and angle trackers are locked onto the target, the tracker then senses any error between the current target position and that predicted by the tracker and automatically and contin­uously adjusts the tracker functions either on a pulse-to-pulse or scan-to-scan basis. As a result, automatic radar tracking can maintain target track more accurately than a human operator and can better follow fast maneuvering targets.

Sporadic E

General Characteristics. Even though the normal E region is Chapman-like in nature, isolated forms of ionization are often observed in the E-region, having a variety of shapes and sizes. These ionization forms have been termed sporadic E, because they appear quasirandomly from day to day, and they generally defy deterministic prediction methods. Sporadic E (Es) ionization has been observed during rocket flights and with incoherent backscatter radar, and a layer thickness of the order of 2 km has been observed. It generally takes the form of large-scale structures, having horizontal dimensions of hundreds of kilometers at middle latitudes.

Fig. 12. Variations in the ionosphere thought to be associated with traveling ionospheric disturbances. The foF2 variations shown here are of the order of ±2% and have periods of ~20 min. The NmaxF2 variations are ~ ±1%. [From Paul (63).]

Fig. 13. Effect of a large geomagnetic storm on Nmax. [By permission of J. M. Goodman and Kluwer Academic Publishers, Norwell, MA (11).]

T f Г I 1———————————— 1——- 1——— г

1944 46 48 50 52 54


Fig. 14. Variation in R12, foF2, foE, and 4 MHz absorption at noontime. The seasonal effects are clearly evident, the foE and D-layer variations being out of phase with the foF2 variations (i. e., seasonal anomaly). [By permission of J. M. Goodman and Kluwer Academic Publishers, Norwell, MA (11).]

Polar and equatorial forms have different structures and causal mechanisms. Although sporadic E consists of an excess of ionization (against the normal E-region background), it does not appear to be strongly tied to solar photoionization processes. Still, midlatitude Es occurs predominantly during summer days. Sporadic E does exhibit seasonal and diurnal tendencies, which have been examined statistically, and at least three different types of sporadic-E ionization have been discovered with distinct geographical regimes: low-latitude

Fig. 15. Long-term variation inRi2, foF2, and foE at noontime. Since running 12-month averages were taken, the seasonal effects observed in Fig. 14 are smoothed out. [By permission of J. M. Goodman and Kluwer Academic Publishers, Norwell, MA (11).]

(or equatorial), midlatitude (or temperate), and high-latitude ionization. Figure 16 depicts the probability of Es occurrence.

Formation of Midlatitude Sporadic E. It has suggested that wind-shears in the upper atmosphere are responsible for the formation of sporadic E at midlatitudes. We shall review this process briefly.

It should be recalled from the examination of photochemistry in the ionosphere that molecular ions such as those that exist in the E region introduce rapid electron loss by recombination. At the same time it is recognized that an enormous number of meteors burn up in the E region. This meteoric debris is largely comprised of metallic ions, which are monatomic. Their presence has been confirmed by mass spectroscopy measurements using rockets, and they include iron, sodium, magnesium, etc. Since monatomic ions exhibit a small cross section for electron capture, the process by which atomic ions become concentrated in well-defined layers will lead to reduced loss rates for ambient free electrons in the interaction region.

The influx of this foreign mass of metallic ions, when distributed over the whole of the E region, would be insufficient to overwhelm the omnipresent molecular species (such as NO+), which are in a state of photo­chemical equilibrium, were it not for a mechanism that preferentially concentrates the meteoric debris ions. Apparently wind shear is this mechanism. The basic wind shear theory was proposed by Whitehead (26), but it remained for Gossard and Hooke (27) to outline a process for meteoric ion concentration based upon the interaction of the meteoric debris with atmospheric gravity waves, the latter wave structures being responsible for the development of TIDs as well. The ultimate process involves a corkscrew propagation of atmospheric gravity waves and atmospheric tides, which results in a rotation of wind velocity as a function of altitude. This

Auroral zone

High temperature zone

1951 1952

Fig. 16. Probability of Es occurrence as observed in the period 1951-1952. It is representative of the global, seasonal, and diurnal variation of sporadic-E ionization. [From Davies (1).]

effect can cause the wind to change direction over an altitude of only a kilometer or so, so as to trap meteoric ions at an intermediate point having zero velocity. ’This buildup in a narrow region is sufficient to generate an intense sporadic-E patch.

Sporadic E at Non temperate Latitudes. The high-latitude sources are evidently of two types, depending upon whether the observation is made in the neighborhood of the auroral oval or poleward of it

Anchorage Fairbanks

55 Є0 * j 65

Invariant latitude (deg)

Fig. 17. Idealized picture of ionospheric plasma frequencies in a north-south plane through Fairbanks and Anchorage, Alaska. E, region equatorward of trough; B, equatorward edge of trough: C, plasma frequencies (MHz); D, trough minimum; E, plasmapause field line; F, poleward edge of trough; G, F-region blobs; H, enhanced D-region absorption; I, E-region irregularities. [By permission of J. M. Goodman and Kluwer Academic Publishers, Norwell, MA (11), after Hunsucker (28).]

(i. e., in the polar cap region). It has been found that auroral Es is basically a nocturnal phenomenon; it is associated with the optical aurora and is due to auroral electron precipitation. Because of its proximity to the seat of auroral substorm activity, it is not surprising to find some correlation between auroral Es and some appropriate magnetic index. Indeed, it has been found that auroral Es is positively correlated with magnetic activity. On the other hand, polar-cap Es may be relatively weak, and is negatively correlated with substorm activity.

Turning equatorward, it has been found that equatorial Es is most pronounced during daylight hours, and evidence points to the formation of ionization irregularities within the equatorial electrojet as the responsible agent at low latitudes.

Body Temperature Monitoring

The term body temperature usually means the body core tem­perature, which is the temperature of the central part of the body. Many different techniques have been used for monitor­ing body temperature (22). Although different body parts have different temperatures, such differences are small when the temperature is stable, so that body temperature can be monitored fairly well at many measurement sites. Body tem­perature is usually measured by a clinical thermometer at the oral cavity. Recently, the tympanic thermometer is also used. For continuous monitoring, it is measured at the rectum, esophagus, bladder, auditory canal, tympanum, nasal cavity, or digestive tract. However, when body temperature varies, significant differences in observed temperatures may occur between sites. Thus when rapid changes of body temperature have to be monitored the measurement site used is important.

Rectal temperature has been used widely in patient moni­toring because the rectum is a convenient site into which a thermometer probe can be inserted far enough to protect it from heat loss. Rectal temperature is always higher than oral temperature as well as temperatures of other sites, and has been considered to be a reliable indicator of body core temper­ature. However, when body temperature varies, changes in rectal temperature are delayed comparable to those of other, more central parts of the body, and thus rectal temperature cannot be accurate enough for monitoring in such conditions.

The esophagus has been used most frequently as a site for body temperature monitoring during anesthesia. Esophageal temperature is measured by inserting a probe through the mouth or nose so that the sensor tip is positioned at near­heart level. Under stable conditions, esophageal temperature is intermediate between oral and rectal temperature, and fol­lows internal temperature changes rapidly.

Bladder temperature can be monitored using a thermistor – tipped bladder catheter as shown in Fig. 7(a). Although blad­der temperature is close to rectal temperature in stable condi­tions, it follows internal temperature changes rapidly. Blad­der temperature is recommended as a measurement site for

Body temperature can also be monitored across the skin using the zero-heat-flow method as shown in Fig. 7(b) (23). The probe that is used in this method has two thermistors to detect heat flow across the probe. It also has a heater, and the heater current is controlled so that the temperatures of two thermistors are equal, which means that we can compen­sate for the heat flow from the skin to the outer air. Under such conditions, the probe can be regarded as an ideal ther­mal insulator. When the skin surface is insulated, the tem­perature gradient in the tissue near the surface will vanish, and finally the temperature of the surface of the skin will reach that of the deep tissue. A commercial model (Coretemp, Terumo Co., Tokyo) has now been developed for which disc­shaped probes of different sizes, from 15 mm to 80 mm in diameter, are available. By applying a probe to the forehead, chest, or abdomen, body temperature can be monitored con­tinuously for several days in intensive care units (24). Simul­taneous monitoring of body core and peripheral temperatures by applying probes to the forehead and to the sole of a pa­tient’s foot, temperature differences between the body core and the limbs can be observed which can be a useful index of peripheral circulation (25).

Long-Term Solar-Activity Dependence of the Ionospheric Layers

There is a clear tendency for the ionospheric critical frequencies to increase with sunspot number. Figure 14 shows the long-term variation of R12, foF2, and foE, and the D-layer absorption level (at 4 MHz), for noontime conditions. The D region is best characterized by the amount of absorption it introduces (see the subsection “Ionospheric Layering” above). A device for monitoring the D-region absorption is the riometer, which evaluates it as the product of D-region electron concentration and the electron collision frequency. From Figure 14, a slow 11-year modulation in the ionospheric parameters is evident. After smoothing, the results correlate well with sunspot number. Superimposed on this solar epochal variation is an annual variation, with D-region absorption and foE exhibiting summertime maxima, while foF2 exhibits a wintertime maximum (i. e., seasonal anomaly).

The slow but definite dependence upon mean sunspot number is illustrated in Fig. 15. This plot is unusual in that it presents running 12-month averages of the specified ionospheric parameters as well as of the sunspot number. This obscures the seasonal effects observed in Fig. 14.

Fig. 11. Variations in the hourly values of foF2 as a function of the time of day, for January solar maximum conditions at a northern-hemisphere midlatitude site. The range of day-to-day variability in foF2 is ~ ±10%, suggesting a variation in NmaxF2 of ~ ±5%. [From Davies (1).]