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Radiometer systems Chris Allen ([email protected]) Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm 1 Outline Equivalent noise temperature – Characterization of noise – Noise of a cascaded system – Noise characterization of an attenuator – Equivalent-system noise power at the antenna terminals – Equivalent noise temperature of a superheterodyne receiver Radiometer operation – Effects of gain variations – Dicke radiometer Examples of developed radiometers Synthetic-aperture radiometers 2 Radiometer systems A radiometer is a very sensitive microwave receiver that outputs a voltage, Vout, that is related to the antenna temperature, TA. Based on the output voltage, the radiometer estimates TA with finite uncertainty, T, which is referred to as the radiometer’s sensitivity or radiometric resolution. Radiometric resolution is a key parameter that characterizes the radiometer’s performance. An understanding of the factors affecting radiometer’s performance characteristics requires an understanding of noise, radiometer design, and calibration techniques. 3 Equivalent noise temperature In any conductor with a temperature above absolute zero, the electrons move randomly with their kinetic energy proportional to the temperature T. The randomly moving electrons produce a fluctuating voltage Vn called thermal noise, Johnson noise, or Nyquist noise. Other kinds of noise include quantum noise (related to the discrete nature of electron energy), shot noise (fluctuations due to discrete nature of current flow in electronic devices), and flicker noise (also known as pink noise or 1/f noise) that arises from surface irregularities in cathodes and semiconductors. Thermal noise is characterized with a zero mean, Vn = 0, and is has equal power content at all frequencies, hence it is often called white noise. 4 Equivalent noise temperature For a conductor with resistance R connected to an ideal filter with bandwidth B, the output noise power Pn is Pn k T B where k is Boltzmann’s constant (1.38 10-23 J K-1), T is the absolute temperature (K). The thermal noise power delivered by a noisy resistor at temperature T is found by replacing the noisy resistor with a noise-free resistor and a voltage generator Vrms. The reactance X represents the resistor’s inductive and capacitive aspects. 2 Vrms Vn2 t 4 R k T B 5 Why V2rms = 4 R k T B ? Experimental studies in 1928 by J.B. Johnson and theoretical studies by H. Nyquist of Bell Laboratories showed that the mean-squared voltage from a metallic resistor is Vn2 t 4 R k T B Therefore when attached to a matched load, RL = R, the voltage developed across the load is cut in half (voltage divider) and therefore the mean-squared voltage is reduced by a factor of 4 Open circuit voltage VL2 t R L k T B The power transferred to the matched load is Pn VL2 t RL k T B 6 Is it really white noise Quantum theory shows that the mean square spectral density of thermal noise is G v f 2R h f e h f kT 1 V 2 Hz At “low” frequencies this expression reduces to hf G v f 2 R k T 1 2 k T for f kT h For most applications where To 290 K (63 ºF) [which conveniently simplifies the numerical work as kTo = 4 x 10-21 J] If the resistance is at To then Gv(f) is essentially constant for f 0.1k To h 1012 Hz or 1 THz This conclusion holds even for cryogenic temperatures (T 0.001 To) 7 Equivalent noise temperature Now replace the noisy resistor with an antenna with radiometric antenna temperature TA′. TA′ is the antenna weighted apparent temperature that includes the self-emission of the lossy antenna. If the same average power is delivered into the matched load, then we can relate TA′ to the thermodynamic temperature T of the resistor. 8 Characterization of noise Now consider the added noise of a linear two-port device (e.g., amplifier, filter, attenuator, cable). Input to this device is a signal, Psi, and noise, Pni. Output from this device is a signal, Pso, and noise, Pno. The signal-to-noise ratio, SNR, can be determined at the input as well as the output. SNR in Psi Pni SNR out Pso Pno For an ideal component (e.g., ideal amplifier), the input signal and noise would both be amplified by the same gain resulting in an SNRout = SNRin. However noise sources within the component will cause SNRout < SNRin. 9 Characterization of noise The ratio of SNRin to SNRout is called the noise figure, F. P P F SNR in SNR out si ni Pso Pno Psi Pno 1 G k T0 B Pno F Pso Pni G k T0 B Pno F 1 G k T0 B where T0 is defined to be 290 K. Therefore F 1 and is may be expressed in decibels FdB 10 log 10 F 10 Characterization of noise The noise added by the two-port component, Pno, is Pno (F 1) G k T0 B and the total output noise power, Pno, is Pno G k T0 B (F 1) G k T0 B Pno F G k T0 B F G Pni The two-port device may be treated as an ideal (noise-free) device with an external noise source added to the device’s input. 11 Characterization of noise Alternatively the noise added by the two-port component, Pno, can be expressed in terms of an equivalent input noise temperature, TE, such that Pno (F 1) G k T0 B G k TE B TE (F 1) T0 Therefore if the noise power input to the device is characterized in terms of its noise temperature, TI, then the output noise temperature is TI + TE such that Pno G k TI TE B 12 Characterization of noise 13 Characterization of noise Example cases The NEXRAD (WSR-88D) weather radar has an effective receiver temperature of 450 K. Therefore its receiver noise figure is F=1+TE/T0 so F = 2.55 or 4 dB. The SKYLAB RADSCAT radiometer had a 7.1-dB receiver noise figure. Therefore its effective receiver temperature was TE (F 1) T0 where F = 5.1 so that TE = 1200 K. 14 Noise of a cascaded system Now consider a system composed of two components (systems) in cascade (i.e., connected in series). Assuming B1 = B2, it can be shown that F2 1 F F1 G1 TE 2 TE TE1 G1 15 Noise of a cascaded system So the gain of the first component reduces the impact of the second component’s noise characteristics on the overall system’s noise performance. For a system with N components or subsystems cascaded FN 1 F2 1 F3 1 F F1 G1 G1 G 2 G1 G 2 G N 1 TE TE1 T TEN TE 2 E3 G1 G1 G 2 G1 G 2 G N 1 Clearly if components with “large” gain values are placed nearest the input, their noise characteristics will determine the system’s noise characteristics. 16 Noise characterization of an attenuator Next consider an attenuator with a physical temperature Tp and a loss factor L. L 1 G Pin Pout For L > 1, Pout < Pin. Examples include a lossy cable, a filter with insertion loss, or an RF switch. For L = 1 dB, L =1.26; if L = 1.5 dB, then Pout = 70.8% of Pin The noise figure, F, of an attenuator is F 1 (L 1) TP T0 where T0 = 290 K. If TP = T0, then F = L. Similarly the equivalent temperature is TE (L 1) T0 17 Noise of a cascaded system Example Preamp Limiter Amplifier Given: Assume B = B = B T (atten) = T F1 = 2 G G = 1/L G F F =L F L = 3 dB, F2 = 2 G3 = 30 dB, F3 = 5 Find Fsys for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB 1 P 1 1 2 2 3 0 3 2 3 F2 1 F3 1 Fsys F1 G1 G1 L (a) G1 = 5 dB or 3, (b) G1 = 10 dB or 10, (c) G1 = 30 dB or 1000, Fsys = 2 + (2-1)3 + (5-1)(3/2) = 5 Fsys = 2 + (2-1)10 + (5-1)5 = 2.9 Fsys = 2 + (2-1)1000 + (5-1)500 = 2.01 Therefore, if G1 » L Fsys F1 18 Noise of a cascaded system Example Given: G G = 1/L F F =L F1 = 2, TE1 = 290 K T T L = 3 dB, F2 = 2, TE2 = 290 K G3 = 30 dB, F3 = 5, TE3 = 1160 K Find TE for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB 1 1 E1 2 2 E2 G3 F3 TE3 Assume B1 = B2 = B3 TP (atten) = T0 TE 3 TE 2 TE TE1 G1 G1 L (a) G1 = 5 dB or 3, TE = 290 + 2903 + 1160(3/2) = 1160 K (b) G1 = 10 dB or 10, TE = 290 + 29010 + 11605 = 551 K (c) G1 = 30 dB or 1000, TE = 290 + 2901000 + 1160500 = 293 K Therefore, if G1 » L TE TE1 19 Equivalent-system noise power at the antenna terminals Losses in the antenna (radiation efficiency, l < 1) add noise to the antenna’s output TA l TA 1 l TP And transmission-line losses raise the receiver’s equivalent input noise temperature L 1TP L TREC TREC 20 Equivalent-system noise power at the antenna terminals The overall system input noise temperature, TSYS, is TSYS l TA 1 l TP L 1TP L TREC Assuming the antenna and transmission line are at the same temperature, TP. Recall that TA, the desired parameter, must be estimated from PSYS PSYS k TSYS B Estimation of TA from PSYS requires accuracy and precision Accuracy: conformity of a measured value to its actual value without bias Bias: a systematic deviation of a value from a reference value Precision: ability to produce the same value on repeated independent observations 21 Equivalent-system noise power at the antenna terminals Calibration provides a means to achieve the desired accuracy. A linear transfer function relates Vout to TA′ TA a Vout b Find a and b using two different calibration temperatures, TCAL thus removing any systematic biases. Why is Vout TA′? Isn’t TA′ P instead of V? 22 Equivalent-system noise power at the antenna terminals Vout is the output of a square-law detector ( )2 Vin Vout Vout Vin2 Vout Pin TA Pin so Vout TA 23 Equivalent-system noise power at the antenna terminals Precision relates to T, the radiometric resolution which is the smallest detectable change in TA′. Determination of T requires an understanding of the signal’s statistical properties. Consider the total-power radiometer Total-power radiometer block diagram 24 Equivalent-system noise power at the antenna terminals The total system input noise power is PSYS where k TSYS B PSYS PA PREC and TSYS TA TREC The average power at the IF amplifier output, PIF, is PIF G k TSYS B PIF 25 Equivalent-system noise power at the antenna terminals 26 Equivalent-system noise power at the antenna terminals The instantaneous IF voltage, VIF(t), has the characteristics of thermal noise, i.e., Gaussian probability distribution and a zero mean and standard deviation, while the envelope of VIF(t) has a Rayleigh distribution Ve Ve2 2 e pVe 0 , 22 , for Ve 0 for Ve 0 For a Rayleigh distribution, the mean value of Ve2 is Ve2 2 2 27 Equivalent-system noise power at the antenna terminals After the square-law detector we have Vd = Cd Ve2 where Cd is the power-sensitivity constant of the square-law detector (V W-1) and Vd is the output voltage. Vd Cd PIF Cd G k B TSYS Vd will have an exponential distribution 1 Vd Vd pVd e Vd with the property that the variance of Vd is d, which leads to d / Vd = 1. This is significant since the variance is the uncertainty, so the measured uncertainty = the mean value. 28 Equivalent-system noise power at the antenna terminals So without additional signal processing, a measured value of 250 K would have an uncertainty of ±250 K! (unacceptable) To reduce the measurement uncertainty, multiple independent samples of the signal are averaged. The low-pass filter which acts as an integrator, performs this averaging. Assuming the signal is constant over the averaging interval, the mean value should remain unchanged while the variance is reduced. 2 out d2 1 2 2 Vout Vd B out Vout 1 B Here B is the RF bandwidth and is the integration time (s) constant which is related to the low-pass filter’s bandwidth by BLPF 1/(2 ), Hz. 29 Equivalent-system noise power at the antenna terminals So the ratio of the measurement uncertainty to the measured value is TSYS 1 TSYS B and since TSYS = TA′ + TREC′ TSYS TA TREC B So the measurement uncertainty due to noise processes, TN, is TSYS TN B 30 Equivalent-system noise power at the antenna terminals Besides uncertainties due to noise processes, variations in the receiver gain will also introduce measurement uncertainty, TG. Since Vd = CdG k B TSYS, variations in G will cause variations in the detected signal, Vd. The uncertainty resulting from gain variations is TG TSYS G S GS where GS is the average system power gain and GS is the RMS variation of the power gain. The magnitude of GS can be reduced (though not to 0) by periodically calibrating the radiometer output voltage when inputting a known noise source. 31 Equivalent-system noise power at the antenna terminals The combination of these two uncertainty terms, TN and TG , produce an total uncertainty, T through a root-sumsquare (RSS) process T TN 2 TG 2 or T TSYS 1 G S B GS 2 32 Equivalent-system noise power at the antenna terminals Example Radiometer center frequency, f = 1.4 GHz Bandwidth, B = 100 MHz Receiver noise temperature, TREC′ = 600 K (F = 3 or 4.9 dB) Antenna temperature, TA′ = 300 K Low-pass filter bandwidth, BLPF = 50 Hz ( = 10 ms) System gain, GS = 50 dB ± 0.044 dB over 10 ms interval Find T and determine which factor (noise or gain variation) dominates. 33 Equivalent-system noise power at the antenna terminals Example (cont.) Find TN: TSYS = TREC′ + TA ′ = 600 + 300 = 900 K TN = TSYS (B )- ½ = 900 (108 ·10-2)- ½ = 0.9 K Find TG: GS = 50 dB or 100,000 GS + GS = 50.044 dB or 101,018 GS GS = 49.956 dB or 98,992 so |GS| 1013 GS / GS = 1013/100,000 = 1% TG = TSYS (GS / GS) = 9 K T = [TN2 + TG2] ½ = [(0.9)2 + (9)2]½ = 9.05 K 34 Equivalent-system noise power at the antenna terminals Example (cont.) T = 9.05 K and is dominated by TG (9K) To reduce the affect of TG so that it is comparable to TN requires that GS/GS = 0.001 or G = 100 so that GS = 100,000 ± 100 or GS = 50 dB ± 0.004 dB over a 10 ms interval A study of GS properties shows the following: GS varies as 1/f for f 1 kHz, GS 0 worst for f < 1 Hz Therefore we want < 1 ms to make TG small. However to make TN small we want > 1 ms. 35 Dicke radiometer The Dicke radiometer solves the dilemma concerning . Synchronous switching and detection permits fs > 1 kHz with » 1 ms 36 Dicke radiometer The Dicke radiometer alternates between two configurations, one where it samples the TA′ and the other where it samples a reference load, TREF. When the switch connects the antenna to the receiver , Vd ANT Cd G k B TA TREC for 0 t S 2 When the switch connects the reference load to the receiver , Vd REF Cd G k B TREF TREC for S 2 t S These are combined in the synchronous detector to form 1 The ½ term is due to the dwell Vd SYN Vd ANT Vd REF time in each switch position 2 Vd SYN 1 Cd G k B TA TREF 2 Notice that TREC′ cancels out 37 Dicke radiometer VSYN is integrated in the low-pass filter to yield VOUT VOUT 1 G S TA TREF 2 where GS is a constant representing the radiometer’s transfer characteristics. The low-pass filter not only integrates the signal but also rejects the components at fs and its harmonics that are introduced by the square-wave modulation. This requires that fs 2 BLPF. Under these conditions VOUT (TA′ – TREF) and is independent of TREC′. 38 Dicke radiometer To evaluate the Dicke radiometer’s sensitivity T begin with VOUT 1 TREF TREC G S TA TREC 2 Three components contribute to T Gain variations TG TA TREF GS GS Noise uncertainty in TA′ 2 TA TREC TN ANT B Noise uncertainty in TREF So that T TN REF 2 TREF TREC B TG 2 TN ANT 2 TN REF 2 39 Dicke radiometer Now it might appear that we’re no better off than we were with the total-power radiometer (and maybe worse off with 3 terms comprising T now) T TG 2 TN ANT 2 TN REF 2 However notice the difference in TG total power GS GS TG TA TREC Dicke TG TA TREF GS GS In the Dicke radiometer this term (which dominated T in the total-power radiometer) is significantly smaller. 40 Dicke radiometer Example Bandwidth, B = 100 MHz Low-pass filter bandwidth, BLPF = 0.5 Hz ( = 1 s) Receiver noise temperature, TREC′ = 700 K (F = 3.4 or 5.3 dB) Reference temperature, TREF = 300 K System gain variations, GS/ GS = 1% When viewing a 0-K target (TA′ ~ 0 K) T (total-power) = 7.0 K T (Dicke) = 3.0 K [TG = 7.0 K, TN ANT = 0.07 K] [TG = 3.0 K, TN ANT = 0.1 K, TN REF = 0.14 K] When viewing a 300-K target (TA′ ~ 300 K) T (total-power) = 10.0 K T (Dicke) = 0.2 K [TG = 10.0 K, TN ANT = 0.1 K] [TG = 0.0 K, TN ANT = 0.14 K, TN REF = 0.14 K] (Note that TREF – TA′ = 0, a balanced condition) 41 Balanced Dicke radiometer Operating in a balanced mode requires adjusting TREF. Using a “cold” noise source and a variable attenuator (TP = 290 K) permits balanced mode operation for a wide range of targets. 42 Radiometer calibration As mentioned earlier calibration is needed for accurate measurements. For ground-based systems warm calibration targets are abundant so the cold target calibration poses a challenge. Shown here is a cryoload that is useful for periodic calibration of modestsized antennas. When filled with liquid nitrogen this cold target has a radiometric temperature of around 77 K. 43 Radiometer calibration Another approach that may accommodate modest-sized as well as medium sized antennas is the bucket method that uses the naturally cold sky as a cold target. As seen previously, TSKY is dependent on the operating frequency and on the weather conditions. For clear-sky conditions the zenith sky temperature will range between about 5 and 120 K. Using this calibration technique the antenna efficiency, l, can be estimated. 44 Radiometer calibration Calibration of spaceborne radiometer systems requires features that enable periodic calibration during flight. 45 Scanning Multichannel Microwave Radiometer (SMMR) Flew on two platforms SEASAT (28 June 1978 to 10 October 1978) NIMBUS-7 (26 October 1978 to 20 August 1987) Intended to obtain ocean circulation parameters such as sea surface temperatures, low altitude winds, water vapor and cloud liquid water content on an all-weather basis. Ten channels: five frequencies, dual polarized Mechanically scanned antenna 46 Scanning Multichannel Microwave Radiometer (SMMR) 47 Scanning Multichannel Microwave Radiometer (SMMR) Antenna system • Shared 79-cm diameter offset parabolic reflector used by all channels • Mechanical scanning, 42 off-nadir look angle, ±25 azimuth angle range, scan period 4.096 s • Provided constant 50.3 incidence angle across 780-km swath Offset-fed parabolic reflector geometry 48 Scanning Multichannel Microwave Radiometer (SMMR) Antenna scan characteristics 49 Radiometer antennas Antennas pose a challenge in some radiometer applications. Spatial resolution (x, y) is set by the antenna beamwidth. Consider an antenna with L 20 or = 3. A spot diameter at nadir of 520 m results at aircraft altitudes (10 km). At spacecraft altitudes (700 km) a spot diameter at nadir of 37 km is produced. To achieve a finer resolution requires a smaller beamwidth, i.e., a larger antenna. In addition, mechanical beamsteering limits the scan rate and reliability. 50 Synthetic-aperture radiometers From antenna array theory we know that arraying separate apertures produces a radiation pattern that is the product of the pattern of the individual element and the array pattern. However grating lobes result from large element spacings. Tapers (weighting functions) are used for sidelobe suppression. 51 Synthetic-aperture radiometers The underlying idea of the synthetic-aperture radiometer is that with an array of receiving elements, multiple beams can be formed simultaneously to image a swath. This is accomplished by cross-correlated signals from a pair of antennas with overlapping fields of view. From Ruf CS; Swift CT; Tanner AB; LeVine DM; “Interferometric aperture synthesis,” IEEE Trans. Geoscience and Remote Sensing, 26(5), pp 597-611, 1988. The approximate null-to-null beamwidth () is 2 D , radians Where D is the maximum antenna spacing. 52 Synthetic-aperture radiometers The Electronically Steered Thinned Array Radiometer (ESTAR) is a hybrid which uses real aperture for alongtrack resolution and aperture synthesis for crosstrack resolution. From Elachi C; van Zyl J; Introduction to the physics and techniques of remote sensing, Wiley, 2006. 53 Synthetic-aperture radiometers HYDROSTAR concept For mapping soil moisture and sea salinity 54 Synthetic-aperture radiometers SMOS concept (Soil Moisture and Ocean Salinity) Aperture synthesis in two dimensions 55 SMOS satellite SMOS satellite – 1,451-pound, $464M – launched on 1 Nov 2009 – altitude of 465 miles to 476 miles – inclination of 98.4° SMOS carries as the L-band MIRAS radiometer that uses a Y-shaped antenna resembling the rotors of a helicopter, is a first-of-a-kind payload comprising 69 individual antennas strung together in an inferometer-like array to maximize the sensor's sensitivity. A Rockot launch vehicle blasts off on Nov. 1, 2009 with the Europe's Proba 2 and Soil Moisture Observation Satellite (SMOS) from the Plesetsk Cosmodrome in northern Russia. 56 MIRAS radiometer 3-year mission is to investigate Earth's water cycle – measures soil moisture, 4% accuracy, 30-mile resolution – measures ocean salt concentration, 120-mile resolution Soil moisture is a key factor in determining humidity in the atmosphere and the formation of precipitation. These data will also aid researchers studying plant growth and vegetation distributions. Ocean salinity maps reveal how the atmosphere and oceans interact by providing new insights on ocean circulation, a major driver of world climate. An artist's concept of the Soil and Moisture Observation Satellite (SMOS) satellite with deployed solar arrays and instrument 57 MIRAS radiometer The MIRAS radiometer operates in the L-band of the electromagnetic spectrum in a band (1400-1427 MHz) reserved (by the International Telecommunications Union) for space research, radio astronomy and a radio communication service between Earth stations and space, known as the Earth Exploration Satellite Service. Since its 2009 launch and system check out, project scientists noticed that over certain areas the MIRAS radiometer data were badly contaminated by radio-frequency interference (RFI). The unwanted signals have mainly come from TV transmitters, radio links and networks such as security systems. Terrestrial radars appear to also cause some problems. SMOS data revealed that there were many instances of other signals within this protected band, particularly in southern Europe, Asia, the Middle East and some coastal zones. 58 MIRAS radiometer data Google Earth image March 2010 SMOS image from, over Spain showing contamination by unwanted transmissions from various radio systems. 59 MIRAS radiometer data Google Earth image July 2010 image following cooperation between ESA and the National Spectrum Authority, SMOS data over Spain showing far less RFI contamination. 60 RFI mitigation in radiometers In their paper [1] “RFI detection and mitigation for microwave radiometry with an agile digital detector,” the authors state that: – A new type of radiometer has been developed that incorporates an “agile digital detector” (ADD) – This radiometer is capable of identifying high and low levels of radio frequency interference (RFI) – The effects of this RFI on measured brightness temperature can be reduced or eliminated High-level RFI has a high SNR and a narrow bandwidth • communication source Low-level RFI has a low SNR and a broad bandwidth or is persistent • radar The agile digital detector exploits – Difference of signal probability density function (pdf) • noise Gaussian pdf, sinusoid non-Gaussian pdf – Spectrally localized RFI [1[ Ruf CS; Gross SM; Misra S; “RFI detection and mitigation for microwave radiometry with an agile digital detector,” IEEE Transactions on Geoscience and Remote Sensing, 44 (3), pp. 694-706, 2006. 61 RFI mitigation in radiometers Signal pdf analysis – Conventional radiometers use analog square-law detector 2nd moment – With a digitized waveform the 2nd moment can be computed thus replicating conventional signal processing; but it can also compute the higher-order moments, e.g., 4th moment – The ratio between the 4th moment and the 2nd moment is stable for Gaussian signals and “quite responsive to low-level RFI – Subbands filtering allows isolation of subband containing RFI – Channel crosscorrellation is possible permitting cross-polarization analysis 62 RFI mitigation in radiometers Functional block diagram of ADD signal processor 63 RFI mitigation in radiometers ADD filter bank characteristics Predicted transfer function of ADD filter banks using a Kaiser = 3.2 window with 47 taps and nine-bit signed coefficients. 64 RFI mitigation in radiometers Sample ADD measurement of the pdf of the signal entering the radiometer while viewing a continuous sine wave at 1412 MHz (centered on subband #4) added to background radiometric emission with the antenna pointed toward cold sky. The pdf is shown for four of the eight frequency subbands. ADD measurements over 1 min of the continuous sine wave plus background cold sky scene as above. Brightness temperature is shown versus time for four of the eight frequency subbands. The RFI is centered in subband #4, which exhibits a brightness temperature of ~2000 K. Subband #3 has 50–60K levels of RFI due to the out-of-band rejection limitations of their filters. Subbands #1–2 are essentially RFI free. 65 RFI mitigation in radiometers ADD measurements as before. The normalized ratio between the fourth moment and the square of the second moment of the signal is shown for four of the eight frequency subbands. A normalized ratio of unity indicates that the signal has a Gaussian distributed amplitude consistent with natural thermal emission. The ratio for subband #4 is approximately 0.6 due to the strong sine wave present. Subband #3 also has small nonunity ratios as a result of the RFI. The other subbands are RFI free. Note the scale change for subbands #3–4. 66