Jeffrey Hilton Miles and Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

Application of an Aligned and Unaligned Signal 

Processing Technique to Investigate Tones and 

Broadband Noise in Fan and Contra-Rotating 

Open Rotor Acoustic Spectra

NASA/TM—2015-218865

September 2015

ISABE-2015-20243
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Jeffrey Hilton Miles and Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

Application of an Aligned and Unaligned Signal 

Processing Technique to Investigate Tones and 

Broadband Noise in Fan and Contra-Rotating 

Open Rotor Acoustic Spectra

NASA/TM—2015-218865

September 2015

ISABE-2015-20243

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

22nd International Symposium on Air Breathing Engines (ISABE 2015) 

sponsored by the International Society for Air Breathing Engines

Phoenix, Arizona, October 25–30, 2015
Acknowledgments

The NASA Advanced Air Vehicles Program, Advanced Air Transport Technology Project, supported the current work. The open 

rotor data was obtained under a previous effort supported by the NASA Environmentally Responsible Aviation Project (ERA) 

of the Integrated Systems Research Program in collaboration with GE Aviation. Dr. David B. Stephens is thanked for providing 

the data for the redrawing of previous fi gures and many helpful discussions about his work. Due to the unexpected passing of 

Dr. Jeffrey Hilton Miles, Dr. Lennart S. Hultgren completed this paper.

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This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
Application of an Aligned and Unaligned Signal Processing 

Technique to Investigate Tones and Broadband Noise in 

Fan and Contra-Rotating Open Rotor Acoustic Spectra 

Jeffrey Hilton Miles and Lennart S. Hultgren 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The study of noise from a two-shaft contra-rotating open rotor (CROR) is challenging since the shafts 

are not phase locked in most cases. Consequently, phase averaging of the acoustic data keyed to a single 

shaft rotation speed is not meaningful. An unaligned spectrum procedure that was developed to estimate a 

signal coherence threshold and reveal concealed spectral lines in turbofan engine combustion noise is 

applied to fan and CROR acoustic data in this paper. 

Introduction 

Interest has been growing in using contra-rotating open rotor (CROR) engines for aircraft propulsion 

since they are estimated to burn less fuel than equivalent thrust turbofans (Ref. 1). CRORs are complex 

aeroacoustic systems which produce tonal and broadband noise. The determination of tonal and 

broadband noise components from a total noise signature obtained during testing is an important aspect 

when studying aircraft noise control parameters and also when validating aircraft noise prediction codes 

(Refs. 2 to 7). The current status of aircraft turbomachinery aeroacoustics, in general, is discussed in 

Peake and Parry (Ref. 8) and the aeroacoustics of CROR systems is discussed in Soulat, Kernemp, 

Sanjose, and Moreau (Ref. 7) and Rossikhin, Brailko and Mileshin (Ref. 9). 

Fan tones from a single set of rotating blade rows on a single shaft can be studied using phase 

averaging keyed to the shaft rotation speed. This procedure removes the parts of the signal unrelated to 

the rotation rate. Studying noise from a two-shaft CROR is more challenging since the two shafts are not, 

in many cases, phase locked. Hence, a need exists to develop effective methods of analyzing CROR 

noise. A signal processing technique for separating tonal and broadband noise components from CROR 

data was developed by Sree (Ref. 10) and was applied by Sree and Stephens (Ref. 11) to wind-tunnel 

CROR data obtained at the NASA Glenn Research Center. In addition, this same data set was processed 

using a two-shaft Vold-Kalman order-tracking filter by Stephens and Vold (Ref. 12). 

The present paper describes a simple procedure to calculate the tonal components of the noise spectra 

from CROR tests. The tonal frequencies are identified using the unaligned spectrum procedure discussed 

by Miles (Refs. 13 and 14). The broadband noise is then obtained by removing the now identified tonal 

content from the original aligned spectra. 

Acoustic Data 

The acoustic data used herein are from two rig tests conducted in the NASA Glenn Research Center 

9- by 15-ft Low Speed Wind Tunnel (Ref. 15). The first set is a baseline test case from the NASA fan 

trailing edge blowing experiment (Ref. 16). This test campaign used a single-shaft modular fan stage in a 

nacelle with 18 rotor blades and 45 radial stator vanes in order to evaluate exit-guide-vane-noise 

reduction by filling in fan wakes. The baseline setup used a fan (Fan 1) without blowing capability and 

thus represented a typical turbofan stage. The acoustic data used herein was measured at a sideline angle 

of 75.1° for approach conditions (microphone location 30; reading 2338). 

NASA/TM—2015-218865 1
The second set of measurements covers some of the ones used by Sree and Stephens (Ref. 11) and 

Stephens and Vold (Ref. 12). It is from a CROR test that used a baseline, vintage 1990s, blade design, 

known as F31/A31, whose aerodynamic and acoustic data can be disseminated (Refs. 17 and 18). The test 

program was conducted by NASA in collaboration with GE Aviation. The F31/A31 blade set consists of 12 

front rotor blades and 10 aft rotor blades. Data obtained using this two-shaft blade set is discussed by Sree 

and Stephens (Ref. 11),Stephens and Vold (Ref. 12), Elliott (Ref. 17), Stephens (Ref. 18), Stephens and 

Envia (Ref. 19), and Horvath, Envia, and Podboy (Ref. 20). The two shafts are nominally rotating at the 

same speed, but they are not phase locked. Sideline acoustic measurements at 90° (microphone location 8, 

readings 470 and 472, Escort program D074), corresponding to takeoff conditions, were used here. 

Uncertainty in the sideline acoustic measurements is estimated to be 1 dB (Ref. 21). 

Data Processing Procedure 

Only a brief description of the aligned/unaligned method is given here. More details can be found in 

papers by Miles (Refs. 13 and 14). 

Aligned and Unaligned Spectra 

All the spectra and cross-spectra are estimated using Welch’s non-parametric method which is based 

on averaging multiple windowed periodograms using overlapping time sequences (Ref. 22). In this 

procedure the time history is divided into segments. The segment size or length, N, depends on the 

desired bandwidth resolution, ∆f, given by ∆f = rs/N, where rs is the sampling rate. To get the aligned 

spectrum, Ga(f), the time history is duplicated and the cross-spectrum is calculated, i.e., an aligned autospectrum (real and positive definite) is actually calculated. To get the deliberately unaligned spectrum, 

|Gu(f)|, the second time history is shifted/displaced at least one segment length and the cross-spectrum is 

calculated. The unaligned spectrum is the magnitude of this (complex) cross-spectrum and contains only 

tones and random noise. These tones are present in each of the unmatched segments used to calculate the 

deliberately unaligned spectrum. All the other spectral values are averaged to smaller and smaller values 

by the calculation procedure. The spectral estimation parameters are shown in Table 1. 

By varying the time displacement, it was observed that the major unaligned tones largely remained 

unchanged. However, minor tones showed a slight magnitude variation depending on the displacement. 

Consequently, the unaligned tonal amplitudes depend weakly on the displacement factor used in the data 

processing procedure. This is believed to be a consequence of shaft rpm drifts. 

The results presented herein were, in general, calculated using a deliberate unalignment time shift 

with a displacement factor of unity. Consequently, the number of displacement points was 16 384 

corresponding to 0.08192 s. Thus one time history was made shorter by removing the first 0.08192 s 

before calculating the cross spectrum. 

Unaligned Magnitude-Squared Coherence 

For the case considered herein, where the two signals are simply related by a time shift, the usual 

magnitude-squared coherence (MSC) function reduces to 

γ2 = |Gu(f)|2 ⁄ Ga(f)2, (1) 

which, from now on, will be referred to as the unaligned magnitude-squared coherence (UMSC). 

Theoretically the UMSC ranges from zero to unity. A value of zero at a particular frequency would 

indicate the signal and the displaced signal are uncorrelated while a value of unity would signify that the 

two signals are perfectly correlated. However, the time series used are finite. Consequently, the UMSC

will never be zero. Instead, a UMSC threshold value, ε2

, is calculated from (Refs. 13 and 14) 

NASA/TM—2015-218865 2
ε2

 = 1 − (1 − P)

1/(M−1) , (2)

where 0 ≤ P ≤ 1 is the confidence interval and M is the number of independent sets. If the computed 

UMSC falls below this value at certain frequencies then the two signals are uncorrelated at those 

frequencies with a confidence level P. P = 0.95 is used herein, which corresponds to ε2 = 0.00824. 

Broadband and Tonal Noise Spectra 

A common practice to determine the broadband noise spectrum is to set the aligned tones to zero and 

use a multi-point average to interpolate the missing values. This procedure is not very exact since the 

decision of which spectrum point is or is not a tone is not well defined. This ad hoc procedure can be 

improved by selecting the tones to be set to zero based on their UMSC value. For example, replacing only 

tones with computed UMSC values larger than the 95 percent confidence-level threshold value, obtained 

from Equation (2), then using a multi-point averaging technique, leads to a well-defined process that can 

easily be automated. Here, the four nearest non-tonal spectral values are used. The dominant tonal spectrum 

can then be obtained by subtracting this broadband spectrum from the original aligned spectrum. 

Results 

A comparison to existing results (Ref. 11) for the simpler single-shaft fan-stage configuration is 

discussed first. This includes a comparison to phase-averaged results (generally considered the gold 

standard in this case) as well as Sree-method (Ref. 10) results. Using the insights from these comparisons, 

two-shaft CROR data is then analyzed and compared to existing results (Refs. 11 and 12). 

Single-Shaft Fan Stage

Figure 1(a) shows aligned (black) and unaligned (red and magenta) fan sound pressure level (SPL) 

spectra, normalized to 1 Hz bin width, for frequencies up to10 kHz. The red curve shows the thresholdlimited unaligned spectrum, where computed values less than εGa(f) have been replaced by this limit 

value. The magenta curve shows the unaligned spectrum result without applying this lower bound. 

Figure 1(a) shows that the broadband noise is clearly absent in the deliberately unaligned spectrum. In 

general, if they are large enough, the tones in the unaligned spectrum appear as tones in the aligned 

spectrum at the identical frequency. However, the tones in the unaligned spectrum are generally lower 

than the corresponding tones in the aligned spectrum, occasionally by as much as 3 dB. This loss of tonal 

energy is believed to be caused by shaft rpm drift since it is more pronounced for higher harmonics. Note 

that the deliberately unaligned spectrum also identifies tones that are masked by broadband noise. For the 

subdominant tones, the current method is expected to correctly determine tonal frequencies, while likely 

underestimating the magnitudes.

Figure 1(b) shows the computed UMSC for the 0 to 10 kHz frequency range using a logarithmic scale 

on the vertical axis. The magenta line indicates the 95 percent confidence level threshold curve (M = 363; 

50 percent segment overlap). If a point falls below the coherence threshold value, the unaligned signals 

are independent at that frequency. 

Figure 2 compares the current tonal (red) and broadband (blue) spectra with the corresponding results 

obtained by Sree and Stephens (Ref. 11). Panel 2(a) shows the current results obtained by using the 

UMSC threshold criteria for the tones and the multi-point averaging technique for the broadband signature 

as described above. Panels 2(b) and (c) are replots of the results obtained by Sree and Stephens (Ref. 11). 

Panel 2(b) is their phase-averaged result (Fig. 3, Ref. 11) and Panel 2(c) is their Sree-method result 

(Fig. 4, Ref. 11). Good agreement (< 1 dB difference on the strongest tones) with their results 

(particularly the phase-averaged ones) is shown. 

NASA/TM—2015-218865 3
Contra-Rotating Open Rotor 

Figure 3(a) shows aligned (black) and unaligned (red and magenta) CROR sound pressure level 

(SPL) spectra, normalized to 1 Hz bin width, versus frequency for reading 470. Again, the red curve 

shows the threshold-limited unaligned spectrum, where computed values have been limited from below 

by εGa(f), and the magenta curve shows the unlimited result. Figure 3(b) shows the corresponding UMSC

results. Apart from the much richer tonal structure, a striking difference, when comparing the CROR 

Figure 3(a) with the corresponding singe-shaft fan Figure 1(a), is the much larger tonal-amplitude 

reduction between the aligned (black) and unaligned (red) spectra for the CROR. This is particularly so 

for the interaction tones at shaft orders 32, 34, and 42 (these three tones are also the overall strongest 

tones in the aligned spectra). However, the corresponding reduction for the (fundamental) aft and front 

rotor blade-passing frequencies (shaft order 10 and 12) are within 1 and 2 dB, respectively. These two 

observations support the previous inference that the difference in tonal energy between the two spectra is 

due to rpm drifts, which are larger for the CROR (20 rpm) than for the single shaft fan (3 rpm). In 

addition, even though the rpm drifts for the two CROR shafts somewhat track each other, they are not in 

sync, see Appendix. 

Figure 4 shows CROR tonal (red) and broadband (blue) spectra for reading 470. Panels 4(a) and 4(b) 

show the current results with a dealignment of one, and one and a half windows, respectively. Due to the 

loss of tonal energy in the unaligned spectra, it can be seen that certain, but mainly different, tones have 

been misidentified as broadband in these two examples. However, a good result can be obtained by using 

information based on more than one displacement case. If the UMSC value in at least one case is above 

the threshold value, then there is a tone at that particular frequency. The results in Panel 4(c) are obtained 

by using the computed UMSC from both of the displacement cases shown in Panels 4(a) and 4(b). 

Panel 4(d) is a replot of existing Sree-method results (Fig. 6, Ref. 11). The spectra in Panels 4(c) and 4(d) 

agree quite well. 

Figure 5 compares the current tonal (red) and broadband (blue) spectra with the corresponding results 

obtained by Stephens and Vold (Ref. 12). Panel 5(a) shows the current results obtained by using a single 

displacement of one window length. Panel 5(b) shows the results when applying the UMSC threshold 

criteria using multiple displacement factors (1, 1.5, and 2). Clearly, using multiple displacements 

improves the tone detection. The most significant frequency range (up to shaft order 80) (Ref. 11) is well 

resolved in Panel 5(b). Panels 5(c) and (d) are replots of the results obtained by Stephens and Vold 

(Ref. 12). Panel 5(c) shows their moving-median and modified moving-median (peak-finding) results 

(Fig. 6(a), Ref. 12) and Panel 5(d) is their Vold-Kalman-filter results (Fig. 9(b), Ref 12). The results 

shown in Panels 5(b) to (d) are in good agreement. 

Concluding Remarks 

Special signal processing tools are needed to characterize open rotor acoustics. The aligned/unaligned 

signal processing technique has been applied to fan and counter-rotating open rotor acoustic data. The 

method offers an effective means of identifying tones in the acoustic data. It will not only detect 

dominant tones but also tones that may be masked by broadband noise. The use of this method, in 

combination with magnitude-squared coherence threshold values, leads to a well defined, easily 

implemented, and effective procedure for extracting, in turn, the broadband and dominant tonal spectra 

from complex experimental acoustic data sets. 

NASA/TM—2015-218865 4
Appendix—Shaft-Speed Variation 

Figure 6 shows the shaft-speed deviations, normalized by the mean rotation rate, as a function of 

data-segment count (groups of 16 384 samples) as well as time for (a) the single-shaft fan stage, and (b) 

and (c) the two CROR cases, respectively. In all these panels, the blue lines indicate plus and minus one 

root-mean-square, r.m.s., deviation of the data. Panel 6(a) shows that the shaft speed is controlled to 

within 0.05 percent (about 3 rpm) for the single-shaft case. 

Panels 6(b) and 6(c) are for the CROR readings 470 and 472, respectively. The black and green 

curves denote the front- and aft-rotor shafts, respectively. As can be seen in both these panels, even 

though the shaft-rotation rate excursions for the front and aft rotors somewhat trace each other, they are 

not synchronized. For reading 470, the deviations are within 0.3 percent (about 20 rpm), and for reading 

472, they are within 0.23 percent (about 15 rpm). 

 

NASA/TM—2015-218865 5
References 

1. Guynn, M. D., Berton, J. J., Hendricks, E. S., Tong, M. T., Haller, W. J., and Thurman, D. R., “Initial 

Assessment of Open Rotor Propulsion Applied to an Advanced Single-Aisle Aircraft,” AIAA-2011-

7058, September 2011. 

2. Magliozzi, B., Hanson, D. B., and Amiet, R. K., “Propeller and Propfan Noise,” Aeroacoustics of 

Flight Vehicles: Theory and Practice, edited by H. H. Hubbard, .Chapter 1, NASA Reference 

Publication 1258, Vol. 1; WRDC Technical Report 90-3052, 1991, pp. 1–64. 

3. Blandeau, V. P. and Joseph, P. F., “BroadbandNoise Due to Rotor-Wake/Rotor Interaction in ContraRotating Open Rotors,” AIAA Journal, Vol. 48 (11), November 2010, pp. 2674–2686. 

4. Roger, M., Schram, C., and Moreau, S., “On Open Rotor Blade-Vortex Interaction Noise,” 

AIAA-2012-2216, June 2012. 

5. Sharma, A. and Chen, H., “Prediction of Tonal Aerodynamic Noise from Open Rotors,” 

AIAA-2012-2265, June 2012. 

6. Kingan, M. J., “Open Rotor Broadband Interaction Noise,” AIAA-2012-2304, June 2012. 

7. Soulat, L., Kernemp, I., Sanjose, M., and Moreau, S., “Assessment an comparison of tonal noise 

models for Counter-Rotating Open Rotors,” AIAA-2013-2201, May 2013. 

8. Peake, N. and Parry, A. B., “Modern Challenges Facing Turbomachinery Acoustics,” Annual Review 

of Fluid Mechanics, Vol. 44, 2012, pp. 227–248. 

9. Rosikhin, A. A., Brailko, I. A., and Mileshin, V. I., “Numerical investigation of tonal noise of counterrotating open rotors,” International Journal of Aeroacoustics, Vol. 13 No. 3&4, 2014, pp. 303–320.

10. Sree, D., “A novel signal processing technique for separating tonal and broadband noise components 

from counter-rotating open-rotor acoustic data,” International Journal of Aeroacoustics, Vol. 12 (1+2), 

2013, pp. 169–188. 

11. Sree, D. and Stephens, D. B., “Tone and Broadband Noise Separation from Acoustic Data of a ScaleModel Contra-Rotating Open Rotor,” AIAA-2014-2744, June 2014. 

12. Stephens, D. B. and Vold, Håvard, “Order tracking signal processing for open rotor acoustics,” 

Journal of Sound and Vibration, Vol. 333, 2014, pp. 3818-3830. 

13. Miles, J. H., “Aligned and Unaligned Coherence: A New Diagnostic Tool,” Tech. Rep. AIAA-2006-

0010, AIAA, 2006, Presented at the 44th AIAA Aerospace Science Meeting, 9-12 Jan 2006 Reno 

Hilton Reno, Nevada, also NASA/TM—2006-214112. 

14. Miles, J. H., “Estimation of signal coherence threshold and concealed spectral lines applied to 

detection of turbofan engine combustion noise,” The Journal of the Acoustical Society of America, 

Vol. 129 No. 5, May 2011, pp. 3068–3081. 

15. Arrington, E. A. and Gonsalez, J. C., “Flow Quality Improvements in the NASA Lewis Research 

Center 9- by 15-Foot Low Speed Wind Tunnel,” AIAA-1995-2390, July 1995. 

16. Fite, E. B., Woodward, R. P., and Podboy, G. G., “Effect of Trailing Edge Flow Injection on Fan 

Noise and Aerodynamic Performance,” AIAA-2006-2844, 2006. 

17. Elliott, D. M., “Initial Investigation of the Acoustics of a Counter Rotating Open Rotor Model With 

Historical Baseline Blades in a Low Speed Wind Tunnel,” AIAA-2011-2760, June 2011. 

18. Stephens, D. B., “Nearfield Unsteady Pressures at Cruise Mach Numbers for a Model Scale CounterRotation Open Rotor,” AIAA-2012-2264, June 2012. 

19. Stephens, D. B. and Envia, E., “Acoustic Shielding for a Model Scale Counter-rotation Open Rotor,” 

AIAA-2011-2940; also NASA TM—2012-217227, 2011. 

 

NASA/TM—2015-218865 6
20. Horvath, C., Envia, E., and Podboy, G. G., “Limitations of Phased Array Beamforming in Open Rotor 

Noise Source Imaging,” AIAA-2013-2098, May 2013. 

21. Envia, E., Tweedt, D. L., Woodward, R. P., Elliot, D. M., Fite, E. B., Hughes, C. E., Podboy, G. G. and 

Sutliff, D. L., “Fan Noise Prediction,” in Assessment of NASA’s Aircraft Noise Prediction Capabiliy,”

editor Dahl, M. D., NASA TP—2012-215653, 2012, pp. 115-156. 

22. Welch, P. D., “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method 

Based on Time Averaging Over Short, Modified Periodograms, “IEEE Trans-actions on audio and 

electroacoustics, Vol. AU-15 No.2, June 1967, pp. 70–73. 

NASA/TM—2015-218865 7
TABLE 1.—SPECTRAL ESTIMATION PARAMETERS 

Parameter Value 

Sample rate, rs, samples/s 200 000 

Segment length, N, samples 16 384 

Segment length, Td = N/rs, s 0.08192 

Bandwidth resolution, Δf = 1/Td, Hz 12.2 

Overlap 0.50 

Data window type Hamming 

Total sample length, Ttotal, s 15 

Displacement shift in samples, 1×N 16 384 

Displacement shift, s 0.08192 

Number of independent sets, M 363 

UMSC threshold (95%), ε2 0.00824 

Figure 1.—Single-shaft fan results: (a) – aligned (black) and 

unaligned (red, threshold-limited, and magenta) 1 Hz normalized 

SPL; (b) – UMSC (black) and threshold value (magenta). 

NASA/TM—2015-218865 8
Figure 2.—Single-shaft fan tonal (red) and broadband (blue) 1 Hz normalized SPL: (a) – current aligned/unaligned m

(b) – phased averaged results (Ref. 11); (c) – Sree’s method (Ref. 11). 

NASA/TM—2015-218865 9
Figure 3.—CROR (reading 470) results: (a) – aligned (black) 

and unaligned (red, threshold-limited, and magenta) 1 Hz 

normalized SPL; (b) – UMSC (black) and threshold value 

(magenta). 

NASA/TM—2015-218865 10
Figure 4.—CROR (reading 470) tonal (red) and broadband (blue) SPL spectra: current aligned/unaligned method using 

(a) – 1 window offset; (b) – 1.5 window offset; (c) – both 1 and 1.5 window offsets; and (d) – Sree’s method (Ref. 11)

NASA/TM—2015-218865 11
Figure 5.—CROR (reading 472) tonal (red), broadband (blue and green), and total (black) SPL spectra: current 

aligned/unaligned method using (a) – 1 window offset; (b) – 1, 1.5 and 2 window offsets; (c) – moving-median result(Ref. 12); and (d) – Vold-Kalman filtering (Ref. 12). 

NASA/TM—2015-218865 12
Figure 6.—Normalized shaft-speed deviations versus data-segment count and time, blue lines indicate plus/minus 

one r.m.s. deviation: (a) – single-shaft fan stage; (b) – CROR reading 470 front (black) and aft (green) rotor; 

(c) – CROR reading 472 front (black) and aft (green) rotor. 

NASA/TM—2015-218865 13