1. Audio Processing for Detector Characterization at 40 m lab SURF 2016 LIGO-T1600199
Varun Kelkar
Mentors: Eric Quintero and Rana Adhikari
California Institute of Technology
LIGO Project, MS Pasadena, CA 91125

2. Objective
To develop a generic audio processing block in order to implement various real time audio processing algorithms on various interferometer signals.
To integrate these audio processing algorithms into the existing system and to control them via an MEDM graphical user interface.

3. The Real Time Control System
Includes the following models used for controlling the interferometer.
Length sensing and Control System (LSC)
Physical Environment monitoring system (PEM)
Seismic Isolation System (SEI)
Angular Sensing and Control System (ASC)
The real time control system is a sensing and control system, which consists of various sensors, like seismometers, accelerometers, length and angular sensing systems, which give analog output, which are then digitized, go into the digital domain. They then undergo various signal processing algos, and various feedback and feedforward control signals are produced, which are then converted to analog and applied to actuators controlling the motion of test masses.
LSC is basically the length sensing and control system measuring the differential/common arm lengths, lengths of various cavities, etc.
The PEM consists of the seismic and the accelerometer signals, which then go the the suspensions for noise cancelling.
Angular sensing and control measures and processes the pitch, yaw, etc of various test masses.

4. Offline Implementation of Audio Processing Algorithms
Automatic Gain Control
Giving suitable gain to the signal in order to adjust to the signal power to a suitable level.
Frequency Shifting
Shifts frequency in linear scale.
Achieved using heterodyning.
Pitch Shifting/Frequency warping
Shifts frequency in the logarithmic scale.
Achieved using phase vocoder and then resampling.

5. Offline Implementation of Audio Processing Algorithms
Automatic Gain Control
Giving suitable gain to the signal in order to adjust to the signal power to a suitable level.
Input: 𝑥 𝑛 Output: 𝑦 𝑛 Frame Length: 𝑚
𝑃 𝑖𝑛 = 1 𝑚 𝑖=0 𝑚 𝑥 2 [𝑖]
𝐺 = 𝑃 0 𝑃 𝑖𝑛
𝑦[𝑛] = 𝐺𝑥[𝑛]
It will calculate appropriate gain to be given based on the input power.

6. Offline Implementation of Audio Processing Algorithms
Frequency Shifting
Shifts frequency in linear scale.
Achieved using heterodyning.
Input: 𝑥 𝑛 Output: 𝑦 𝑛
𝑦 𝑛 =𝑐𝑜𝑠 𝜔 𝑚 𝑛 𝐹 𝑠 𝑥[𝑛]
In frequency domain:
𝑌 𝜔 = 𝑋 𝜔 − 𝜔 𝑚 + 𝑋 𝜔 + 𝜔 𝑚
This is achieved by heterodyning. Multiplication by a sinusoid shifts the signal frequencies two ways: up by omega m and down by omega m. one of them is then filtered off to give the required freq.

7. Offline Implementation of Audio Processing Algorithms
Pitch Shifting/Frequency warping
Shifts frequency in the logarithmic scale.
Achieved using phase vocoder and then resampling.
Phase Vocoder:
X and Y : DFTs of input and output respectively.
𝑌 𝑖 𝑘 = 𝑋 𝑟𝑖 𝑘
∠ 𝑌 𝑖 [𝑘]=∠ 𝑋 0 [𝑘] + 2𝜋𝑖ℎ 𝑘 𝑚
Phase vocoder changes the time duration without changing the pitch.
Resampling then brings back the time duration and changes the pitch.

8. Online Implementation of Audio Processing Algorithms
1) LSC Control Signals
2) LSC Photodiode Signals
3) PEM (Environmental) Signals
(Seismometer, Accelerometer)
DAFI INPUT MATRIX
AGC
FREQ SHIFT
ARB. MATH
FREQ WARP
CUSTOM
MATRIX 2_L
MATRIX 1_L
MATRIX 2_R
MATRIX 1_R
LEFT DAFI OUTPUT MATRIX
RIGHT DAFI OUTPUT MATRIX
DAC
FIBOX
LEFT
RIGHT
Through 1 IPC link for each block
INPUTS
Fig. 1: DAFI Signal Flow

9. MEDM GUI for the DAFI Block
Add the latest screenshots of the DAFI block
Fig. 2: MEDM GUI for DAF block

10. Inputs
Signals from Seismometers, Accelerometers, LSC Control Signals, LSC Photodiode signals.
Add the latest screenshots of the DAFI block
Fig. 3: Inputs to the DAF block

11. Online Implementation of Audio Processing Algorithms
Automatic Gain Control
Fig. 4: AGC input and output

12. Online Implementation of Audio Processing Algorithms
Frequency Shifting
Fig. 5: AGC + frequency shifting: input and output

13. Online Implementation of Audio Processing Algorithms
Frequency Warping
The DFT of a frame 𝑥 𝑖 𝑛 is given by
𝑋 𝑖 𝑘 = 𝑛=0 𝑚−1 𝑥 𝑖 𝑛 𝑒 −𝑗2𝜋 𝑘𝑛 𝑚
A matrix W containing all 𝑒 −𝑗2𝜋 𝑘𝑛 𝑚 is predefined in the code.
DFT and iDFT coefficients are calculated cumulatively in each cycle to distribute the computational load.

14. Summary
Offline and online implementation of various real-time audio processing algorithms, in order to create audio for meaningful noise hunting.
Integration with the existing system, with collection of inputs from various environmental and LSC photodiode sensors as well as control signals.

15. References
Fitzgerald J. Archibald, “Software Implementation of Automatic Gain Controller for Speech Signal”, Texas Instruments, white paper SPRAAL1 July 2008
D. Shoemaker, “Detector Subsystems Requirements.” LIGO Document Control Center LIGO-E
“Digital Up and Down Conversion for Family Radio Service”, Math-Works Documentation down-conversion-for-family-radio-service.html
Mark Dolson, “The phase vocoder: A tutorial”, Computer Music Journal, vol. 10, no. 4, pp , 1986.
Sundance Systems, Inc. Fibox Digital Fiber-Optic Audio Transmission System: FBAI-M sl.pdf