I. What Is Forensic Interpretation?

Three Pillars of Audio Forensics

• Authentication — objective measurement
• Enhancement — partly subjective processing
• Interpretation — objective + subjective judgment

The Interpretation Challenge

• Strives for objectivity
• Relies on examiner experience
• Requires induction and contextual reasoning
• Findings may influence legal outcomes

Discussion

• Where is the line between objective measurement and subjective interpretation?
• Can forensic audio ever be fully objective? Should it try to be?
• How should an expert communicate uncertainty to a jury?

II. Scientific Integrity

Transparency and Reproducibility

• Methods must be explainable
• Results must be verifiable by others
• No “black box” or proprietary claims

Ethical Concerns

• Reject claims of “golden ears”
• No secret analytical techniques
• Lack of transparency undermines the field

The NAS Report (2009)

Strengthening Forensic Science in the United States: A Path Forward

https://www.ojp.gov/pdffiles1/nij/grants/228091.pdf

NAS: Two Key Questions

• Is the method scientifically valid and reliable?
• How much depends on subjective judgment?

Discussion

• Have you encountered “black box” claims in other forensic fields?
• How does cognitive bias affect forensic analysis?
• What safeguards could reduce bias in audio forensics?

III. Measurement Fundamentals

Four Measurement Domains

• Time — when events occur
• Frequency — pitch and spectral content
• Amplitude — loudness and signal level
• Spectrum — frequency distribution over time

Precision vs. Accuracy

• Precision — repeatability and resolution
• Accuracy — correctness relative to a standard

Discussion

• Why is it important to distinguish precision from accuracy in court testimony?
• What happens if you report a precise measurement that isn’t accurate?
• How would you explain measurement uncertainty to a non-technical jury?

IV. Case Study: Gunshot Localization

The Scenario

• Two police cruisers record gunshots
• Key questions:
  • Where did the shots originate?
  • Same or different firearm(s)?

TDOA: The Core Idea

• Sound travels at a known speed
• Different distances = different arrival times
• Time difference → distance difference

Speed of Sound

$$c = 331.45\sqrt{1 + \frac{T}{273}}$$

• c = speed of sound (m/s)
• T = temperature in Celsius
• ~343 m/s at 20°C

https://www.omnicalculator.com/physics/speed-of-sound

The Hyperbolic Locus

• Two receivers → one TDOA measurement
• Defines a hyperbola of possible locations
• Source lies somewhere on that curve

Multilateration

• Third receiver → second hyperbola
• Intersection = source location
• More receivers → more confidence

Sources of Uncertainty

• Unsynchronized recordings
• Vehicle position estimation errors
• Speed of sound variability
• Event alignment ambiguity

Gunshot Acoustic Components

• Muzzle blast — spherical propagation
• Ballistic shockwave — conical “N-wave”
• Mach angle: $\theta = \arcsin\left(\frac{c}{v}\right)$

Discussion

• Why is multilateration preferred over triangulation for gunshot localization?
• What real-world factors would make TDOA unreliable in an urban setting?
• How would you explain a hyperbolic locus to a jury?

V. Case Study: Doppler Effect

The Scenario

• 911 call captures a truck horn before a crash
• Can we determine the truck’s speed?

Doppler Effect

• Approaching source → higher frequency
• Receding source → lower frequency
• Frequency shift reveals velocity

The Doppler Equation

$$f = f_0 \cdot \frac{c}{c - v}$$

• f = observed frequency
• f₀ = source frequency at rest
• c = speed of sound
• v = source velocity

Solving the Case

• Horn at rest: 295 Hz
• Observed in recording: 329 Hz
• Temperature: 17°C → c = 341.5 m/s
• Result: ~35.3 m/s ≈ 79 mph

Sources of Uncertainty

• Frequency estimation accuracy
• Sampling rate errors
• Air temperature variation
• Non-radial motion (angle of approach)

Discussion

• How would a 2.4% sampling rate error affect a court case about speeding?
• What other scenarios could Doppler analysis help investigate?
• Why must the approach angle be considered?

VI. Case Study: Distance Estimation

The Scenario

• Dispute over distance of a shouted threat
• Competing claims: 1 meter vs. 8+ meters
• Recording exists from a consumer device

Spherical Spreading Law

• Sound intensity follows inverse square law
• ~6 dB loss per doubling of distance
• 1 m to 8 m ≈ 18 dB difference

Complicating Factors

• Unknown vocal intensity
• Microphone characteristics
• Automatic Gain Control (AGC)
• Reflections and reverberation

Recommended Approach

• Controlled reconstruction experiment
• Same device, same location
• Documented procedure (video)
• Compare reconstruction to original

Discussion

• Why can’t we simply measure the recorded volume to determine distance?
• When might a reconstruction experiment not be feasible?
• How should an expert present inconclusive distance findings?

VII. Likelihood Ratios

The Concept

$$LR = \frac{P(\text{evidence} \mid H_p)}{P(\text{evidence} \mid H_d)}$$

• H_p = prosecution hypothesis
• H_d = defense hypothesis

DNA as the Benchmark

• Highly discriminative patterns
• Quantifiable probabilities
• LRs in the quadrillions

Application to Audio

• Possible but difficult
• Speech signals are inherently variable
• Dependent on recording conditions
• Limited statistical models

Challenges

• Estimating probability of a match
• Building relevant population databases
• Variability in recording conditions
• Limited adoption in practice

Discussion

• Why are likelihood ratios preferable to “match/no match” conclusions?
• What makes audio LRs harder than DNA LRs?
• How might an expert explain a likelihood ratio to a jury?