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Digital Audio Watermarking: Properties, characteristics of audio signals, and measuring the
performance of a watermarking system
نيما خادمي کالنتريEmail: [email protected]
Properties (1)Inaudibility
◦ Similarity between the original and watermarked signal
Robustness◦ Ability to detect the watermark after common
signal processing and malicious attacksData Payload
◦ The number of embedded bits per second
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Properties (2)Statistical invisibility
◦ Performing statistical tests on a set of watermarked files should not reveal any information about the nature of the embedded information, nor about the technique used for watermarking
Redundancy◦ To ensure robustness the watermark information is
embedded in multiple places on audio file
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Different types of watermarksRobust
◦ Watermarks that are robust against attacksFragile
◦ Have only very limited robustnessSemi-Fragile
◦ Robust to some limited attacksPerceptible
◦ Watermark that can be easily perceived by the user
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Different types of watermarksBitstream watermark
◦ Marks that embedded directly into compressed audio
Fingerprinting◦ A special application of watermarking in which
information such as recipient of the data is used to form the watermark
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How Sound Perceived
The cochlea, an organ in our inner ears, detects sound. The cochlea is joined to the eardrum by three tiny bones. It consists of a spiral of tissue filled with liquid and thousands of tiny
hairs. The hairs get smaller as you move down into the cochlea. Each hair is connected to a nerve which feeds into the auditory nerve
bundle going to the brain. The longer hairs resonate with lower frequency sounds, and the
shorter hairs with higher frequencies. Thus the cochlea serves to transform the air pressure signal
experienced by the ear drum into frequency information which can be interpreted by the brain as sound.
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Digitization of Sound
Sampling◦ Most humans can’t hear anything over 20 kHz.◦ The sampling rate must be more than twice the highest frequency
component of the sound (Nyquist Theorem).◦ CD quality is sampled at 44.1 kHz.◦ Frequencies over 22.01 kHz are filtered out before sampling is
done.Quantization
◦ Telephone quality sound uses 8 bit samples.◦ CD quality sound uses 16 bit samples (65,536 quantization levels)
on two channels for stereo.
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Encoder Design
A . Apply bandlimiting filter to remove highfrequency components.
B. Sample at regular time intervals.C. Quantize each sample.
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Sampling Error (Undersampling)
If you undersample, one frequency will alias as another.
For CD quality, frequencies above 22.05 kHz are filtered out, and then the sound is sampled at 44.1 kHz.
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Quantization Interval
If Vmax is the maximum positive and negative signal amplitude and n is the number of binary bits used, then the magnitude of the quantization interval, q, is defined as follows:
For example, what if we have 8 bits and the values range from –1000 to +1000?
n
Vq
2
2 max
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Quantization Error (Noise)
Any values within a quantization interval will be represented by the same binary value.
Each code word corresponds to a nominal amplitude value that is at the center of the corresponding quantization interval.
The actual signal may differ from the code word by up to plus or minus q/2, where q is the size of the quantization interval.
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QuantizationIntervals andResultingError
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Insufficient Quantization Levels
Insufficient quantization levels result from not using enough bits to represent each sample.
Insufficient quantization levels force you to represent more than one sound with the same value. This introduces quantization noise.
Dithering can improve the quality of a digital file with a small sample size (relatively few quantization levels).
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Linear Vs. Non-Linear Quantization
In linear quantization, each code word represents a quantization interval of equal length.
In non-linear quantization, you use more digits to represent samples at some levels, and less for samples at other levels.
For sound, it is more important to have a finer-grained representation (i.e., more bits) for low amplitude signals than for high because low amplitude signals are more sensitive to noise. Thus, non-linear quantization is used.
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u-Law
Used in North America and Japan
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A-Law
Used in Europe and the rest of the world and international routes
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Discrete Fourier Transform
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Fourier Transform of rect(t/τ)
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Window function (1)
Rectangular window
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Window function (2)
hamming window
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Window function (3)
hanning window
Critical bands
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Bark to frequency conversion
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Critical bands by Zwicker
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Absolute Threshold of Hearing (ATH)
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Frequency masking (1)
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Frequency masking (2)
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Cepstrum domain
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Discrete Cosine Transform
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Measuring transparency (1)
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Subjective tests◦ Discriminative test◦ Mean Opinion Score (MOS)
Measuring transparency (2)
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Objective measures
Measuring transparency
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Feature Extraction
Feature Extraction
Feature Comparison
Quality Estimation ODG
Original Signal
Watermarked
Signal
Objective Difference Grade
Measuring transparencyObjective test
◦ Perceptual Audio Quality Measurement (PAQM)◦ Noise to Mask Ratio (NMR)◦ Perceptual Evaluation of Audio Quality (PEAQ)
Report a value between 0 and -4. higher values show more transparency and vice versa
◦ Perceptual Evaluation of Speech Quality (PESQ) Report a value between 4.5 and 0.5. higher values
show more transparency and vice versa
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Measuring Robustness• 1.Embed a random watermark W on the audio signal A.
does not diminish the fidelity of the cover below a
specified minimum
2.Apply a set of relevant signal processing operations to
the watermarked audio signal A’.
3.Extract the watermark W using the corresponding detector and measure the success of the recovery process
※ Bit-error rate(BER): ratio of incorrect extracted bits to the total number of embedded bits
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1
0
1, 100
0,
ln n
n n n
W WBER
W Wl
Measuring Robustness
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Normalized Correlation
False Negative Alarm◦ Detecting no watermark in a work that actually
contain oneFalse Positive Alarm
◦ Detection of a watermark in a work that does not actually contain one
