Digital Audio Watermarking: Properties, characteristics of audio signals, and measuring the performance of a watermarking system نيما خادمي کلانتري

Properties (1) Inaudibility ◦ Similarity between the original and watermarked signal Robustness ◦ Ability to detect the watermark after common signal processing and malicious attacks Data Payload ◦ The number of embedded bits per second 2

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 3

Different types of watermarks Robust ◦ Watermarks that are robust against attacks Fragile ◦ Have only very limited robustness Semi-Fragile ◦ Robust to some limited attacks Perceptible ◦ Watermark that can be easily perceived by the user 4

Different types of watermarks Bitstream 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 5

6 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.

7 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 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.

8 Encoder Design A. Apply bandlimiting filter to remove high frequency components. B. Sample at regular time intervals. C. Quantize each sample.

9 Sampling Error (Undersampling) If you undersample, one frequency will alias as another. For CD quality, frequencies above kHz are filtered out, and then the sound is sampled at 44.1 kHz.

10 Quantization Interval If V max 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?

11 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.

12 Quantization Intervals and Resulting Error

13 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).

14 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.

15 u-Law Used in North America and Japan

16 A-Law Used in Europe and the rest of the world and international routes

17 Discrete Fourier Transform

18 Fourier Transform of rect(t/τ)

19 Window function (1) Rectangular window

20 Window function (2) hamming window

21 Window function (3) hanning window

Critical bands 22

Bark to frequency conversion 23

Critical bands by Zwicker 24

Absolute Threshold of Hearing (ATH) 25

Frequency masking (1) 26

Frequency masking (2) 27

Cepstrum domain 28

Discrete Cosine Transform 29

Wavelet Transform 30

Measuring transparency (1) 31 Subjective tests ◦ Discriminative test ◦ Mean Opinion Score (MOS)

Measuring transparency (2) 32 Objective measures

Measuring transparency 33 Feature Extraction Feature Comparison Quality Estimation ODG Original Signal Watermarke d Signal O bjective D ifference G rade

Measuring transparency Objective 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 34

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 35

Measuring Robustness 36 Normalized Correlation False Negative Alarm ◦ Detecting no watermark in a work that actually contain one False Positive Alarm ◦ Detection of a watermark in a work that does not actually contain one