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Source Title: Signal Processing, Perceptual Coding and Watermarking of Digital Audio: Advanced Technologies and Models

Copyright: © 2012
|Pages: 7
DOI: 10.4018/978-1-61520-925-5.ch007

Top## 7.1 Matched Filter Approach

*(7.1)**(7.2)* with impulse response*(7.3)**(7.4)* where *α* is a strength control factor. Then the output of the matched filter is*(7.5)**(7.6)*## 7.2 Savitzky-Golay Smoothing Filters

*(7.7)*

Some watermarking system employs a pseudo random sequence (PN sequence) for synchronization purpose. Matched filter is usually used in such cases to detect the existence of the PN sequence and to precisely locate the starting sample of the PN sequence.

In the watermarking system, the PN sequence is considered as noise added to the host signal. Since the PN sequence only lasts a very short period of time, it could be treated as transient noise pulses and detected by a filter whose impulse response is matched to the PN sequence. Such is the matched filter whose frequency response is defined as (Vaseghi, 2000):

Where *K* is a scaling factor, is the complex conjugate of the spectrum of PN sequence {*u*} and *PSx*(*f*) is the power spectrum of the host signal *x*.

In real world applications, the host signal is very close to a zero mean process with variance and is uncorrelated to the PN sequence. Then, Equation (7.1) becomes

When the received signal contains the PN sequence, it is defined as

Since the host signal and PN sequence are uncorrelated, *d _{μx}* is expected to be zero. The PN sequence itself is orthogonal to the host signal, and so

Therefore, the detected starting location of the PN sequence in a block will be

Figure 1 shows a typical output of such matched filter. Note that the peak location marks the beginning of the embedded PN sequence.

The described matched filter detection is optimal for additive white Gaussian noise (Cvejic, 2004). However, the host audio signal is usually far from being white Gaussian noise. Adjacent audio sample are usually highly correlated with large variance, which increases the detection error for spread spectrum. Several techniques have been developed to decrease such correlation.

TopCvejic (2004) applied least squares Savitzky-Golay smoothing filters in the time domain to smooth out a wideband noise audio signal. By doing so the variance of the host audio signal is greatly reduced.

Let’s recall the equal error extraction probability p as given by

It is clear that a reduced variance *σ _{x}* will result in a decreased detection error rate.

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