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Autocorrelation Method in Microsoft Office Build Data Matrix 2d barcode in Microsoft Office Autocorrelation Method

Autocorrelation Method use microsoft office datamatrix generating topaint data matrix in microsoft office Java Platform A commonly used Microsoft Office barcode data matrix method to estimate pitch is based on detecting the highest value of the autocorrelation function in the region of interest. This region must exclude m = 0 , as that is. Speech Signal Representations the absolute ma Microsoft Office 2d Data Matrix barcode ximum of the autocorrelation function [37]. As discussed in 5, the statistical autocorrelation of a sinusoidal random process. x[n] = cos( 0 n + ). is given by R[m Microsoft Office ECC200 ] = E{x [n]x[n + m]} = 1 cos( 0 m) 2. (6.157). (6.158). which has maxim a for m = lT0 , the pitch period and its harmonics, so that we can find the pitch period by computing the highest value of the autocorrelation. Similarly, it can be shown that any WSS periodic process x[n] with period T0 also has an autocorrelation R[m] which exhibits its maxima at m = lT0 . In practice, we need to obtain an estimate R[m] from knowledge of only N samples.

If we use a window w[n] of length N on x[n] and assume it to be real, the empirical autocorrelation function is given by 1 R[m] = N. N 1 . m. w[n]x[n]w[n + m ]x[n + m ]. (6.159). whose expected value can be shown to be E R[m] = R[m] ( w[m] w[ m]) where w[m] w[ m] =. N . m. 1 . (6.160). w[n]w[n+ m . ]. (6.161). which, for the case of a rectangular window of length N, is given by m. 1 w[m] w[ m] = N 0 m <N m N (6.162). which means t hat R[m] is a biased estimator of R[m]. So, if we compute the peaks based on Eq. (6.

159), the estimate of the pitch will also be biased. Although the variance of the estimate is difficult to compute, it is easy to see that as m approaches N, fewer and fewer samples of x[n] are involved in the calculation, and thus the variance of the estimate is expected to increase. If we multiply Eq.

(6.159) by N /( N m) , the estimate will be unbiased but the variance will be larger. Using the empirical autocorrelation in Eq.

(6.159) for the random process in Eq. (6.

157) results in an expected value of. The Role of Pitch m . cos( 0 m) E R[m] = 1 , N 2 m <N (6.163). whose maximum c oincides with the pitch period for m > m0 . Since pitch periods can be as low as 40 Hz (for a very low-pitched male voice) or as high as 600 Hz (for a very high-pitched female or child s voice), the search for the maximum is conducted within a region. This F0 detection algorithm is illustrated in Figure 6.

31 where the lag with highest autocorrelation is plotted for every frame. In order to see periodicity present in the autocorrelation, we need to use a window that contains at least two pitch periods, which, if we want to detect a 40Hz pitch, implies 50ms (see Figure 6.32).

For window lengths so long, the assumption of stationarity starts to fail, because a pitch period at the beginning of the window can be significantly different than at the end of the window. One possible solution to this problem is to estimate the autocorrelation function with different window lengths for different lags m..

-0.5 0 100 500 Microsoft Office ECC200 1000 1500 2000 2500 3000 3500 4000 4500 5000. 0 10 20 30 40 50 60. Figure 6.31 Wav Microsoft Office ECC200 eform and unsmoothed pitch track with the autocorrelation method. A frame shift of 10 ms, a Hamming window of 30 ms, and a sampling rate of 8kHz were used.

Notice that two frames in the voiced region have an incorrect pitch. The pitch values in the unvoiced regions are essentially random..

The candidate p itch periods in Eq. (6.156) can be simply Tm = m ; i.

e., the pitch period is any integer number of samples. For low values of Tm , the frequency resolution is lower than for high values.

To maintain a relatively constant frequency resolution, we do not have to search all the pitch periods for large Tm . Alternatively, if the sampling frequency is not high, we may need to use fractional pitch periods (often done in the speech coding algorithms of 7) The autocorrelation function can be efficiently computed by taking a signal, windowing it, and taking an FFT and then the square of the magnitude..

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