1. Speech Coding Using LPC

2. What is Speech Coding  Speech coding is the procedure of transforming speech signal into more compact form for Transmission Available Bandwidth Encryption

3. Uncompressed Speech signal  Analog speech is a bandpassed signal between 200 and 3400 Hz.  Uncompressed digital speech is a bit stream at 64kB/s.  Transmission technology must transmit the signals from point A to point B:  with minimum degradation  using minimum bandwidth

4. Speech coding  By coding we mean an efficient representation of the signal – COMPRESSION  The main approaches: waveform coding transform coding Parametric / hybrid coding } smart quantizers

5. { How each of these works:  Waveform coders: try to find an efficient representation of the waveform, directly.  Transform coders: try to find an efficient representation in the frequency domain.  Parametric coders: try to find a small set of parameters that are an efficient representation of the signal. FFT, etc. exc. speech

6. Comparison of Comparison of speech coders

7. LPC (Linear Predictive coding)  LPC is a model for signal production: it is based on the assumption that the speech signal is produced by a very specific model.

8. Speech Production in Huma Speech Production in Humans  The speech signal is created by: A pressure source (lungs), exciting... A Filter (Vocal tract: pharynx - mouth [soft palate, tongue] - nasal cavity)

9. For DSP Engineer  An excitation source  A time varying filter H(t,) filter: Excitation speech

10. The model and its representation The model and its representation  The LPC model looks at speech as: Excitation:  periodic (voiced) - originating in the larynx  noise (unvoiced) - fricative, produced in the mouth An all-pole filter representing the vocal tract H() all pole filter:....

11. Block Diagram

12. Why the name “Linear Predictive Coding”  It is assumed that the new sample is the weighted linear combination of previous samples

13. Z-Plane Representation  In the z-plane we can write the model as a transfer function: Clearly this transfer function has only poles - which is why it represents an all pole filter.

14. Mathematical analysis Mathematical analysis  Reminder: our problem is to find the LPC parameters, for a given speech signal. This is called the Inverse Problem.  How do we find the set of parameters that gives the best match to the signal?

15. What are these Parameters  The Coefficients of the All Pole Filter  Pitch of the speech

16.  How do we find the Coefficients: least squares  Formulation: Given a signal s(n); Defining an error as: Find the set of that will minize the mean square error:

17. Solution:  Simply equate the derivative of E to zero: Which gives us the Normal Equations: These are no more than p linear equations in p unknowns...

18. Or in matricial form:

19.  A correlation; in other words: take the signal, multiply it by a shifted version, and sum.  Since our signal is long and time varying- we did it on short windows  Two variants: autocorrelation method covariance method What is each element of the form-

20. Solving the Matrix  Found the Coefficients a(i) by Using the Levinson-Durbin recursion method

21. Second Parameter  Pitch was found by the finding the correlation of the signal window with itself  Then these parameters were transmitted

22. Predictor coefficients18 * 8 = 144 Gain5 Pitch period6 Voiced/unvoiced switch 1 Total156 Overall bit rate 50 * 156 = 7800 bits / second Bit rate for plain LPC vocoder

23. Predictor coefficients 18 * 8 = 144 Gain5 DCT coefficients 40 * 4 = 160 Total309 Overall bit rate 50 * 309 = 15450 bits / second Bit rate for voice-excited LPC vocoder with DCT

24. Conclusion  Sound produced through LPC method is not exactly the real sound but it sounds intelligibly understandable  LPC can be used in Speech recognition systems  LPC was widely used in Military because of low bit rate in transmission  There are many variants over the basic scheme: LPC-10, CELP, MELP, RELP, VSELP, ASELP, LD-CELP...