Speech Signal Processing I

1. Speech Signal Processing I Edmilson Morais and Prof. Greg. Dogil October, 25, 2001

2. Second Class • The Speech Signal • Digitalization • Digital filters : FIR, IIR • Linear Systems • Fourier Analysis • Z-Transform • Z-Transform and Linear Systems • Sampling Theorem • The Source-Filter Model of Speech

3. The Speech Signal : Basic characteristics • No-stationary • Voiced segments – almost periodic • Unvoiced segments – aleatory signal • Transitions – Bursts ... • In reality : • Voiced = Periodic + Aleatory • Unvoiced also contain some periodic component • Usual sampling rate : 16000 Hz • Usual quantization : Uniform, 16 bits

4. Continous time Discrete time The Speech Signal : Digitalization Sampling With fs = 2 x fmax Low-Pass filter Digital signal Quantization Sampling Quantization

5. -1 -1 -1 -1 -1 Z Z Z Z Z Digital Filters FIR – Finite impulse response In a more compact way is a linear combination of the previous and the current input Defining as an unit delay

6. X(n) -1 -1 -1 -1 -1 -1 -1 -1 Z Z Z Z Z Z Z Z y(n) Digital Filters IIR – Infinite impulse response

7. T[ ] X(n) y(n) = T[y(n)] LSIS - Linear Shift-Invariant System LSIS - Linear shift-invariant system Convolution and Impuse response The LSIS are useful for performing filtering operations The LSIS are also useful as model for speech production

8. 4 3 2 1 1 4 3 9 2 7 1 6 4 3 1 1 Convolution Note : A convolution can also be used for multiplying polynoms P1(x) = 1 + ax P2(x) = 1 + bx Conv([1 a ],[1 b]) = 1 + (a+b) + a.b

9. Fourier Analysis Continuous Fourier Transform Fourier Transform of a Discrete Sequence Direct Direct Inverse Inverse Note : DFT : Discrete Fourier Transform Note : The DFT is basicaly a Linear transformation, where the base function are complex exponential function with phase multiples of : Direct Direct Inverse Inverse

10. Fourier Analysis Normalization of frequency and amplitude Sampling

11. Fourier Analysis Magnitude and Phase of the DFT Properties of the Fourier Transform of a discrete sequency and Defining : Linearity Shift in time Shift in frequency (Modulation) Convolution Convolution in frequency

12. Z-Transform Definition The sequence x(n) is known and Z is a complex number. X(Z) is just a weighted sum. Example : x(0) = 1; x(1) = 1; x(2) = 3; x(3) = 1; Importante properties Defining : Linearity : Convolution :

13. Z-Transform and Linear Filters Linear filters can now be expressed in terms of Z-transforms. The general linear filter is expressed as : Where H(z) is called the <system function> and is the Z-transform of the unit-sample response : h(n) T[ ] The FIR filter of order q can be expressed as : or in terms of system function Where :

14. Z-Transform and Linear Filters Z-Transform and Linear Filters Symilarly for IIR filter In terms of diference equation In terms of System function System function zeroes Usefull representation poles

15. zeroes j -1 1 -j Z-Transform and Linear Filters poles

16. Sampling Theorem 1

17. Sampling Theorem

18. 1 Sampling Theorem : Ideal lowpass filter

19. The Source-Filter model of Speech Av Vocal tract parameters Impulse train generator Glotal pulse model G(Z) Vocal tract model V(Z) Radiation model R(Z) s(n) V/UV T=1/fo Random nose generator An