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

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

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

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

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

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

7. LSIS - Linear Shift-Invariant System T[ ] X(n)y(n) = T[y(n)] 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. 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 1 2 3 4 1 1 2 3 4 1 1 3 6 9 7 4

9. Fourier Analysis Continuous Fourier Transform Fourier Transform of a Discrete Sequence DFT : Discrete Fourier Transform Note : The DFT is basicaly a Linear transformation, where the base function are complex exponential function with phase multiples of : Note : Direct Inverse Direct Inverse Inverse Direct Direct 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 Defining : and 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 and is the Z-transform of the unit-sample response : The FIR filter of order q can be expressed as : or in terms of system function Where : T[ ] h(n)

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

15. 1 j -j -1zeroespoles Z-Transform and Linear Filters

16. Sampling Theorem 1

18. Sampling Theorem : Ideal lowpass filter 1

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