Unformatted text preview: UCLA Dept. of Electrical Engineering EE214A: Digital Speech Processing Problem Set 5 Due: 2/16/2011 Reading Assignment: Chapter 4 except for Section 4.5. Chapter 9: till Section 9.4 1. Problem 4.3. 2. Problem 4.4. 3. Problem 4.5. 4. Four consecutive samples of a speech signal have the values: 3 1 = 2 2 = ; 1 3 = 1.
s s s s0 = (a) Apply the autocorrelation method of linear prediction analysis to nd a secondorder transfer function of the vocal tract. (b) What is the minimum error of your estimate? At which frequencies would the minimum error occur? Explain. 1 5. As shown in Fig. 1, a segment of a voiced vowel, sampled at 8 kHz, is passed through a lowpass lter with a cuto frequency of 800 Hz and then thru an LPC predictor that estimates the vocaltract transfer function ( ( )).
Hz LPF s(n) (800 Hz) s l (n) LPC {a i ’s} Figure 1 (a) Sketch a 'typical' magnitude spectrum of the signal ( ).
sl n (b) What is a su cient value of , the order of the LPC?
p Suppose now that we construct an inverse lter ( ^ ( ) = 1( ) ) and pass through it ( ). The autocorrelation function of the output is then computed as shown in Fig. 2.
Hz Hz sl n s l (n) ^ H(z) ε (n) Autocorrelation R ε (n) Figure 2 (c) Express the inverse lter ^ ( ) in terms of the 's.
Hz ai (d) Sketch the spectrum of the residual signal ( ). (Assume that the LPC model estimated well the original transfer function.)
n (e) How is the pitch period determined from the autocorrelation signal ( )? Sketch a typical ( ).
R n R n (f) What is the advantage of lowpass ltering at the outset of the problem? What is the advantage of inverse ltering? This method of pitch detection is often used in practical applications and is referred to as the SIFT (simple inverse lter tracking) algorithm, rst developed in 1972.
2 Computer Assignment: Linear Predictive Analysis Introduction: This assignment explores the role of linear prediction in spectral analysis of speech. Speci cally, this assignment focuses on the e ect of prediction order on resulting spectral approximations. Questions: 1. What is the lowest prediction orders that provides for accurate formant estimation? Estimate the spectral location of the rst three formant frequencies of the rst 2 vowels in the sentence you have been analyzing and compare the values with those obtained by the STFT. 2. Perform LPC analysis with =100. Comment on the resulting spectral representation. What do the ne ripples in the spectral representation correspond to?
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 Winter '11
 ALWAN
 Electrical Engineering, Signal Processing, Autocorrelation, LPC, inverse lter

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