... Enâ1 + x2 (n),where the window h (n), is defined as h (n) = anu(n), x (n) is. the speech signal, and 0 < a
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II Semester M.E. (Electronics & Communication) Degree Examination, January 2015 (2K9 Scheme) EL 215 : SPEECH AND AUDIO SIGNAL PROCESSING Time : 3 Hours
Max. Marks : 100
Instruction : Answer any five full questions. 1. a) With a neat block diagram, explain the speech production mechanism in terms of i) excitation along with the type of speech sounds produced and ii) system (filter). b) Write a note on : Articulators.
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c) Explain the following : i) Formants, ii) Pitch, and iii) Spectrograms.
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2. a) Define short time autocorrelation function. Discuss the clipping autocorrelation pitch detector algorithm.
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b) Explain the significance of short time energy and short time average zero crossing rate in the context of speech signal processing.
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c) Show that the short time energy can be expressed recursively as, En = a2 En–1 + x2 (n), where the window h (n), is defined as h (n) = anu(n), x (n) is the speech signal, and 0 < a < 1. Draw a digital network diagram of this equation.
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3. a) Explain short time Fourier transform. Discuss the Fourier transform interpretation of STFT, specifically in terms of i) periodicity, ii) & recovering the signal x (n) from its STFT.
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b) Discuss the filter bank summation method of short time synthesis and derive the expression for necessary constraints.
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STFT c) Let x(n) ←⎯ ⎯ ⎯→ Xn (e jω)
i) If v(n) = x (n) + y (n), then show that
( )
( ) ( )
Vn e jω = Xn e jω + Yn e jω .
ii) If v (n) = x (n – k), then show that
( )
( )
Vn e jω = e−jωkXn e jω .
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4. a) Define complex cepstrum and real cepstrum of a sequence x (n). Show that the complex cepstrum of a sequence can be computed as,
xˆ (n) =
−1 2πnj
1 xˆ (0) = 2π
∫
∫
π
−π
π
x′(e jω ) jωn e dω, n ≠ 0 & x(e j ω )
log X(e jω ) dω
−π
where symbols have usual meanings.
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b) Find the cepstrum of the sequence whose Z-transform is V(z) =
1+ 0.98z−1
π π j −j −1 6 6 (1 − 0.9e z )(1 − 0.9e z−1)
.
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c) Explain with a block diagram steps involved in computing the real cepstrum of a speech signal. Draw block diagram to explain how pitch of the speech signal is estimated from the computed cepstrum and justify the steps.
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5. a) Define a pth order linear predictor. Show that the following relation holds for a pth order linea predictor s (n)
p
∑ k =1αks(n − k) + e(n),
where { α k} are LP
coefficients and e (n) is the prediction error.
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b) Explain the autocorrelation method of LP analysis and show that i)
p
∑ k =1α k Rn ( i− k ) = Rn (i),
1 ≤ i ≤ p, and
assuming p = 4, write the above equation in the matrix form. ii) minimum mean squared prediction error En = Rn(0) − ∑ pk =1 αkRn (k) .
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c) Using Durbin’s recursive algorithm compute the transfer function of 2nd order LP model for a speech signal having autocorrelation coefficients R (0) = 1, R (1) = 0.5 and R (2) = 0.25.
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6. a) Explain the following : i) JND, ii) frequency masking and iii) temporal masking. b) Discuss two broad classes of speech quality measures.
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7. a) With a block diagram explain ADPCM system with feed-forward adaptive quantization.
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b) Discuss the salient features of the LD_CELP G.728 speech compression standard.
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c) With a block diagram explain MPEG audio compression algorithm.
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8. a) Explain the following in the context of speech signal processing. i) Dynamic time warping and ii) Hidden Markov model. b) Write a short note on Text to speech synthesis.
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