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Unformatted text preview: ruary 11, 2012 Veton Kpuska - 2x x 10 PDF of Speech February 11, 2012 Veton Kpuska 11 PDF of Modeled Speech February 11, 2012 Veton Kpuska 12 PDF of Speech Knowing pdf of speech is essential in order to optimize the quantization process of analog/continous valued samples. February 11, 2012 Veton Kpuska 13 Quantization of Speech & Audio Signals
Scalar Quantization Vector Quantization Time Quantization (Sampling) of Analog Signals
a) 1 fs = T
Analog Analog Low-pass Low-pass Filter Filter Sample Sample and and Hold Hold b) xa ( nT ) Analog to Analog to Digital Digital Converter x[ n] DSP DSP AnalogtoDigital Conversion. a) Continuous Signal x(t). b) Sampled signal with sampling period T satisfying Nyquist rate as specified by Sampling Theorem. c) Digital sequence obtained after sampling and quantization x[n] c) February 11, 2012 Veton Kpuska 15 Example Assume that the input continuoustime signal is pure periodic signal represented by the following expression: x( t ) = A sin ( 0 t + ) = A sin ( 2f 0 t + )
where A is amplitude of the signal, 0 is angular frequency in radians per second (rad/sec), is phase in radians, and f0 is frequency in cycles per second measured in Hertz (Hz). Assuming that the continuoustime signal x(t) is sampled every T seconds or alternatively with the sampling rate of fs=1/T, the discretetime signal x[n] representation obtained by t=nT will be: x[ n] = A sin ( 0 nT + ) = A sin ( 2f 0 nT + )
February 11, 2012 Veton Kpuska 16 Example (cont.) Alternative representation of x[n]: f0 x[ n] = A sin 2 n + = A sin ( 2F0 n + ) = A sin ( 0 n + ) fs reveals additional properties of the discretetime signal. The F0= f0/fs defines normalized frequency, and 0 digital frequency is defined in terms of normalized frequency: 0 = 2F0 = 0T , 0 0 2
February 11, 2012 Veton Kpuska 17 Reconstruction of Digital Signals
a) b) c) fs = 1 T DSP y[n] Digital to Analog Converter ya(nT) Analog Low-pass Filter y(t) DigitaltoAnalog Conversion. a) Processed digital signal y[n]. b) Continuous signal representation ya(nT). c) Lowpass filtered continuous signal y(t).
February 11, 2012 Veton Kpuska 18 Scalar Quantization Conceptual Representation of ADC fs =
x(t) 1 T 1 C/D fs = T ^ x[ n]
x[ n ]
Quantizer ^ xQ [ n] Coder This conceptual abstraction allows us to assume that the sequence is obtained with infinite precession. Those values of are scalar quantized to a set of finite precision ^ xQ [ n] amplitudes denoted here by . Furthermore, quantization allows that this finiteprecision set of amplitudes to be represented by corresponding set of (bit) patterns or symbols, . ^ xn Without loss of generality, it can be assumed that input signals cover finite range of values defined by minimal, xmin and maximal values xmax respectively. This assumption in turn implies that the set of symbols representing is finite. The process of ^ xn representing finite set of values to a finite set of symbols is know as encoding; performed by the coder, as in Figure above. Thus one can view quantization and coding as...
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