Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 96

and β i =− α i where α i are the LPC.

φ(kf s ) =− (n + 1 )( 2 πTkf s )

n

β i sin ( 2 π iTkf s )

i = 1

2tan − 1 − (5.34)

n

1 − β i cos ( 2 π iTkf s )

i = 1

where T is the sampling period, f s is the frequency step, and k = 1 , 2 , 3 , ... ,

K max .
By performing a Discrete Fourier Transform (DFT) on the coefficient
sequence, A k and B k , ω i can be solved as the zero-valued frequencies of a
power spectrum. A typical plot, showing the partial minima of the spectrum,
is shown in Figure 5.7.
If the spectrum were to be obtained directly, it would involve an enormous
number of computations. Fortunately, a number of computation reductions
can be made. The aim is to find the partial minima of the response, thus

5.0

Q'(z)
P'(z)

4.0

3.0

2.0

1.0

0.0

0.0 100.0 200.0

Frequency/4000/512Hz per div

Figure 5.7 Zero frequency plot for one frame of the DFT-LSF method