Rockwell RFX144V24-S23, Руководство дизайнера

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RFX144V24-S23 and RFX96V24-S23 Modem Designer’s Guide
1070 6-3
From Equation 8:
β
2
=
β
’
2
= -r
2
/2 = -0.494048699
Rewriting Equation 7 in terms of the offsets ƒA and ƒ’A:
β
1
= r cos [360° (ƒ
O
- ƒ
A
)/ƒ
S
] (Eq. 9)
β
’
1
= r cos [360° (ƒ
O
+ ƒ’
A
)/ƒ
S
] (Eq. 10)
The frequency offset is approximately 72% of B/2 (half the bandwidth) for most applications:
β
’
2
≅
0.72 (B/2) (Eq. 11)
The value of ƒA should be equal to ƒ’A. However, ƒA may be chosen 1% smaller than ƒ’A to compensate for the fact that
the overall cascade response is not perfectly symmetrical, i.e., near DC (see Figure 6-5).
The values for the coefficients
α
0 and
α
’0 that set |H(ƒO)| = 0 dB in equations 1 and 2 were measured and plotted versus
center frequency ƒO as shown in Figure 6-6. Three equations corresponding to three linear approximations result:
α
0
=
α
’
0
= [(104/319)ƒ
O
- 78.62]/32767
400 ² ƒ
O
≤
1100 Hz (Eq. 12a)
α
0
=
α
’
0
= [(44/275)ƒ
O
+ 104]/32767
1100
≤
ƒ
O
≤
1650 Hz (Eq. 12b)
α
0
=
α
’
0
= [(4/45)ƒ
O
+ 221]/32767
1650
≤
ƒ
O
≤
3000 Hz (Eq. 12c)
6.1.2 Energy Averaging Filter
The coefficients of the energy averaging filter are determined by a Z-domain approximation to an RC circuit of transfer
function H(S) = 1/(1 + S
τ
):
α
" = 1/( 1 + f
S
τ)
(Eq. 13)
β
” = 1/[ 1 + (1/f
S
τ)]
(Eq. 14)
Upon power up,
α
" and
β
” are set for
τ
= 0.1 seconds. Unless different tone detector response times are required, these
coefficients need not be changed. In Audio and Voice/Audio Codec modes, the coefficients should be changed to
compensate for the 4000 and 8000 Hz sample rate.
The Tone Detector Threshold value is programmable in DSP RAM (see parameter No. 47 in Section 4).