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AD9853
–20–
REV. C
cos(2
p
f .
.
.
.
BW
0
h1(t) :=
R := 6
f
b
.
SRRC (f).
H(0,R)
H
Freqf
,1
MODIFICATION OF SQUARE-ROOT RAISED COSINE (SRRC) FIR FILTER RESPONSE
TO COMPENSATE FOR CASCADED INTEGRATOR-COMB (CIC) FILTER RESPONSE
COMPUTE SRRC FILTER COEFFICIENTS:
...MAP THE FILTER TAP INDEX TO TIME DOMAIN (CENTERED AT t = 0)
...INVERSE FOURIER INTEGRAL COMPUTES SRRC IMPULSE RESPONSE
(TIME DOMAIN) FROM THE SRRC FREQUENCY RESPONSE (FREQUENCY DOMAIN).
THE COS() FUNCTION REPLACES THE NORMAL COMPLEX EXPONENTIAL
BECAUSE WE ARE RESTICTED TO REAL FILTER COEFFICIENTS.
...SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED
COMPUTE SRRC FILTER COEFFICIENTS MODIFIED
FOR CORRECTION OF CIC RESPONSE:
...CIC INTERPOLATION RATIO (USER PROGRAMMABLE)
...INVERSE FOURIER INTERGRAL MODIFIES THE SRRC RESPONSE
BY THE RECIPROCAL OF THE NORMALIZED CIC FREQUENCY
RESPONSE. THE MODIFICATION IS ONLY PERFORMED OVER THE
FRACTION OF THE SRRC BANDWIDTH AS SPECIFIED BY
b
.
...MODIFIED SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED TO 10-BIT RANGE
SRRC AND MODIFIED SRRC IMPULSE RESPONSE
...FIR FILTER COEFFICIENTS
FOR SRRC RESPONSE
...FIR FILTER COEFFICIENTS
FOR SRRC RESPONSE
WITH CIC COMPENSATION
DISPLAY FREQUENCY RESPONSE PLOTS:
f:= 0,0.001.. 0.5
...NORMALIZED FREQUENCY RANGE [A REQUIREMENT OF MATHCAD'S GAIN() FUNCTION]
...SCALE FACTORS TO ADJUST SRRC,
COMPENSATED SRRC, AND CIC
FREQUENCY RESPONSES TO UNITY AT f = 0
...FUNCTION TO COMPUTE NORMALIZED, UNCOMPENSATED FIR RESPONSE (SRRC) IN dB
...FUNCTION TO COMPUTE NORMALIZED CIC RESPONSE IN dB
...FUNCTION TO COMPUTE NORMALIZED, COMPENSATED FIR RESPONSE (SRRC + CIC
–1
) IN dB
...FUNCTION TO COMPUTE OVERALL SYSTEM RESPONSE OF SRRC AND CIC TOGETHER IN dB
...FUNCTION TO COMPUTE OVERALL SYSTEM RESPONSE OF COMPENSATED SRRC AND CIC TOGETHER
SRRC, CIC, AND CORRECTED SRRC RESPONSE
10
5
0
15
20
TAP
25
30
35
40
500
0
h
tap
h1
tap
FREQUENCY SCALE – fn
0
0
–20
–40
–60
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
FIR(f)
CIC(f)
COMP(f)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
0
3
2
–2
–5
–2
5
7
1
–7
–7
7
19
7
–34 –71 –48
71
260 438 511
hT =
h1T =
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
1
4
2
–3
–6
–1
7
9
1
–10 –9
8
24
12
–34 –78 –61
56
251 435 511
tap := 0..TAPS – 1 t
tap
:=
1
FreqScale
tap –
TAPS – 1
2
.
BW
0
h(t) :=
SRRC(f) .
p
f .
.
.
htap := h(ttap)
h := INT
h.
max(h)
SCALEsrrc := (| gain(h,0) |)
–1
SCALEsrrc := 5.559 .
–4
h1tap := h1(ttap)
h1 := INT
h1 .
max(h1)
SCALEcompsrrc := (| gain(h1,0) |)
–1
SCALEcompsrrc := 5.79.
–4
SCALEcic := (| H(0,R) |)
–1
SCALEcic := 7.716 .
–4
FIR(f) := dB(SCALEsrrc .
CIC(f) := dB(SCALEcic.
COMP(f) := dB(SCALEcompsrrc .
SYSuncomp(f) := FIR(f) + CIC(f)
SYScomp(f) := COMP(f) + CIC(f)
Figure 34. Mathcad Simulation of 41-Tap SRRC Filter with CIC Compensation