
AD9853
–18–
REV. A
SQUARE-ROOT RAISED COSINE (SRRC) FIR FILTER
COMPUTE AND PLOT SRRC FILTER COEFFICIENTS:
...MAP THE FILTER TAP INDEX TO TIME DOMAIN (CENTERED AT T=0)
...INVERSE FOURIER INTEGRAL COMPUTE SRRC IMPULSE RESPONSE (TIME DOMAIN) FROM
THE SRRC FREQUENCY RESPONSE (FREQUENCY DOMAIN). THE COS() FUNCTION REPLACES
THE NORMAL COMPLEX EXPONENTIAL BECAUSE WE ARE RESTRICTED TO REAL
FILTER COEFFICIENTS.
...SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED
...FIR FILTER
COEFFICIENTS
COMPUTE AND PLOT SRRC FREQUENCY RESPONSE:
...DEFINE NUMBER OF FREQUENCY POINTS AND FREQUENCY STEP SIZE (FOR PLOTTING PURPOSES)
...CREATE VECTOR OF UNIFORMLY SPACED FREQUENCY POINTS {f
max
= 0.5; A REQUIREMENT OF THE GAIN() FUNCTION},
...NORMALIZED FREQUENCY RESPONSE
...EXCESS BANDWIDTH FACTOR FOR SRRC FREQUENCY RESPONSE
...BANDWIDTH OF SRRC FILTER (RELATIVE TO SYMBOL RATE)
...PROCESSING GAIN OF CIC FILTERS (USED TO CORRELATE RESULTS WITH AD9853 EVAL. BD.)
...SETS MAX VALUE OF SRRC FILTER BASED ON FINITE WORD SIZE
...NUMBER OF FIR PULSE SHAPING FILTER TAPS
...UPSAMPLING RATIO OF FIR PULSE SHAPING FILTER (RELATIVE TO THE SYMBOL RATE)
...RETURNS 1 IF a <= x <= b, 0 OTHERWISE
...RETURNS NEAREST INTEGER TO x
...RATIO TO DECIBEL CONVERSION FUNCTION
...SRRC FREQUENCY RESPONSE FUNCTION
(f IS RELATIVE TO THE SYMBOL RATE)
500
0
10
5
0
15
20
TAP
25
30
35
40
h
t
SRRC IMPULSE RESPONSE
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
FREQUENCY SCALED TO SYMBOL RATE
SRRC NORMALIZED FREQUENCY RESPONSE
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
hT =
0
0
3
2
–2
–5
–2
5
7
1
–7
–7
7
19
7
–34 –71 –48
71
260 438 511
tap := 0..TAPS – 1 t
tap
:=
1
FreqScale
tap –
TAPS – 1
2
.
BW
0
h(t) :=
htap := h(ttap)
h := INT
h .
max(h)
0.5
freq_pts – 1
D
f :=
freq_pts := 250
n := 0..freq_pts – 1
fn :=
D
f .
K := (| gain(h,0) |)
–1
Hn := K.
GLOBAL DECLARATIONS
CONSTANTS:
0.5
BW
0.5 .
a
)
a
PROC_GAIN
SCALE
TAPS
FreqScale
1
511
41
4
FUNCTIONS:
InRange (x,a,b)
INT(x) floor (x + 0.5)
dB(x) if (| x | = 0, 200, 20.
SRRC(f) passband 0.5 .
a
)
stopband 0.5 (1 +
a
)
if InRange (f, 0, stopband)
1 if InRange (f, 0, passband)
(x a).(x b)
cos
p
.
4
a
.
(2 .
a
– 1) if InRange (f, passband, stopband)
0 otherwise
SRRC(f).
p
f .
.
.
Figure 33. Mathcad Simulation of a 41-Tap SRRC Filter