AD9853

–18–

REV. C

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 {fmax = 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

1520

2530

35

40

TAP

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

10111213

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

1

FreqScale

tap –

TAPS – 1

2

.

BW

0

h(t) :=

htap := h(ttap) h := INT

h SCALEPROC GAIN

max(h)

.

0.5

freq_pts – 1

f :=

freq_pts := 250

n := 0..freq_pts – 1

fn := f n

.

.

GLOBAL DECLARATIONS

CONSTANTS:

0.5

PROC_GAIN

1

BW

0.5 (1 +

)

.

SCALE

511

TAPS

41

FreqScale

4

FUNCTIONS:

InRange (x,a,b)

(x

a) . (x

b)

INT(x)

floor (x + 0.5)

dB(x)

if (| x | = 0, 200, 20 log (| x |))

.

SRRC(f)

passband

0.5 (1 –

)

.

stopband

0.5 (1 +

)

if InRange (f, 0, stopband)

1 if InRange (f, 0, passband)

cos

4 .

.

.

(2 f +

– 1) if InRange (f, passband, stopband)

0 otherwise

SRRC(f) cos(2

f t)df

..

.

.

Figure 33. Mathcad Simulation of a 41-Tap SRRC Filter