Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 68

0.32

0.3

Orignal and demodulated

0.28

0.26

0.24

0.22

0.2

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Sample number

Figure 3.26 Demodulated BFSK signal p

tracking the mark and space frequencies. An implementation for an FSK signal with
SNR ¼ 10 dB is shown in Figure (3.26).

3.10 Phase Shift via Adaptive Filter
In the application of detection, array processing and direction finding, we need to
take the given narrowband signal (here we have chosen a sinusoidal wave) and shift
it by a given value. The following example generates a 2 phase shift by adjusting

the coefficient of the first-order all-pass filter. Consider the given signal u k as

=

Figure 3.27 Adaptive phase shifting

u k ¼ cos ð 2 fk þ Þ where f is the normalised frequency and is an arbitrary phase

value. Figure 3.27 depicts the macro view of the filter.

u k ¼ cos ð 2 fk þ Þ;

ð 3 :

44 Þ

x k ¼ r k x k 1 r k u k þ u k 1 ; ð 3 : 45 Þ

z k z k N

1
N

z k ¼ u k x k and e k ¼ ½ ; ð 3 : 46 Þ

p k ¼ p k 1 þ e k ; ð 3 : 47 Þ

r k ¼ r k 1 g loop p k if j r k j 0 : 95 then r k ¼ 0 : 95 : ð 3 : 48 Þ

The above filter is implemented for N ¼ 40 ; g loop ¼ 0 : 01 and 1 = f ¼ 77 with

¼ = 20 and an initial value of r k ¼ 0 : 2. Figure 3.28 shows the phase shift.