DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 341

MATLAB Simulations

Task 1

Write a MATLAB code to simulate the locking process of the 1st-order
SDPLL. First, plot the locking range. Then, let A = 1, x o = 2p (rad/s), W = 0.9,
K 1 = 0.8 and take h o = / (0) = 0 rad. Hence, the incoming frequency is f = f o /
W = 1/0.9 = 1.1 Hz. Make sure that the loop is inside the lock range. As we
expect locking normally in less than 50 cycles, consider only 50 samples. Plot the
input signal and the sampled signal. Also plot the phase /(k) and the instantaneous
frequency [x(k) = 2p/T(k)] as functions of time. Check with the theoretical value
of / ss . Vary the initial phase / (0) = h o to take on the values -3, -2, -
1, 0, 1, 2, 3 and see the difference in the locking process. Does the initial phase
affect / ss ?

Task 2

Repeat Tasks 1 and 2 for various combinations of (W,K 1 ) as follows: (0.9,1.5),
(1.2,1.7), and (1.4,3). Let (W,K 1 ) be outside the locking range and plot the phase
and frequency transients.

Task 3

Plot the phase plane diagram of the 1st-order SDPLL for Tasks 1 and 2.

Experiment # 9: Adaptive Wiener Filter for Noise Reduction
and Channel Estimation

Introduction

Wiener filter is an optimum filter for estimation or prediction signals corrupted by
noise or distorted by the transmission channel. Adaptive Wiener filter is a
programmable filter whose coefficients [i.e., its impulse response non-zero values,
{h(k)}] are changed (adapted) according to the current available samples of the
observed signal {y(n)} and a desired (reference) signal {d(n)}, to give an optimal
estimate x ð n Þ of the original signal {x(n)} at the time instant n [see Fig. D.15 ]. An
adaptive filter utilize s a feedback algorithm to update the filter coefficients at each
time instant n; hence, it can compensate for time-varying channel conditions.
The filter coefficients are adapted according to an algorithm, which can be
implemented by hardware or simulated on a microprocessor or a computer. The
adaptive

FIR Wiener filter algorithm is a least mean-squared (LMS) error