Adaptive Filters and Applications - Digital Signal Processing: Fundamentals and Applications - page 493

b. Plot the corrupted signal, reference noise, and enhanced signal, respectively.
c. Compare the spectral plots between the corrupted signal and the enhanced signal.

10.26. A line enhancement system ( Figure 10.31 ) has following specifications:
Sampling rate ¼ 1,000 Hz
Corrupted signal: 100 Hz tone with the unit amplitude added with the unit power Gaussian
noise
Adaptive filter: FIR type, 16 taps
Convergence factor: 0.001
Delay value D : to be decided according to the experiment
LMS algorithm
a. Write a MATLAB program to perform the line enhancement for a one-second corrupted
signal. Run the developed program with a trail of delay value D and plot the noisy signal,
the enhanced signals, and their spectra.
b. Run your simulation to find the delay value D that achieves the largest noise reduction.
10.7.2 MATLAB Projects
10.27. Active noise control:

The ANC (active noise control) system is based on the principle of superposition of the primary
noise source and secondary source with its acoustic output being the same amplitude but the
opposite phase of the primary noise source, as shown in Figure 10.32 . The primary noise is
captured using the reference microphone, which is located close to the noise source. The ANC
system uses the sensed reference signal xðnÞ to generate a canceling signal yðnÞ , which drives
the secondary speaker to destructively attenuate the primary noise. An error microphone is
used to detect the residue noise eðnÞ , which is fed back to the ANC system to monitor the
system performance. The residue noise eðnÞ together with the reference signal xðnÞ are used
by the linear adaptive controller whose coefficients are adjusted via an adaptive algorithm to
minimize the measured error signal eðnÞ , or the residue acoustic noise. PðzÞ designates the
physical primary path between the reference sensor and the error sensor, and SðzÞ designates
the physical secondary path between the ANC adaptive filter output and the error sensor. To
control the noise at the cancelling point, the instantaneous power e

2

ðnÞ must be minimized.

Note that

EðzÞ¼DðzÞYðzÞSðzÞ¼DðzÞ½WðzÞXðzÞSðzÞ

where WðzÞ denotes the adaptive control filter. Exchange of the filter order (since the filters are
linear filters) gives

EðzÞ¼DðzÞWðzÞ½SðzÞXðzÞ ¼ DðzÞYðzÞ

Assuming that SðzÞ is the secondary path estimate and noticing that UðzÞ¼SðzÞXðzÞ and
YðzÞ¼WðzÞXðzÞ are the filtered reference signal and adaptive filter output, applying the
LMS algorithm gives the filtered-x LMS algorithm
wðiÞ¼wðiÞþ 2 meðnÞuðn iÞ