Noise Reduction via Adaptive Temporal Filtering
The use of adaptive filters for reducing the noise content is based on the assumption that the frequency content of the event shall be unique from the background noise. This is readily justified for the case in which the background noise is continuous and the event is transient. The transient behavior implies that the frequency content of the event shall be spread out over many frequency bins due to its impulsive temporal characteristics. Additionally, for many sources of background noise, the spectral content is quite low. For engine based noise, the signal is inherently periodic in nature based on the primary excitation modes of the rotating structures. The frequency content between engine types and configurations can vary a great deal. The spectral signature of a single cylinder engine on a test stand is considerably simpler than a turbine or 16 cylinder diesel with their associated gear trains. The frequency components for these sources can be isolated and matched to appropriately tuned FIR or IIR filter banks to reduce their amplitude. The feed forward variety (FIR) formulations offer a higher degree of stability but typically require many more taps to realize a given frequency response. The basic formulation of an LMS adaptive FIR filter is:
This iterative adaptation of the weights utilizes gradient descent to assign filter tap coefficients such that the observed difference between the filter and the desired output are minimized. There are two key tuning parameters that directly affect the convergence behavior; the number of filter taps used and the step size m . This algorithm is typically extended to include a normalization factor to the weight adaptation:
Additionally, a leakage factor may be introduced to allow the filter to "forget" its learned weights over time. This helps the weights adapt to different learning modes and avoid local minima.
There are several variations on the filter tap update algorithms, including the Recursive Least Square , Fast Newton Transversal Filter, Affine Projection Algorithm, and the Fast Affine Projection. All are viable candidates for noise reduction with varying convergence and computation characteristics.
To evaluate the applicability of adaptive filters to suppression of background noise for transient event identification, a dataset of background noises and events were obtained. The background noises were of 4 main classes; boats, diesel engines, jet engines, and helicopters. For each of these four classes 3 distinct examples were obtained, bringing the number of background noises to 12. The transient events that were obtained were of two footsteps, one lock being turned, one glass breaking, one door creaking, and one hammer striking. The event amplitudes were then reduced and combined with the various background noises to define signatures which were dominated by the noise. The SNR of these corrupted events ranged from -43dB to -22dB.
, where x is the event, M = number of samples in event, y is the noise and N = 1sec worth of samples (22000).
A total of 72 noise corrupted signatures were processed using adaptive filters to determine the applicability of adaptive filters to this problem domain. This dataset was processed using an adaptive FIR containing 91 taps, m = .5 with a = 1.0.