MATLAB Code Implementation of Wiener Filter for Noise Reduction

Wiener filtering is a classical linear filtering method primarily used for recovering original signals from noise-corrupted observations. Its core principle involves optimal signal estimation under the minimum mean square error (MMSE) criterion.

For implementing Wiener filter denoising functionality in MATLAB, recursive algorithms can be employed to enhance computational efficiency. The key aspect of recursive Wiener filtering lies in progressively updating filter coefficients to adapt to non-stationary signal characteristics. The specific implementation approach includes:

Signal Modeling: First assume the observed signal consists of the original signal and additive noise, requiring estimation of noise statistical properties (such as mean and variance) along with signal prior information. Code implementation typically involves using MATLAB's statistical functions like mean() and var() for parameter estimation.

Wiener Filter Coefficient Calculation: Based on the autocorrelation functions of both signal and noise, compute optimal weights for the Wiener filter. Recursive algorithms commonly utilize Recursive Least Squares (RLS) or Kalman filter concepts to dynamically adjust filter parameters, enabling better tracking of signal variations. In MATLAB, this can be implemented using adaptive filter objects or custom RLS algorithms with matrix operations.

Filtering Process: Apply the computed filter coefficients to the noisy signal, performing sample-by-sample or block-wise filtering to gradually optimize the estimated output signal. This can be achieved through MATLAB's filter() function or real-time processing using for-loops with buffer management.

Performance Evaluation: Filter effectiveness can be verified by calculating Mean Square Error (MSE) or Signal-to-Noise Ratio Improvement (SNR Improvement). MATLAB provides functions like mse() and snr() for quantitative analysis, along with visualization tools for comparing original and filtered signals.

This recursive implementation approach not only suits stationary signals but also effectively handles denoising problems for non-stationary signals, offering high flexibility and practical utility in real-world applications.