Weiner filtering.pptx
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The Wiener filter is used to estimate a desired signal by filtering an observed noisy signal using linear time-invariant filtering, assuming known stationary signal and noise spectra with additive noise. The Wiener filter coefficients are calculated to minimize the average squared distance between the filter output and desired signal. The input signal is convolved with the Wiener filter and compared to a reference signal to obtain the filtering error, with the output being an estimate of noise or interference subtracted from the desired signal.
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- 2. Introduction to Wiener Filtering The Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise.
- 3. Wiener Filter Design The steps involved in designing a Wiener filter: ● Estimating autocorrelation functions. ● Computing the Wiener filter coefficients. ● Filtering process.
- 4. Estimating Autocorrelation Functions ● Sample autocorrelation. ● Periodogram.
- 5. Computing Wiener Filter Coefficients The coefficients of a Wiener filter are calculated to minimise the average squared distance between the filter output and a desired signal. In its basic form, the Wiener theory assumes that the signals are stationary processes.
- 6. Filtering Process ● Input and reference signals. ● Filtering operation. ● Output signal.
- 7. In sum, the "desired signal" is often a signal contaminated with noise or interference, and the output of the Wiener filter is an estimate of that noise or interference, which is subtracted from the "desired signal".
- 8. Input and reference signals. An input signal w[n] is convolved with the Wiener filter g[n] and the result is compared to a reference signal s[n] to obtain the filtering error e[n].
- 9. Filtering operation Wiener filters are comparatively slow to apply, since they require working in the frequency domain. To speed up filtering, one can take the inverse FFT of the Wiener filter G(u,v) to obtain an impulse response g(n,m). This impulse response can be truncated spatially to produce a convolution mask.
- 10. Output signal In sum, the "desired signal" is often a signal contaminated with noise or interference, and the output of the Wiener filter is an estimate of that noise or interference, which is subtracted from the "desired signal".