# Noise reduction using pKDTW averaging principle from (2) noisy instances of a speech signal

## Signal ("quatre vingt onze"(91))+noise: Signal to Noise Ratio (SNR) is 0dB

x_{1}(t)=s(t)+ε_{1}(t), where ε_{1} is an iid Gaussian noise with zero mean and variance σ. σ is selected such that the SNR is 0dB.
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## Clean Signal and Spectrogram

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## pKDTW average Signal and Spectrogram (from two noisy instances)

x_{1}(t)=s(t)+ε_{1}(t), x_{2}(t)=s(t+τ)+ε_{2}(t)
where ε_{1} and ε_{2} are two iid Gaussian noises with zero mean and variance σ, τ is a delay randomly selected in [5,15].
σ is selected such that the SNR is 0dB.

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## DBA average Signal and Spectrogram (from two noisy instances)

Same conditions as above.
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## Euclidean average Spectrogram (from two noisy instances)

Same conditions as above. The two noisy instances are "aligned" using cross correlation and the Euclidean average is computed.
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## Signal + Noise + Low pass filter and Spectrogram

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## Noisy Signal and Spectrogram

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