Dmitrij
Advanced Member level 4
Smoothing procedure is usually done in order to decrease the influence of noise and to reach analytical equality between all components of the signal. The ways of smoothing are numerous: interpolation, approximation, convolution, wavelets, etc.
My question is connected with convolution. It means that after convolving initial function with the special kernel we get the smoothed representation. Criterion of smoothing - the amount of extrema. The more it is, the less smoothed is the signal.
Lindberg proved that convolution with Gaussian function doesn't generate new extrema. My question is - are there any other functions, that also don't lead to appearance of new extrema? Or may be you'll introduce a well-known smoothing technique, familiar to you?
With respect,
Dmitrij
My question is connected with convolution. It means that after convolving initial function with the special kernel we get the smoothed representation. Criterion of smoothing - the amount of extrema. The more it is, the less smoothed is the signal.
Lindberg proved that convolution with Gaussian function doesn't generate new extrema. My question is - are there any other functions, that also don't lead to appearance of new extrema? Or may be you'll introduce a well-known smoothing technique, familiar to you?
With respect,
Dmitrij