Smoothing 1D data by moving different filter shapes

Smoothing a 1D curve by weighted moving average. The filtering is done by convolution with different filter types. Also with automatic mode.

Smoothing a 1D curve by weighted moving average. The averaging is done by convolution with different filter types. Also with automatic generation of suitable filters.

The main difference to Malab's smoothing filter is: For full curve filtering the curve is linear extrapolated on both sides and not zero padded. Therefore the border values are much better than Matlab's smoothing filters or convolutions.

Features:

Moving average:

• Filter width set as odd whole number: filter is all ones

E.g. 5 -> [1 1 1 1 1]

• Filter width set as floating number: filter is triangle shaped

E.g. 3.5- > [0.5 0.75 1 0.75 0.5]

• Filter width not set: Automatic mode, width determined by FFT

Gaussian shaped filter:

• Width and sigma set: Gaussian filter according those values
• Width set and sigma=0: Gaussian filter according width and default sigma
• Width=0: Automatic mode, width determined by FFT and default sigma

User defined filter:

You may set any filter as long as the sum is not equal zero.

E.g. [1 1]

Manual:

Invoke the function with: [ys,fout,sout]=smooth1Dconv(y,w(optional),s(optional))

Input:

The first argument y is the vector to be smoothed.

The 2nd argument, called w (width of filter), is optional

The 3rd argument, called s (sigma of filter), is optional

Four modes are possible:

1.) w and s omitted: Moving average auto filter.

Filter width is determined by FFT, an odd number.

2.) w is a single integer odd number or floating number, s is omitted:

Moving average, all ones for integer odd numbers

or triangle shaped filter for all other numbers.

The center value is always one; the sum of the filter values is w.

If w<=1, no filtering

Examples:

w=1.5 -> filter=[0.25 1 0.25]

w=2.8 -> filter=[0.9 1 0.9]

w=3 -> filter=[1 1 1], w is an integer odd number!

w=3.5 -> filter=[0.5 0.75 1 0.75 0.5]

w=4 -> filter=[0.667 0.833 1 0.833 0.667]

3.) w and s set: Gaussian shaped filter

w is the width of the filter.

If w is not an odd integer number, then the next lower integer w is taken.

s is the sigma of the filter, if sigma=0, then s=(w-1)/4;

If w=0: Auto Gaussian filter width is determined by FFT, s input is discarded.

w>y-data size: w is resized to fit

4.) w is a vector

w are filter values (e.g. [0.5 1 0.5])

w-size>y-data size: w border values are cut to fit

Output:

ys: smoothed y

fout: filter used

sout: sigma used, NaN if not used

Remark:

The border values of the smoothed output ys are approximations. In order to calculate those values, the input y is extended by extrapolation of the smoothed input. The approximated border output is one half of the filter width.

If you want to smooth sine curves, you should also look at:

https://de.mathworks.com/matlabcentral/fileexchange/66793-sine-fitting