Two Simple Smoothers

Four lines of code. Good smoothing properties.

SMOOTH1 and SMOOTH2 each smooth a data sequence by convolving it with a filter that's well-suited to smoothing. The output and its first two derivatives will be smooth.

Each smoother is controlled by a user-supplied response time, in units of samples, which produces about the same agility as a moving average of that many samples. The output is much smoother though, due to far greater high-frequency attenuation.

SMOOTH1's impulse response is nonnegative, like a Gaussian but compact. SMOOTH2's impulse response has just enough of a negative outer lobe to flatten the low-frequency response and give perfect response to a quadratic input component. Which to prefer is hard to say, or may depend on the application.

Both smoothers provide strong high-frequency attenuation. Their frequency response "sidelobes" start below -60 dB and fall 18 dB per octave, making even the double-differentiated output smooth.

See also LSSMOOTH (ID:49789), IRLSSMOOTH (ID:49788)