detrend

Builtin index · Noise

result = detrend(x, [order=1])

Input: x, order · Output: result

What it is

Subtracts a least-squares polynomial trend from x, a length-N number vector. order is an optional positional integer: 0 removes the mean, 1 (default) a linear drift, 2 a quadratic bow.

Overloads

One call shape — this function is not overloaded.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

print(detrend([1, 2, nan, 4], 0))   # [NaN, NaN, NaN, NaN]

[NaN, NaN, NaN, NaN]

from noise

fs = 1000
n = 500
t = (0 to n - 1) / fs
clean = sin(2 * pi * 7 * t)

spike = 5 * impulse(n, index = 200)
corrupted = clean + spike + 0.01 * (0 to n - 1)   # a spike, plus baseline drift


fixed = medfilt(corrupted, 5)     # the spike

flat = detrend(fixed, 1)          # the ramp

sg = savgol(flat, 11, 2)          # a final polish, shape-preserving

sm = smooth(flat, 11)             # same thing, one word (default method is savgol)

print("after cleanup: {measure_snr(clean, sg):.2f} dB (savgol), {measure_snr(clean, sm):.2f} dB (smooth)")

after cleanup: 17.81 dB (savgol), 17.81 dB (smooth)

from noise

How it works

detrend(x, [order]) — remove a least-squares polynomial trend. 0 the mean, 1 a linear drift, 2 a bow. Usually the first step of an analysis, because baseline wander is what brown noise looks like after the fact.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.