# Name

- noise_corrected_PW - returns a noise corrected power spectrum and the factors a and b which were used to subtract the function f(x)=exp( a*x*x+b ) from the original power spectrum

# Usage

- freq,pw_ns,b_factor,norm = noise_corrected_PW(pw,lo_limit,hi_limit,abs_limit)

## Input

- ps
- a list containing the values of a power spectrum
- lo_limit
- lower frequency threshold for minima search (value between 0.0 and 0.5)
- hi_limit
- upper frequency threshold for minima search (value between 0.0 and 0.5)
- abs_limit
- upper limit of the power spectrum, no usable information is contained above this threshold

## Output

- freq
- list of corresponding frequency values
- pw_ns
- noise corrected power spectrum
- b_factor
- exponential factor
- norm
- normalization factor

# Description

- This function returns a noise corrected power spectrum, a list of corresponding frequency values and the factors a and b which were used to subtract the function f(x)=exp( a*x*x+b ) from the original power spectrum pw

# Method

- Fist the minima of the power spectrum (in the specified freq. range) are searched, then a regression (linreg) fits f(x) as described above. This function is subtracted from the original power spectrum to yield an estimate of the noise corrected spectrum. Minima are searched again. This leads to a more accurate fit of f(x) and thereby to an accurate estimation of the noise background. After subtraction a noise corrected power spectrum is returned.

# Suggested frequencies

- noise_corrected_PW(pw,0.06,0.3,0.35) worked out well for the power spectra investigated so far.

# Author / Maintainer

- Jan-Christian Schuette

# Keywords

- category 1
- STATISTICS
- category 2
- SPECTRUM
- category 3
- NOISE

# Files

statistics.py

# Maturity

- stable
- works for most people, has been tested; test cases/examples available.