_rms.py

# -*- coding: utf-8 -*-
# _rms.py
# This module provides the rms function.
# Copyright 2013 Giuseppe Venturini
# This file is part of python-deltasigma.
#
# python-deltasigma is a 1:1 Python replacement of Richard Schreier's 
# MATLAB delta sigma toolbox (aka "delsigma"), upon which it is heavily based.
# The delta sigma toolbox is (c) 2009, Richard Schreier.
#
# python-deltasigma is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# LICENSE file for the licensing terms.

"""This module provides the rms() function, which calculates the Root Mean 
Square (RMS) of a vector.
"""

import numpy as np
import numpy.linalg as la

def rms(x, no_dc=False):
	"""Calculates the RMS value of x

	The Root Mean Square value of an array :math:`x` of length :math:`n` is defined as:

	.. math::

	    x_{RMS} = \\sqrt{\\frac{1}{n}(x_1^2 + x_2^2 + ...+x_n^2)}

	**Parameters:**

	x : (N,) ndarray
	    The input vector

	no_dc : boolean, optional
	    If set to ``True``, the DC value gets subtracted from ``x`` first and the RMS is computed on the result.

	**Returns:**

	xrms : scalar
	    as defined above

	"""
	if no_dc:
	    x = x - np.mean(x)
	return la.norm(x)/np.sqrt(max(x.shape))
	
def test_rms():
	"""Test function for rms()
	"""
	tv = np.arange(100)
	res1 = np.sqrt(np.sum(tv**2.)/float(tv.shape[0]))
	res2 = np.sqrt((np.sum((tv - tv.mean())**2.))/tv.shape[0])
	assert np.allclose(rms(tv), res1, rtol=1e-05, atol=1e-08)
	assert np.allclose(rms(tv, no_dc=True), res2, rtol=1e-05, atol=1e-08)