# Source code for deltasigma._ds_hann

# -*- coding: utf-8 -*-
# _ds_hann.py
# This module provides the ds_hann function.
# 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 ds_hann() function, used to generate a Hann
window that does not smear tones located exactly in a bin.
"""

import numpy as np

[docs]def ds_hann(n):
"""A Hann window of length :math:n.

The Hann window, aka *the raised cosine window*, is defined as:

.. math::

w(x) = 0.5\\ \\left(1 - cos\\left(\\frac{2 \\pi x}{n}\\right) \\right)

This windowing function does not smear tones located exactly in a bin.

**Parameters:**

n : integer
The window length, in number of samples.

**Returns:**

w : 1d nd_array
The Hann window.

.. note:: Functionally equivalent to numpy's hanning(), provided
to ease porting of code from MATLAB. Also, we take care always to
return an array of dimensions (n,) and type float_.

.. plot::

import pylab as plt
from deltasigma import ds_hann
x = ds_hann(100)
plt.figure(figsize=(12, 5))
plt.plot(x, 'o-')
ax = plt.gca()
ax.set_ylim(0, 1.02)
plt.grid(True)
plt.title("100-samples Hann window")
plt.xlabel("Sample #")
plt.ylabel("Value")

"""
x = np.arange(n, dtype='float_')
return .5*(1 - np.cos(2*np.pi*x/n))