Source code for deltasigma._zinc

# -*- coding: utf-8 -*-
# _zinc.py
# The zinc 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 zinc() function which calculates the magnitude
response of a cascade of comb filters.
"""

import numpy as np


def zinc(f, m=64, n=1):
    """Calculate the magnitude response of a cascade of ``n`` ``m``-th order comb filters.

    The magnitude of the filter response is calculated mathematically as:

    .. math::

        \\left|H(f)\\right| = \\left|\\frac{\\mathrm{sinc}(m f)}{\\mathrm{sinc}(f)}\\right|^n

    **Parameters:**

    f : ndarray
        The frequencies at which the magnitude response is evaluated.

    m : int, optional
        The order of the comb filters.

    n : int, optional
        The number of comb filters in the cascade.

    **Returns:**

    HM : ndarray
        The magnitude of the frequency response of the cascade filter.

    """
    return np.fabs(np.sinc(m * f) / np.sinc(f)) ** n