# Author: Travis Oliphant
# 2003
#
# Feb. 2010: Updated by Warren Weckesser:
#   Rewrote much of chirp()
#   Added sweep_poly()
from __future__ import division, print_function, absolute_import

import numpy as np
from numpy import asarray, zeros, place, nan, mod, pi, extract, log, sqrt, \
    exp, cos, sin, polyval, polyint

from scipy._lib.six import string_types


__all__ = ['sawtooth', 'square', 'gausspulse', 'chirp', 'sweep_poly',
           'unit_impulse']


def sawtooth(t, width=1):
    """
    Return a periodic sawtooth or triangle waveform.

    The sawtooth waveform has a period ``2*pi``, rises from -1 to 1 on the
    interval 0 to ``width*2*pi``, then drops from 1 to -1 on the interval
    ``width*2*pi`` to ``2*pi``. `width` must be in the interval [0, 1].

    Note that this is not band-limited.  It produces an infinite number
    of harmonics, which are aliased back and forth across the frequency
    spectrum.

    Parameters
    ----------
    t : array_like
        Time.
    width : array_like, optional
        Width of the rising ramp as a proportion of the total cycle.
        Default is 1, producing a rising ramp, while 0 produces a falling
        ramp.  `width` = 0.5 produces a triangle wave.
        If an array, causes wave shape to change over time, and must be the
        same length as t.

    Returns
    -------
    y : ndarray
        Output array containing the sawtooth waveform.

    Examples
    --------
    A 5 Hz waveform sampled at 500 Hz for 1 second:

    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> t = np.linspace(0, 1, 500)
    >>> plt.plot(t, signal.sawtooth(2 * np.pi * 5 * t))

    """
    t, w = asarray(t), asarray(width)
    w = asarray(w + (t - t))
    t = asarray(t + (w - w))
    if t.dtype.char in ['fFdD']:
        ytype = t.dtype.char
    else:
        ytype = 'd'
    y = zeros(t.shape, ytype)

    # width must be between 0 and 1 inclusive
    mask1 = (w > 1) | (w < 0)
    place(y, mask1, nan)

    # take t modulo 2*pi
    tmod = mod(t, 2 * pi)

    # on the interval 0 to width*2*pi function is
    #  tmod / (pi*w) - 1
    mask2 = (1 - mask1) & (tmod < w * 2 * pi)
    tsub = extract(mask2, tmod)
    wsub = extract(mask2, w)
    place(y, mask2, tsub / (pi * wsub) - 1)

    # on the interval width*2*pi to 2*pi function is
    #  (pi*(w+1)-tmod) / (pi*(1-w))

    mask3 = (1 - mask1) & (1 - mask2)
    tsub = extract(mask3, tmod)
    wsub = extract(mask3, w)
    place(y, mask3, (pi * (wsub + 1) - tsub) / (pi * (1 - wsub)))
    return y


def square(t, duty=0.5):
    """
    Return a periodic square-wave waveform.

    The square wave has a period ``2*pi``, has value +1 from 0 to
    ``2*pi*duty`` and -1 from ``2*pi*duty`` to ``2*pi``. `duty` must be in
    the interval [0,1].

    Note that this is not band-limited.  It produces an infinite number
    of harmonics, which are aliased back and forth across the frequency
    spectrum.

    Parameters
    ----------
    t : array_like
        The input time array.
    duty : array_like, optional
        Duty cycle.  Default is 0.5 (50% duty cycle).
        If an array, causes wave shape to change over time, and must be the
        same length as t.

    Returns
    -------
    y : ndarray
        Output array containing the square waveform.

    Examples
    --------
    A 5 Hz waveform sampled at 500 Hz for 1 second:

    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> t = np.linspace(0, 1, 500, endpoint=False)
    >>> plt.plot(t, signal.square(2 * np.pi * 5 * t))
    >>> plt.ylim(-2, 2)

    A pulse-width modulated sine wave:

    >>> plt.figure()
    >>> sig = np.sin(2 * np.pi * t)
    >>> pwm = signal.square(2 * np.pi * 30 * t, duty=(sig + 1)/2)
    >>> plt.subplot(2, 1, 1)
    >>> plt.plot(t, sig)
    >>> plt.subplot(2, 1, 2)
    >>> plt.plot(t, pwm)
    >>> plt.ylim(-1.5, 1.5)

    """
    t, w = asarray(t), asarray(duty)
    w = asarray(w + (t - t))
    t = asarray(t + (w - w))
    if t.dtype.char in ['fFdD']:
        ytype = t.dtype.char
    else:
        ytype = 'd'

    y = zeros(t.shape, ytype)

    # width must be between 0 and 1 inclusive
    mask1 = (w > 1) | (w < 0)
    place(y, mask1, nan)

    # on the interval 0 to duty*2*pi function is 1
    tmod = mod(t, 2 * pi)
    mask2 = (1 - mask1) & (tmod < w * 2 * pi)
    place(y, mask2, 1)

    # on the interval duty*2*pi to 2*pi function is
    #  (pi*(w+1)-tmod) / (pi*(1-w))
    mask3 = (1 - mask1) & (1 - mask2)
    place(y, mask3, -1)
    return y


def gausspulse(t, fc=1000, bw=0.5, bwr=-6, tpr=-60, retquad=False,
               retenv=False):
    """
    Return a Gaussian modulated sinusoid:

        ``exp(-a t^2) exp(1j*2*pi*fc*t).``

    If `retquad` is True, then return the real and imaginary parts
    (in-phase and quadrature).
    If `retenv` is True, then return the envelope (unmodulated signal).
    Otherwise, return the real part of the modulated sinusoid.

    Parameters
    ----------
    t : ndarray or the string 'cutoff'
        Input array.
    fc : int, optional
        Center frequency (e.g. Hz).  Default is 1000.
    bw : float, optional
        Fractional bandwidth in frequency domain of pulse (e.g. Hz).
        Default is 0.5.
    bwr : float, optional
        Reference level at which fractional bandwidth is calculated (dB).
        Default is -6.
    tpr : float, optional
        If `t` is 'cutoff', then the function returns the cutoff
        time for when the pulse amplitude falls below `tpr` (in dB).
        Default is -60.
    retquad : bool, optional
        If True, return the quadrature (imaginary) as well as the real part
        of the signal.  Default is False.
    retenv : bool, optional
        If True, return the envelope of the signal.  Default is False.

    Returns
    -------
    yI : ndarray
        Real part of signal.  Always returned.
    yQ : ndarray
        Imaginary part of signal.  Only returned if `retquad` is True.
    yenv : ndarray
        Envelope of signal.  Only returned if `retenv` is True.

    See Also
    --------
    scipy.signal.morlet

    Examples
    --------
    Plot real component, imaginary component, and envelope for a 5 Hz pulse,
    sampled at 100 Hz for 2 seconds:

    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> t = np.linspace(-1, 1, 2 * 100, endpoint=False)
    >>> i, q, e = signal.gausspulse(t, fc=5, retquad=True, retenv=True)
    >>> plt.plot(t, i, t, q, t, e, '--')

    """
    if fc < 0:
        raise ValueError("Center frequency (fc=%.2f) must be >=0." % fc)
    if bw <= 0:
        raise ValueError("Fractional bandwidth (bw=%.2f) must be > 0." % bw)
    if bwr >= 0:
        raise ValueError("Reference level for bandwidth (bwr=%.2f) must "
                         "be < 0 dB" % bwr)

    # exp(-a t^2) <->  sqrt(pi/a) exp(-pi^2/a * f^2)  = g(f)

    ref = pow(10.0, bwr / 20.0)
    # fdel = fc*bw/2:  g(fdel) = ref --- solve this for a
    #
    # pi^2/a * fc^2 * bw^2 /4=-log(ref)
    a = -(pi * fc * bw) ** 2 / (4.0 * log(ref))

    if isinstance(t, string_types):
        if t == 'cutoff':  # compute cut_off point
            #  Solve exp(-a tc**2) = tref  for tc
            #   tc = sqrt(-log(tref) / a) where tref = 10^(tpr/20)
            if tpr >= 0:
                raise ValueError("Reference level for time cutoff must "
                                 "be < 0 dB")
            tref = pow(10.0, tpr / 20.0)
            return sqrt(-log(tref) / a)
        else:
            raise ValueError("If `t` is a string, it must be 'cutoff'")

    yenv = exp(-a * t * t)
    yI = yenv * cos(2 * pi * fc * t)
    yQ = yenv * sin(2 * pi * fc * t)
    if not retquad and not retenv:
        return yI
    if not retquad and retenv:
        return yI, yenv
    if retquad and not retenv:
        return yI, yQ
    if retquad and retenv:
        return yI, yQ, yenv


def chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True):
    """Frequency-swept cosine generator.

    In the following, 'Hz' should be interpreted as 'cycles per unit';
    there is no requirement here that the unit is one second.  The
    important distinction is that the units of rotation are cycles, not
    radians. Likewise, `t` could be a measurement of space instead of time.

    Parameters
    ----------
    t : array_like
        Times at which to evaluate the waveform.
    f0 : float
        Frequency (e.g. Hz) at time t=0.
    t1 : float
        Time at which `f1` is specified.
    f1 : float
        Frequency (e.g. Hz) of the waveform at time `t1`.
    method : {'linear', 'quadratic', 'logarithmic', 'hyperbolic'}, optional
        Kind of frequency sweep.  If not given, `linear` is assumed.  See
        Notes below for more details.
    phi : float, optional
        Phase offset, in degrees. Default is 0.
    vertex_zero : bool, optional
        This parameter is only used when `method` is 'quadratic'.
        It determines whether the vertex of the parabola that is the graph
        of the frequency is at t=0 or t=t1.

    Returns
    -------
    y : ndarray
        A numpy array containing the signal evaluated at `t` with the
        requested time-varying frequency.  More precisely, the function
        returns ``cos(phase + (pi/180)*phi)`` where `phase` is the integral
        (from 0 to `t`) of ``2*pi*f(t)``. ``f(t)`` is defined below.

    See Also
    --------
    sweep_poly

    Notes
    -----
    There are four options for the `method`.  The following formulas give
    the instantaneous frequency (in Hz) of the signal generated by
    `chirp()`.  For convenience, the shorter names shown below may also be
    used.

    linear, lin, li:

        ``f(t) = f0 + (f1 - f0) * t / t1``

    quadratic, quad, q:

        The graph of the frequency f(t) is a parabola through (0, f0) and
        (t1, f1).  By default, the vertex of the parabola is at (0, f0).
        If `vertex_zero` is False, then the vertex is at (t1, f1).  The
        formula is:

        if vertex_zero is True:

            ``f(t) = f0 + (f1 - f0) * t**2 / t1**2``

        else:

            ``f(t) = f1 - (f1 - f0) * (t1 - t)**2 / t1**2``

        To use a more general quadratic function, or an arbitrary
        polynomial, use the function `scipy.signal.sweep_poly`.

    logarithmic, log, lo:

        ``f(t) = f0 * (f1/f0)**(t/t1)``

        f0 and f1 must be nonzero and have the same sign.

        This signal is also known as a geometric or exponential chirp.

    hyperbolic, hyp:

        ``f(t) = f0*f1*t1 / ((f0 - f1)*t + f1*t1)``