ó ˽÷Xc@`s*ddlmZmZmZddlZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZddlmZddddd d gZd d „Zd d„Zdd ddeed„Zdded„Zded„Zdd„Zd„Zde!d„Z"dS(i(tdivisiontprint_functiontabsolute_importN(tasarraytzerostplacetnantmodtpitextracttlogtsqrttexptcostsintpolyvaltpolyint(t string_typestsawtoothtsquaret gausspulsetchirpt sweep_polyt unit_impulseic C`set|ƒt|ƒ}}t|||ƒ}t|||ƒ}|jjdkrb|jj}nd}t|j|ƒ}|dk|dkB}t||tƒt|dtƒ}d|||dtk@}t ||ƒ}t ||ƒ} t|||t| dƒd|d|@} t | |ƒ}t | |ƒ} t|| t| d|td| ƒ|S(s™ 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)) tfFdDtdiii(R( RtdtypetcharRtshapeRRRRR ( tttwidthtwtytypetytmask1ttmodtmask2ttsubtwsubtmask3((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyRs&&(gà?c C`st|ƒt|ƒ}}t|||ƒ}t|||ƒ}|jjdkrb|jj}nd}t|j|ƒ}|dk|dkB}t||tƒt|dtƒ}d|||dtk@}t||dƒd|d|@}t||dƒ|S(s' 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) RRiiiiÿÿÿÿ(sfFdD( RRRRRRRRR( RtdutyRR R!R"R#R$R'((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyR[s0ièiúÿÿÿiÄÿÿÿc C`s¨|dkrtd|ƒ‚n|dkr>td|ƒ‚n|dkr]td|ƒ‚ntd|dƒ}t||d dt|ƒ}t|tƒrþ|d krï|dkrÇtd ƒ‚ntd|dƒ} tt| ƒ |ƒStd ƒ‚nt| ||ƒ} | tdt||ƒ} | t dt||ƒ} | r]| r]| S| rt|rt| | fS|r‹| r‹| | fS|r¤|r¤| | | fSd S( sD Return a Gaussian modulated sinusoid: ``exp(-a t^2) exp(1j*2*pi*fc*t).`` If `retquad` is True, then return the real and imaginary parts (in-phase and quadrature). If `retenv` is True, then return the envelope (unmodulated signal). Otherwise, return the real part of the modulated sinusoid. Parameters ---------- t : ndarray or the string 'cutoff' Input array. fc : int, optional Center frequency (e.g. Hz). Default is 1000. bw : float, optional Fractional bandwidth in frequency domain of pulse (e.g. Hz). Default is 0.5. bwr : float, optional Reference level at which fractional bandwidth is calculated (dB). Default is -6. tpr : float, optional If `t` is 'cutoff', then the function returns the cutoff time for when the pulse amplitude falls below `tpr` (in dB). Default is -60. retquad : bool, optional If True, return the quadrature (imaginary) as well as the real part of the signal. Default is False. retenv : bool, optional If True, return the envelope of the signal. Default is False. Returns ------- yI : ndarray Real part of signal. Always returned. yQ : ndarray Imaginary part of signal. Only returned if `retquad` is True. yenv : ndarray Envelope of signal. Only returned if `retenv` is True. See Also -------- scipy.signal.morlet Examples -------- Plot real component, imaginary component, and envelope for a 5 Hz pulse, sampled at 100 Hz for 2 seconds: >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> t = np.linspace(-1, 1, 2 * 100, endpoint=False) >>> i, q, e = signal.gausspulse(t, fc=5, retquad=True, retenv=True) >>> plt.plot(t, i, t, q, t, e, '--') is'Center frequency (fc=%.2f) must be >=0.s+Fractional bandwidth (bw=%.2f) must be > 0.s7Reference level for bandwidth (bwr=%.2f) must be < 0 dBg$@g4@ig@tcutoffs.Reference level for time cutoff must be < 0 dBs'If `t` is a string, it must be 'cutoff'N( t ValueErrortpowRR t isinstanceRR R R R( RtfctbwtbwrttprtretquadtretenvtreftattreftyenvtyItyQ((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyR¥s6;    !       tlinearcC`s7t||||||ƒ}|td9}t||ƒS(s\ 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.waveforms.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)`` f0 and f1 must be nonzero. i´(t _chirp_phaseRR (Rtf0tt1tf1tmethodtphit vertex_zerotphase((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyRsUc C`s#t|ƒ}t|ƒ}t|ƒ}t|ƒ}|dkro|||}dt||d|||}n°|dkré|||d}|r¸dt||||d d }qdt|||||d |d d }n6|dkrw||d krtdƒ‚n||kr5dt||}q|t||ƒ}dt||t||||ƒd}n¨|dkr|dks›|dkrªtdƒ‚n||krËdt||}q| |||}dt| |ttjd||ƒƒ}ntd|ƒ‚|S(s… Calculate the phase used by chirp_phase to generate its output. See `chirp_phase` for a description of the arguments. R9tlintliigà?t quadratictquadtqit logarithmicR tlogsJFor a logarithmic chirp, f0 and f1 must be nonzero and have the same sign.gð?t hyperbolicthypis2For a hyperbolic chirp, f0 and f1 must be nonzero.isbmethod must be 'linear', 'quadratic', 'logarithmic', or 'hyperbolic', but a value of %r was given.(R9RBRC(RDRERF(RGslogslo(RIRJ(RtfloatRR*R R+tnptabs( RR;R<R=R>R@tbetaRAtsing((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyR:cs:     % %1  .  1 cC`s+t||ƒ}|td9}t||ƒS(s@ Frequency-swept cosine generator, with a time-dependent frequency. This function generates a sinusoidal function whose instantaneous frequency varies with time. The frequency at time `t` is given by the polynomial `poly`. Parameters ---------- t : ndarray Times at which to evaluate the waveform. poly : 1-D array_like or instance of numpy.poly1d The desired frequency expressed as a polynomial. If `poly` is a list or ndarray of length n, then the elements of `poly` are the coefficients of the polynomial, and the instantaneous frequency is ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]`` If `poly` is an instance of numpy.poly1d, then the instantaneous frequency is ``f(t) = poly(t)`` phi : float, optional Phase offset, in degrees, Default: 0. Returns ------- sweep_poly : 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 above. See Also -------- chirp Notes ----- .. versionadded:: 0.8.0 If `poly` is a list or ndarray of length `n`, then the elements of `poly` are the coefficients of the polynomial, and the instantaneous frequency is: ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]`` If `poly` is an instance of `numpy.poly1d`, then the instantaneous frequency is: ``f(t) = poly(t)`` Finally, the output `s` is: ``cos(phase + (pi/180)*phi)`` where `phase` is the integral from 0 to `t` of ``2 * pi * f(t)``, ``f(t)`` as defined above. i´(t_sweep_poly_phaseRR (RtpolyR?RA((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyR˜s@cC`s't|ƒ}dtt||ƒ}|S(sƒ Calculate the phase used by sweep_poly to generate its output. See `sweep_poly` for a description of the arguments. i(RRR(RRQtintpolyRA((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyRPÞs cC`st||ƒ}tj|ƒ}|dkr=dt|ƒ}nD|dkr\t|dƒ}n%t|dƒs|ft|ƒ}nd||<|S(s# Unit impulse signal (discrete delta function) or unit basis vector. Parameters ---------- shape : int or tuple of int Number of samples in the output (1-D), or a tuple that represents the shape of the output (N-D). idx : None or int or tuple of int or 'mid', optional Index at which the value is 1. If None, defaults to the 0th element. If ``idx='mid'``, the impulse will be centered at ``shape // 2`` in all dimensions. If an int, the impulse will be at `idx` in all dimensions. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. Returns ------- y : ndarray Output array containing an impulse signal. Notes ----- The 1D case is also known as the Kronecker delta. .. versionadded:: 0.19.0 Examples -------- An impulse at the 0th element (:math:`\delta[n]`): >>> from scipy import signal >>> signal.unit_impulse(8) array([ 1., 0., 0., 0., 0., 0., 0., 0.]) Impulse offset by 2 samples (:math:`\delta[n-2]`): >>> signal.unit_impulse(7, 2) array([ 0., 0., 1., 0., 0., 0., 0.]) 2-dimensional impulse, centered: >>> signal.unit_impulse((3, 3), 'mid') array([[ 0., 0., 0.], [ 0., 1., 0.], [ 0., 0., 0.]]) Impulse at (2, 2), using broadcasting: >>> signal.unit_impulse((4, 4), 2) array([[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 1., 0.], [ 0., 0., 0., 0.]]) Plot the impulse response of a 4th-order Butterworth lowpass filter: >>> imp = signal.unit_impulse(100, 'mid') >>> b, a = signal.butter(4, 0.2) >>> response = signal.lfilter(b, a, imp) >>> import matplotlib.pyplot as plt >>> plt.plot(np.arange(-50, 50), imp) >>> plt.plot(np.arange(-50, 50), response) >>> plt.margins(0.1, 0.1) >>> plt.xlabel('Time [samples]') >>> plt.ylabel('Amplitude') >>> plt.grid(True) >>> plt.show() itmidit__iter__iN(i(RRLt atleast_1dtNonetlenttuplethasattr(RtidxRtout((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyRësI   (#t __future__RRRtnumpyRLRRRRRRR R R R R RRRtscipy._lib.sixRt__all__RRtFalseRtTrueRR:RRPRVRKR(((s5/tmp/pip-build-7oUkmx/scipy/scipy/signal/waveforms.pyts ^  G J b[5 F