tftb.generators package

Submodules

tftb.generators.amplitude_modulated module

tftb.generators.amplitude_modulated.amexpos(n_points, t0=None, spread=None, kind='bilateral')[source]

Exponential amplitude modulation.

amexpos generates an exponential amplitude modulation starting at time t0 and spread proportioanl to spread.

Parameters:
  • n_points (int) – Number of points.
  • kind (str) – “bilateral” (default) or “unilateral”
  • t0 (float) – Time center.
  • spread (float) – Standard deviation.
Returns:

exponential function
Return type:

numpy.ndarray
Examples: 
>>> x = amexpos(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amexpos_bilateral.png 
>>> x = amexpos(160, kind='unilateral')
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amexpos_unilateral.png
tftb.generators.amplitude_modulated.amgauss(n_points, t0=None, spread=None)[source]

Generate a Gaussian amplitude modulated signal.

Parameters:
  • n_points (int) – Number of points in the output.
  • t0 (float) – Center of the Gaussian function. (default: t0 / 2)
  • spread (float) – Standard deviation of the Gaussian. (default 2 * sqrt(n_points)
Returns:

Gaussian function centered at time t0.
Return type:

numpy.ndarray
Example: 
>>> x = amgauss(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amgauss1.png 
>>> x = amgauss(160, 90)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amgauss2.png
tftb.generators.amplitude_modulated.amrect(n_points, t0=None, spread=None)[source]

Generate a rectangular amplitude modulation.

Parameters:
  • n_points (int) – Number of points in the function.
  • t0 (float) – Time center
  • spread (float) – standard deviation of the function.
Returns:

A rectangular amplitude modulator.
Return type:

numpy.ndarray.
Examples: 
>>> x = amrect(160, 90, 40.0)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amrect1.png
tftb.generators.amplitude_modulated.amtriang(n_points, t0=None, spread=None)[source]

Generate a triangular amplitude modulation.

Parameters:
  • n_points (int) – Number of points in the function.
  • t0 (float) – Time center
  • spread (float) – standard deviation of the function.
Returns:

A triangular amplitude modulator.
Return type:

numpy.ndarray.
Examples: 
>>> x = amtriang(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amtriang1.png

tftb.generators.analytic_signals module

tftb.generators.analytic_signals.anaask(n_points, n_comp=None, f0=0.25)[source]

Generate an amplitude shift (ASK) keying signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points of each component.
  • f0 (float) – normalized frequency.
Returns:

Tuple containing the modulated signal and the amplitude modulation.
Return type:

tuple(numpy.ndarray)
Examples: 
>>> x, am = anaask(512, 64, 0.05)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anaask.png
tftb.generators.analytic_signals.anabpsk(n_points, n_comp=None, f0=0.25)[source]

Binary phase shift keying (BPSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each component.
  • f0 (float) – normalized frequency.
Returns:

BPSK signal
Return type:

numpy.ndarray
Examples: 
>>> x, am = anabpsk(300, 30, 0.1)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anabpsk.png
tftb.generators.analytic_signals.anafsk(n_points, n_comp=None, Nbf=4)[source]

Frequency shift keying (FSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each components.
  • Nbf (int) – number of distinct frequencies.
Returns:

FSK signal.
Return type:

numpy.ndarray
Examples: 
>>> x, am = anafsk(512, 54.0, 5.0)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anafsk.png
tftb.generators.analytic_signals.anapulse(n_points, ti=None)[source]

Analytic projection of unit amplitude impulse signal.

Parameters:
  • n_points (int) – Number of points.
  • ti (float) – time position of the impulse.
Returns:

analytic impulse signal.
Return type:

numpy.ndarray
Examples: 
>>> x = 2.5 * anapulse(512, 301)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anapulse.png
tftb.generators.analytic_signals.anaqpsk(n_points, n_comp=None, f0=0.25)[source]

Quaternary Phase Shift Keying (QPSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each component.
  • f0 (float) – normalized frequency
Returns:

complex phase modulated signal of normalized frequency f0 and initial phase.
Return type:

tuple
Examples: 
>>> x, phase = anaqpsk(512, 64.0, 0.05)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(phase)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anaqpsk.png
tftb.generators.analytic_signals.anasing(n_points, t0=None, h=0.0)[source]

Lipschitz singularity. Refer to the wiki page on Lipschitz condition, good test case.

Parameters:
  • n_points (int) – number of points in time.
  • t0 (float) – time localization of singularity
  • h (float) – strength of the singularity
Returns:

N-point Lipschitz singularity centered around t0
Return type:

numpy.ndarray
Examples: 
>>> x = anasing(128)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anasing.png
tftb.generators.analytic_signals.anastep(n_points, ti=None)[source]

Analytic projection of unit step signal.

Parameters:
  • n_points (int) – Number of points.
  • ti (float) – starting position of unit step.
Returns:

output signal
Return type:

numpy.ndarray
Examples: 
>>> x = anastep(256, 128)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anastep.png

tftb.generators.frequency_modulated module

tftb.generators.frequency_modulated.fmconst(n_points, fnorm=0.25, t0=None)[source]

Generate a signal with constant frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnorm (float) – normalized frequency
  • t0 (float) – time center
Returns:

frequency modulation signal with frequency fnorm
Return type:

numpy.ndarray
Examples: 
>>> from tftb.generators import amgauss
>>> z = amgauss(128, 50, 30) * fmconst(128, 0.05, 50)[0]
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmconst.png
tftb.generators.frequency_modulated.fmhyp(n_points, p1, p2)[source]

Signal with hyperbolic frequency modulation.

Parameters:
  • n_points (int) – number of points.
  • p2 (float) – coefficients of the hyperbolic function.
Returns:

vector containing the modulated signal samples.
Return type:

numpy.ndarray
Examples: 
>>> signal, iflaw = fmhyp(128, (1, 0.5), (32, 0.1))
>>> subplot(211), plot(real(signal)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)        #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmhyp.png
tftb.generators.frequency_modulated.fmlin(n_points, fnormi=0.0, fnormf=0.5, t0=None)[source]

Generate a signal with linear frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnormi (float) – initial normalized frequency
  • fnormf (float) – final normalized frequency
  • t0 (float) – time center
Returns:

The modulated signal, and the instantaneous amplitude law.
Return type:

tuple(array-like)
Examples: 
>>> from tftb.generators import amgauss
>>> z = amgauss(128, 50, 40) * fmlin(128, 0.05, 0.3, 50)[0]
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmlin.png
tftb.generators.frequency_modulated.fmodany(iflaw, t0=1)[source]

Arbitrary frequency modulation.

Parameters:
  • iflaw (numpy.ndarray) – Vector of instantaneous frequency law samples.
  • t0 (float) – time center
Returns:

output signal
Return type:
Examples: 
>>> from tftb.generators import fmlin
>>> import numpy as np
>>> y1, ifl1 = fmlin(100)  # A linear instantaneous frequency law.
>>> y2, ifl2 = fmsin(100)  # A sinusoidal instantaneous frequency law.
>>> iflaw = np.append(ifl1, ifl2)  # combination of the two
>>> sig = fmodany(iflaw)
>>> subplot(211), plot(real(sig)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)     #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmodany.png
tftb.generators.frequency_modulated.fmpar(n_points, coefficients)[source]

Parabolic frequency modulated signal.

Parameters:
  • n_points (int) – number of points
  • coefficients (tuple) – coefficients of the parabolic function.
Returns:

Signal with parabolic frequency modulation law.
Return type:

tuple
Examples: 
>>> x, iflaw = fmpar(128, (0.4, -0.0112, 8.6806e-05))
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmpar.png
tftb.generators.frequency_modulated.fmpower(n_points, k, coefficients)[source]

Generate signal with power law frequency modulation.

Parameters:
  • n_points (int) – number of points.
  • k (int) – degree of power law.
  • p2 (float) – coefficients of the power law.
Returns:

vector of modulated signal samples.
Return type:

numpy.ndarray
Examples: 
>>> x, iflaw = fmpower(128, 0.5, (1, 0.5, 100, 0.1))
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmpower.png
tftb.generators.frequency_modulated.fmsin(n_points, fnormin=0.05, fnormax=0.45, period=None, t0=None, fnorm0=None, pm1=1)[source]

Sinusodial frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnormin (float) – smallest normalized frequency
  • fnormax (float) – highest normalized frequency
  • period (int) – period of sinusoidal fm
  • t0 (float) – time reference
  • fnorm0 (float) – normalized frequency at time t0
  • pm1 (int) – frequency direction at t0
Returns:

output signal
Return type:

numpy.ndarray
Examples: 
>>> z = fmsin(140, period=100, t0=20, fnorm0=0.3, pm1=-1)
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmsin.png

tftb.generators.misc module

tftb.generators.misc.altes(n_points, fmin=0.05, fmax=0.5, alpha=300)[source]

Generate the Altes signal in time domain.

Parameters:
  • n_points (int) – Number of points in time.
  • fmin (float) – Lower frequency bound.
  • fmax (float) – Higher frequency bound.
  • alpha (float) – Attenuation factor of the envelope.
Returns:

Time vector containing the Altes signal samples.
Return type:

numpy.ndarray
Examples: 
>>> x = altes(128, 0.1, 0.45)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/altes.png
tftb.generators.misc.atoms(n_points, coordinates)[source]

Compute linear combination of elementary Gaussian atoms.

Parameters:
  • n_points (int) – Number of points in a signal
  • coordinates (array-like) – matrix of time-frequency centers
Returns:

signal
Return type:

array-like
Examples: 
>>> import numpy as np
>>> coordinates = np.array([[32.0, 0.3, 32.0, 1.0], [0.15, 0.15, 48.0, 1.22]])
>>> sig = atoms(128, coordinates)
>>> plot(real(sig)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/atoms.png
tftb.generators.misc.doppler(n_points, s_freq, f0, distance, v_target, t0=None, v_wave=340.0)[source]

Generate complex Doppler signal

Parameters:
  • n_points (int) – Number of points
  • s_freq (float) – Sampling frequency
  • f0 (float) – Target frequency
  • distance (float) – distance from line to observer
  • v_target (float) – Target velocity
  • t0 (float) – Time center
  • v_wave (float) – wave velocity.
Returns:

Tuple containing output frequency modulator, output amplitude modulator, output instantaneous frequency law.
Return type:

tuple
Example: 
>>> fm, am, iflaw = doppler(512, 200.0, 65.0, 10.0, 50.0)
>>> subplot(211), plot(real(am * fm)) #doctest: +SKIP
>>> subplot(211), plot(iflaw)         #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/doppler.png
tftb.generators.misc.gdpower(n_points, degree=0.0, rate=1.0)[source]

Generate a signal with a power law group delay.

Parameters:
  • n_points (int) – Number of points in time.
  • degree (float) – degree of the power law.
  • rate (float) – rate-coefficient of the power law GD.
Returns:

Tuple of time row containing modulated samples, group delay, frequency bins.
Return type:

tuple
tftb.generators.misc.klauder(n_points, attenuation=10.0, f0=0.2)[source]

Klauder wavelet in time domain.

Parameters:
  • n_points (int) – Number of points in time.
  • attenuation (float) – attenuation factor of the envelope.
  • f0 (float) – central frequency of the wavelet.
Returns:

Time row vector containing klauder samples.
Return type:

numpy.ndarray
Example: 
>>> x = klauder(128)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/klauder.png
tftb.generators.misc.mexhat(nu=0.05)[source]

Mexican hat wavelet in time domain.

Parameters:nu (float) – Central normalized frequency of the wavelet. Must be a real number between 0 and 0.5
Returns:time vector containing mexhat samples.
Return type:numpy.ndarray
Example: 
>>> plot(mexhat()) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/mexhat.png

tftb.generators.noise module

tftb.generators.noise.dopnoise(n_points, s_freq, f_target, distance, v_target, time_center=None, c=340)[source]

Generate complex noisy doppler signal, normalized to have unit energy.

Parameters:
  • n_points (int) – Number of points.
  • s_freq (float) – Sampling frequency.
  • f_target (float) – Frequency of target.
  • distance (float) – Distnace from line to observer.
  • v_target (float) – velocity of target relative to observer.
  • time_center (float) – Time center. (Default n_points / 2)
  • c (float) – Wave velocity (Default 340 m/s)
Returns:

tuple (output signal, instantaneous frequency law.)
Return type:

tuple(array-like)
Example: 
>>> import numpy as np
>>> from tftb.processing import inst_freq
>>> z, iflaw = dopnoise(500, 200.0, 60.0, 10.0, 70.0, 128.0)
>>> subplot(211), plot(real(z))                #doctest: +SKIP
>>> ifl = inst_freq(z, np.arange(11, 479), 10)
>>> subplot(212), plot(iflaw, 'r', ifl, 'g')   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/dopnoise.png
tftb.generators.noise.noisecg(n_points, a1=None, a2=None)[source]

Generate analytic complex gaussian noise with mean 0.0 and variance 1.0.

Parameters:
  • n_points (int) – Length of the desired output signal.
  • a1 (float) – Coefficients of the filter through which the noise is passed.
  • a2 (float) – Coefficients of the filter through which the noise is passed.
Returns:

Analytic complex Gaussian noise of length n_points.
Return type:

numpy.ndarray
Examples: 
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> noise = noisecg(512)
>>> print("%.1f" % abs((noise ** 2).mean()))
0.0
>>> print("%.1f" % np.std(noise) ** 2)
1.0
>>> plt.subplot(211), plt.plot(real(noise))                                #doctest: +SKIP
>>> plt.subplot(212), #doctest: +SKIP
>>> plt.plot(linspace(-0.5, 0.5, 512), abs(fftshift(fft(noise))) ** 2) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/noisecg.png
tftb.generators.noise.noisecu(n_points)[source]

Compute analytic complex uniform white noise.

Parameters:n_points (int) – Length of the noise signal.
Returns:analytic complex uniform white noise signal of length N
Return type:numpy.ndarray
Examples: 
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> noise = noisecu(512)
>>> print("%.2f" % abs((noise ** 2).mean()))
0.00
>>> print("%.1f" % np.std(noise) ** 2)
1.0
>>> plt.subplot(211), plt.plot(real(noise))                                #doctest: +SKIP
>>> plt.subplot(212),  #doctest: +SKIP
>>> plt.plot(linspace(-0.5, 0.5, 512), abs(fftshift(fft(noise))) ** 2) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/noisecu.png

tftb.generators.utils module

tftb.generators.utils.scale(X, a, fmin, fmax, N)[source]

Scale a signal with the Mellin transform.

Parameters:
  • X (array-like) – signal to be scaled.
  • a (float) – scale factor
  • fmin (float) – lower frequency bound
  • fmax (float) – higher frequency bound
  • N (int) – number of analyzed voices
Returns:

A-scaled version of X.
Return type:

array-like
tftb.generators.utils.sigmerge(x1, x2, ratio=0.0)[source]

Add two signals with a specific energy ratio in decibels.

Parameters:
  • x1 (numpy.ndarray) – 1D numpy.ndarray
  • x2 (numpy.ndarray) – 1D numpy.ndarray
  • ratio (float) – Energy ratio in decibels.
Returns:

The merged signal
Return type:

numpy.ndarray

Module contents

tftb.generators.amexpos(n_points, t0=None, spread=None, kind='bilateral')[source]

Exponential amplitude modulation.

amexpos generates an exponential amplitude modulation starting at time t0 and spread proportioanl to spread.

Parameters:
  • n_points (int) – Number of points.
  • kind (str) – “bilateral” (default) or “unilateral”
  • t0 (float) – Time center.
  • spread (float) – Standard deviation.
Returns:

exponential function
Return type:

numpy.ndarray
Examples: 
>>> x = amexpos(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amexpos_bilateral.png 
>>> x = amexpos(160, kind='unilateral')
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amexpos_unilateral.png
tftb.generators.amgauss(n_points, t0=None, spread=None)[source]

Generate a Gaussian amplitude modulated signal.

Parameters:
  • n_points (int) – Number of points in the output.
  • t0 (float) – Center of the Gaussian function. (default: t0 / 2)
  • spread (float) – Standard deviation of the Gaussian. (default 2 * sqrt(n_points)
Returns:

Gaussian function centered at time t0.
Return type:

numpy.ndarray
Example: 
>>> x = amgauss(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amgauss1.png 
>>> x = amgauss(160, 90)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amgauss2.png
tftb.generators.amrect(n_points, t0=None, spread=None)[source]

Generate a rectangular amplitude modulation.

Parameters:
  • n_points (int) – Number of points in the function.
  • t0 (float) – Time center
  • spread (float) – standard deviation of the function.
Returns:

A rectangular amplitude modulator.
Return type:

numpy.ndarray.
Examples: 
>>> x = amrect(160, 90, 40.0)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amrect1.png
tftb.generators.amtriang(n_points, t0=None, spread=None)[source]

Generate a triangular amplitude modulation.

Parameters:
  • n_points (int) – Number of points in the function.
  • t0 (float) – Time center
  • spread (float) – standard deviation of the function.
Returns:

A triangular amplitude modulator.
Return type:

numpy.ndarray.
Examples: 
>>> x = amtriang(160)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/amtriang1.png
tftb.generators.fmconst(n_points, fnorm=0.25, t0=None)[source]

Generate a signal with constant frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnorm (float) – normalized frequency
  • t0 (float) – time center
Returns:

frequency modulation signal with frequency fnorm
Return type:

numpy.ndarray
Examples: 
>>> from tftb.generators import amgauss
>>> z = amgauss(128, 50, 30) * fmconst(128, 0.05, 50)[0]
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmconst.png
tftb.generators.fmhyp(n_points, p1, p2)[source]

Signal with hyperbolic frequency modulation.

Parameters:
  • n_points (int) – number of points.
  • p2 (float) – coefficients of the hyperbolic function.
Returns:

vector containing the modulated signal samples.
Return type:

numpy.ndarray
Examples: 
>>> signal, iflaw = fmhyp(128, (1, 0.5), (32, 0.1))
>>> subplot(211), plot(real(signal)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)        #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmhyp.png
tftb.generators.fmlin(n_points, fnormi=0.0, fnormf=0.5, t0=None)[source]

Generate a signal with linear frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnormi (float) – initial normalized frequency
  • fnormf (float) – final normalized frequency
  • t0 (float) – time center
Returns:

The modulated signal, and the instantaneous amplitude law.
Return type:

tuple(array-like)
Examples: 
>>> from tftb.generators import amgauss
>>> z = amgauss(128, 50, 40) * fmlin(128, 0.05, 0.3, 50)[0]
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmlin.png
tftb.generators.fmodany(iflaw, t0=1)[source]

Arbitrary frequency modulation.

Parameters:
  • iflaw (numpy.ndarray) – Vector of instantaneous frequency law samples.
  • t0 (float) – time center
Returns:

output signal
Return type:
Examples: 
>>> from tftb.generators import fmlin
>>> import numpy as np
>>> y1, ifl1 = fmlin(100)  # A linear instantaneous frequency law.
>>> y2, ifl2 = fmsin(100)  # A sinusoidal instantaneous frequency law.
>>> iflaw = np.append(ifl1, ifl2)  # combination of the two
>>> sig = fmodany(iflaw)
>>> subplot(211), plot(real(sig)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)     #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmodany.png
tftb.generators.fmpar(n_points, coefficients)[source]

Parabolic frequency modulated signal.

Parameters:
  • n_points (int) – number of points
  • coefficients (tuple) – coefficients of the parabolic function.
Returns:

Signal with parabolic frequency modulation law.
Return type:

tuple
Examples: 
>>> x, iflaw = fmpar(128, (0.4, -0.0112, 8.6806e-05))
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmpar.png
tftb.generators.fmpower(n_points, k, coefficients)[source]

Generate signal with power law frequency modulation.

Parameters:
  • n_points (int) – number of points.
  • k (int) – degree of power law.
  • p2 (float) – coefficients of the power law.
Returns:

vector of modulated signal samples.
Return type:

numpy.ndarray
Examples: 
>>> x, iflaw = fmpower(128, 0.5, (1, 0.5, 100, 0.1))
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(iflaw)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmpower.png
tftb.generators.fmsin(n_points, fnormin=0.05, fnormax=0.45, period=None, t0=None, fnorm0=None, pm1=1)[source]

Sinusodial frequency modulation.

Parameters:
  • n_points (int) – number of points
  • fnormin (float) – smallest normalized frequency
  • fnormax (float) – highest normalized frequency
  • period (int) – period of sinusoidal fm
  • t0 (float) – time reference
  • fnorm0 (float) – normalized frequency at time t0
  • pm1 (int) – frequency direction at t0
Returns:

output signal
Return type:

numpy.ndarray
Examples: 
>>> z = fmsin(140, period=100, t0=20, fnorm0=0.3, pm1=-1)
>>> plot(real(z)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/fmsin.png
tftb.generators.sigmerge(x1, x2, ratio=0.0)[source]

Add two signals with a specific energy ratio in decibels.

Parameters:
  • x1 (numpy.ndarray) – 1D numpy.ndarray
  • x2 (numpy.ndarray) – 1D numpy.ndarray
  • ratio (float) – Energy ratio in decibels.
Returns:

The merged signal
Return type:

numpy.ndarray
tftb.generators.scale(X, a, fmin, fmax, N)[source]

Scale a signal with the Mellin transform.

Parameters:
  • X (array-like) – signal to be scaled.
  • a (float) – scale factor
  • fmin (float) – lower frequency bound
  • fmax (float) – higher frequency bound
  • N (int) – number of analyzed voices
Returns:

A-scaled version of X.
Return type:

array-like
tftb.generators.dopnoise(n_points, s_freq, f_target, distance, v_target, time_center=None, c=340)[source]

Generate complex noisy doppler signal, normalized to have unit energy.

Parameters:
  • n_points (int) – Number of points.
  • s_freq (float) – Sampling frequency.
  • f_target (float) – Frequency of target.
  • distance (float) – Distnace from line to observer.
  • v_target (float) – velocity of target relative to observer.
  • time_center (float) – Time center. (Default n_points / 2)
  • c (float) – Wave velocity (Default 340 m/s)
Returns:

tuple (output signal, instantaneous frequency law.)
Return type:

tuple(array-like)
Example: 
>>> import numpy as np
>>> from tftb.processing import inst_freq
>>> z, iflaw = dopnoise(500, 200.0, 60.0, 10.0, 70.0, 128.0)
>>> subplot(211), plot(real(z))                #doctest: +SKIP
>>> ifl = inst_freq(z, np.arange(11, 479), 10)
>>> subplot(212), plot(iflaw, 'r', ifl, 'g')   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/dopnoise.png
tftb.generators.noisecg(n_points, a1=None, a2=None)[source]

Generate analytic complex gaussian noise with mean 0.0 and variance 1.0.

Parameters:
  • n_points (int) – Length of the desired output signal.
  • a1 (float) – Coefficients of the filter through which the noise is passed.
  • a2 (float) – Coefficients of the filter through which the noise is passed.
Returns:

Analytic complex Gaussian noise of length n_points.
Return type:

numpy.ndarray
Examples: 
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> noise = noisecg(512)
>>> print("%.1f" % abs((noise ** 2).mean()))
0.0
>>> print("%.1f" % np.std(noise) ** 2)
1.0
>>> plt.subplot(211), plt.plot(real(noise))                                #doctest: +SKIP
>>> plt.subplot(212), #doctest: +SKIP
>>> plt.plot(linspace(-0.5, 0.5, 512), abs(fftshift(fft(noise))) ** 2) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/noisecg.png
tftb.generators.noisecu(n_points)[source]

Compute analytic complex uniform white noise.

Parameters:n_points (int) – Length of the noise signal.
Returns:analytic complex uniform white noise signal of length N
Return type:numpy.ndarray
Examples: 
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> noise = noisecu(512)
>>> print("%.2f" % abs((noise ** 2).mean()))
0.00
>>> print("%.1f" % np.std(noise) ** 2)
1.0
>>> plt.subplot(211), plt.plot(real(noise))                                #doctest: +SKIP
>>> plt.subplot(212),  #doctest: +SKIP
>>> plt.plot(linspace(-0.5, 0.5, 512), abs(fftshift(fft(noise))) ** 2) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/noisecu.png
tftb.generators.anaask(n_points, n_comp=None, f0=0.25)[source]

Generate an amplitude shift (ASK) keying signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points of each component.
  • f0 (float) – normalized frequency.
Returns:

Tuple containing the modulated signal and the amplitude modulation.
Return type:

tuple(numpy.ndarray)
Examples: 
>>> x, am = anaask(512, 64, 0.05)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anaask.png
tftb.generators.anabpsk(n_points, n_comp=None, f0=0.25)[source]

Binary phase shift keying (BPSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each component.
  • f0 (float) – normalized frequency.
Returns:

BPSK signal
Return type:

numpy.ndarray
Examples: 
>>> x, am = anabpsk(300, 30, 0.1)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anabpsk.png
tftb.generators.anafsk(n_points, n_comp=None, Nbf=4)[source]

Frequency shift keying (FSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each components.
  • Nbf (int) – number of distinct frequencies.
Returns:

FSK signal.
Return type:

numpy.ndarray
Examples: 
>>> x, am = anafsk(512, 54.0, 5.0)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(am)      #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anafsk.png
tftb.generators.anapulse(n_points, ti=None)[source]

Analytic projection of unit amplitude impulse signal.

Parameters:
  • n_points (int) – Number of points.
  • ti (float) – time position of the impulse.
Returns:

analytic impulse signal.
Return type:

numpy.ndarray
Examples: 
>>> x = 2.5 * anapulse(512, 301)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anapulse.png
tftb.generators.anaqpsk(n_points, n_comp=None, f0=0.25)[source]

Quaternary Phase Shift Keying (QPSK) signal.

Parameters:
  • n_points (int) – number of points.
  • n_comp (int) – number of points in each component.
  • f0 (float) – normalized frequency
Returns:

complex phase modulated signal of normalized frequency f0 and initial phase.
Return type:

tuple
Examples: 
>>> x, phase = anaqpsk(512, 64.0, 0.05)
>>> subplot(211), plot(real(x)) #doctest: +SKIP
>>> subplot(212), plot(phase)   #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anaqpsk.png
tftb.generators.anasing(n_points, t0=None, h=0.0)[source]

Lipschitz singularity. Refer to the wiki page on Lipschitz condition, good test case.

Parameters:
  • n_points (int) – number of points in time.
  • t0 (float) – time localization of singularity
  • h (float) – strength of the singularity
Returns:

N-point Lipschitz singularity centered around t0
Return type:

numpy.ndarray
Examples: 
>>> x = anasing(128)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anasing.png
tftb.generators.anastep(n_points, ti=None)[source]

Analytic projection of unit step signal.

Parameters:
  • n_points (int) – Number of points.
  • ti (float) – starting position of unit step.
Returns:

output signal
Return type:

numpy.ndarray
Examples: 
>>> x = anastep(256, 128)
>>> plot(real(x)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/anastep.png
tftb.generators.doppler(n_points, s_freq, f0, distance, v_target, t0=None, v_wave=340.0)[source]

Generate complex Doppler signal

Parameters:
  • n_points (int) – Number of points
  • s_freq (float) – Sampling frequency
  • f0 (float) – Target frequency
  • distance (float) – distance from line to observer
  • v_target (float) – Target velocity
  • t0 (float) – Time center
  • v_wave (float) – wave velocity.
Returns:

Tuple containing output frequency modulator, output amplitude modulator, output instantaneous frequency law.
Return type:

tuple
Example: 
>>> fm, am, iflaw = doppler(512, 200.0, 65.0, 10.0, 50.0)
>>> subplot(211), plot(real(am * fm)) #doctest: +SKIP
>>> subplot(211), plot(iflaw)         #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/doppler.png
tftb.generators.gdpower(n_points, degree=0.0, rate=1.0)[source]

Generate a signal with a power law group delay.

Parameters:
  • n_points (int) – Number of points in time.
  • degree (float) – degree of the power law.
  • rate (float) – rate-coefficient of the power law GD.
Returns:

Tuple of time row containing modulated samples, group delay, frequency bins.
Return type:

tuple
tftb.generators.klauder(n_points, attenuation=10.0, f0=0.2)[source]

Klauder wavelet in time domain.

Parameters:
  • n_points (int) – Number of points in time.
  • attenuation (float) – attenuation factor of the envelope.
  • f0 (float) – central frequency of the wavelet.
Returns:

Time row vector containing klauder samples.
Return type:

numpy.ndarray
Example: 
>>> x = klauder(128)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/klauder.png
tftb.generators.mexhat(nu=0.05)[source]

Mexican hat wavelet in time domain.

Parameters:nu (float) – Central normalized frequency of the wavelet. Must be a real number between 0 and 0.5
Returns:time vector containing mexhat samples.
Return type:numpy.ndarray
Example: 
>>> plot(mexhat()) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/mexhat.png
tftb.generators.altes(n_points, fmin=0.05, fmax=0.5, alpha=300)[source]

Generate the Altes signal in time domain.

Parameters:
  • n_points (int) – Number of points in time.
  • fmin (float) – Lower frequency bound.
  • fmax (float) – Higher frequency bound.
  • alpha (float) – Attenuation factor of the envelope.
Returns:

Time vector containing the Altes signal samples.
Return type:

numpy.ndarray
Examples: 
>>> x = altes(128, 0.1, 0.45)
>>> plot(x) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/altes.png
tftb.generators.atoms(n_points, coordinates)[source]

Compute linear combination of elementary Gaussian atoms.

Parameters:
  • n_points (int) – Number of points in a signal
  • coordinates (array-like) – matrix of time-frequency centers
Returns:

signal
Return type:

array-like
Examples: 
>>> import numpy as np
>>> coordinates = np.array([[32.0, 0.3, 32.0, 1.0], [0.15, 0.15, 48.0, 1.22]])
>>> sig = atoms(128, coordinates)
>>> plot(real(sig)) #doctest: +SKIP

(Source code, png, hires.png, pdf)

../_images/atoms.png