Added missing chirpz.py
diff --git a/python/CMakeLists.txt b/python/CMakeLists.txt
index 2c76806..67d45f9 100644
--- a/python/CMakeLists.txt
+++ b/python/CMakeLists.txt
@@ -34,7 +34,8 @@
receiver_hier.py
fcch_burst_tagger.py
sch_detector.py
- fcch_detector.py DESTINATION ${GR_PYTHON_DIR}/gsm
+ fcch_detector.py
+ chirpz.py DESTINATION ${GR_PYTHON_DIR}/gsm
)
########################################################################
diff --git a/python/chirpz.py b/python/chirpz.py
new file mode 100644
index 0000000..3043c44
--- /dev/null
+++ b/python/chirpz.py
@@ -0,0 +1,488 @@
+# This program is public domain
+# Authors: Paul Kienzle, Nadav Horesh
+"""
+Chirp z-transform.
+
+CZT: callable (x,axis=-1)->array
+ define a chirp-z transform that can be applied to different signals
+ZoomFFT: callable (x,axis=-1)->array
+ define a Fourier transform on a range of frequencies
+ScaledFFT: callable (x,axis=-1)->array
+ define a limited frequency FFT
+
+czt: array
+ compute the chirp-z transform for a signal
+zoomfft: array
+ compute the Fourier transform on a range of frequencies
+scaledfft: array
+ compute a limited frequency FFT for a signal
+"""
+__all__ = ['czt', 'zoomfft', 'scaledfft']
+
+import math, cmath
+
+import numpy as np
+from numpy import pi, arange
+from scipy.fftpack import fft, ifft, fftshift
+
+class CZT:
+ """
+ Chirp-Z Transform.
+
+ Transform to compute the frequency response around a spiral.
+ Objects of this class are callables which can compute the
+ chirp-z transform on their inputs. This object precalculates
+ constants for the given transform.
+
+ If w does not lie on the unit circle, then the transform will be
+ around a spiral with exponentially increasing radius. Regardless,
+ angle will increase linearly.
+
+ The chirp-z transform can be faster than an equivalent fft with
+ zero padding. Try it with your own array sizes to see. It is
+ theoretically faster for large prime fourier transforms, but not
+ in practice.
+
+ The chirp-z transform is considerably less precise than the
+ equivalent zero-padded FFT, with differences on the order of 1e-11
+ from the direct transform rather than the on the order of 1e-15 as
+ seen with zero-padding.
+
+ See zoomfft for a friendlier interface to partial fft calculations.
+ """
+ def __init__(self, n, m=None, w=1, a=1):
+ """
+ Chirp-Z transform definition.
+
+ Parameters:
+ ----------
+ n: int
+ The size of the signal
+ m: int
+ The number of points desired. The default is the length of the input data.
+ a: complex
+ The starting point in the complex plane. The default is 1.
+ w: complex or float
+ If w is complex, it is the ratio between points in each step.
+ If w is float, it serves as a frequency scaling factor. for instance
+ when assigning w=0.5, the result FT will span half of frequncy range
+ (that fft would result) at half of the frequncy step size.
+
+ Returns:
+ --------
+ CZT:
+ callable object f(x,axis=-1) for computing the chirp-z transform on x
+ """
+ if m is None:
+ m = n
+ if w is None:
+ w = cmath.exp(-1j*pi/m)
+ elif type(w) in (float, int):
+ w = cmath.exp(-1j*pi/m * w)
+ else:
+ w = cmath.sqrt(w)
+ self.w, self.a = w, a
+ self.m, self.n = m, n
+
+ k = arange(max(m,n))
+ wk2 = w**(k**2)
+ nfft = 2**nextpow2(n+m-1)
+ self._Awk2 = (a**-k * wk2)[:n]
+ self._nfft = nfft
+ self._Fwk2 = fft(1/np.hstack((wk2[n-1:0:-1], wk2[:m])), nfft)
+ self._wk2 = wk2[:m]
+ self._yidx = slice(n-1, n+m-1)
+
+ def __call__(self, x, axis=-1):
+ """
+ Parameters:
+ ----------
+ x: array
+ The signal to transform.
+ axis: int
+ Array dimension to operate over. The default is the final
+ dimension.
+
+ Returns:
+ -------
+ An array of the same dimensions as x, but with the length of the
+ transformed axis set to m. Note that this is a view on a much
+ larger array. To save space, you may want to call it as
+ y = czt(x).copy()
+ """
+ x = np.asarray(x)
+ if x.shape[axis] != self.n:
+ raise ValueError("CZT defined for length %d, not %d" %
+ (self.n, x.shape[axis]))
+ # Calculate transpose coordinates, to allow operation on any given axis
+ trnsp = np.arange(x.ndim)
+ trnsp[[axis, -1]] = [-1, axis]
+ x = x.transpose(*trnsp)
+ y = ifft(self._Fwk2 * fft(x*self._Awk2, self._nfft))
+ y = y[..., self._yidx] * self._wk2
+ return y.transpose(*trnsp)
+
+
+def nextpow2(n):
+ """
+ Return the smallest power of two greater than or equal to n.
+ """
+ return int(math.ceil(math.log(n)/math.log(2)))
+
+
+def ZoomFFT(n, f1, f2=None, m=None, Fs=2):
+ """
+ Zoom FFT transform definition.
+
+ Computes the Fourier transform for a set of equally spaced
+ frequencies.
+
+ Parameters:
+ ----------
+ n: int
+ size of the signal
+ m: int
+ size of the output
+ f1, f2: float
+ start and end frequencies; if f2 is not specified, use 0 to f1
+ Fs: float
+ sampling frequency (default=2)
+
+ Returns:
+ -------
+ A CZT instance
+ A callable object f(x,axis=-1) for computing the zoom FFT on x.
+
+ Sampling frequency is 1/dt, the time step between samples in the
+ signal x. The unit circle corresponds to frequencies from 0 up
+ to the sampling frequency. The default sampling frequency of 2
+ means that f1,f2 values up to the Nyquist frequency are in the
+ range [0,1). For f1,f2 values expressed in radians, a sampling
+ frequency of 1/pi should be used.
+
+ To graph the magnitude of the resulting transform, use::
+
+ plot(linspace(f1,f2,m), abs(zoomfft(x,f1,f2,m))).
+
+ Use the zoomfft wrapper if you only need to compute one transform.
+ """
+ if m is None: m = n
+ if f2 is None: f1, f2 = 0., f1
+ w = cmath.exp(-2j * pi * (f2-f1) / ((m-1)*Fs))
+ a = cmath.exp(2j * pi * f1/Fs)
+ return CZT(n, m=m, w=w, a=a)
+
+def ScaledFFT(n, m=None, scale=1.0):
+ """
+ Scaled fft transform definition.
+
+ Similar to fft, where the frequency range is scaled by a factor 'scale' and
+ divided into 'm-1' equal steps. Like the FFT, frequencies are arranged
+ from 0 to scale*Fs/2-delta followed by -scale*Fs/2 to -delta, where delta
+ is the step size scale*Fs/m for sampling frequence Fs. The intended use is in
+ a convolution of two signals, each has its own sampling step.
+
+ This is equivalent to:
+
+ fftshift(zoomfft(x, -scale, scale*(m-2.)/m, m=m))
+
+ For example:
+
+ m,n = 10,len(x)
+ sf = ScaledFFT(n, m=m, scale=0.25)
+ X = fftshift(fft(x))
+ W = linspace(-8, 8*(n-2.)/n, n)
+ SX = fftshift(sf(x))
+ SW = linspace(-2, 2*(m-2.)/m, m)
+ plot(X,W,SX,SW)
+
+ Parameters:
+ ----------
+ n: int
+ Size of the signal
+ m: int
+ The size of the output.
+ Default: m=n
+ scale: float
+ Frequenct scaling factor.
+ Default: scale=1.0
+
+ Returns:
+ -------
+ function
+ A callable f(x,axis=-1) for computing the scaled FFT on x.
+ """
+ if m is None:
+ m = n
+ w = np.exp(-2j * pi / m * scale)
+ a = w**(m//2)
+ transform = CZT(n=n, m=m, a=a, w=w)
+ return lambda x, axis=-1: fftshift(transform(x, axis), axes=(axis,))
+
+def scaledfft(x, m=None, scale=1.0, axis=-1):
+ """
+ Partial with a frequency scaling.
+ See ScaledFFT doc for details
+
+ Parameters:
+ ----------
+ x: input array
+ m: int
+ The length of the output signal
+ scale: float
+ A frequency scaling factor
+ axis: int
+ The array dimension to operate over. The default is the
+ final dimension.
+
+ Returns:
+ -------
+ An array of the same rank of 'x', but with the size if
+ the 'axis' dimension set to 'm'
+ """
+ return ScaledFFT(x.shape[axis], m, scale)(x,axis)
+
+def czt(x, m=None, w=1.0, a=1, axis=-1):
+ """
+ Compute the frequency response around a spiral.
+
+ Parameters:
+ ----------
+ x: array
+ The set of data to transform.
+ m: int
+ The number of points desired. The default is the length of the input data.
+ a: complex
+ The starting point in the complex plane. The default is 1.
+ w: complex or float
+ If w is complex, it is the ratio between points in each step.
+ If w is float, it is the frequency step scale (relative to the
+ normal dft frquency step).
+ axis: int
+ Array dimension to operate over. The default is the final
+ dimension.
+
+ Returns:
+ -------
+ An array of the same dimensions as x, but with the length of the
+ transformed axis set to m. Note that this is a view on a much
+ larger array. To save space, you may want to call it as
+ y = ascontiguousarray(czt(x))
+
+ See zoomfft for a friendlier interface to partial fft calculations.
+
+ If the transform needs to be repeated, use CZT to construct a
+ specialized transform function which can be reused without
+ recomputing constants.
+ """
+ x = np.asarray(x)
+ transform = CZT(x.shape[axis], m=m, w=w, a=a)
+ return transform(x,axis=axis)
+
+def zoomfft(x, f1, f2=None, m=None, Fs=2, axis=-1):
+ """
+ Compute the Fourier transform of x for frequencies in [f1, f2].
+
+ Parameters:
+ ----------
+ m: int
+ The number of points to evaluate. The default is the length of x.
+ f1, f2: float
+ The frequency range. If f2 is not specified, the range 0-f1 is assumed.
+ Fs: float
+ The sampling frequency. With a sampling frequency of
+ 10kHz for example, the range f1 and f2 can be expressed in kHz.
+ The default sampling frequency is 2, so f1 and f2 should be
+ in the range 0,1 to keep the transform below the Nyquist
+ frequency.
+ x : array
+ The input signal.
+ axis: int
+ The array dimension the transform operates over. The default is the
+ final dimension.
+
+ Returns:
+ -------
+ array
+ The transformed signal. The fourier transform will be calculate
+ at the points f1, f1+df, f1+2df, ..., f2, where df=(f2-f1)/m.
+
+ zoomfft(x,0,2-2./len(x)) is equivalent to fft(x).
+
+ To graph the magnitude of the resulting transform, use::
+
+ plot(linspace(f1,f2,m), abs(zoomfit(x,f1,f2,m))).
+
+ If the transform needs to be repeated, use ZoomFFT to construct a
+ specialized transform function which can be reused without
+ recomputing constants.
+ """
+ x = np.asarray(x)
+ transform = ZoomFFT(x.shape[axis], f1, f2=f2, m=m, Fs=Fs)
+ return transform(x,axis=axis)
+
+
+def _test1(x,show=False,plots=[1,2,3,4]):
+ norm = np.linalg.norm
+
+ # Normal fft and zero-padded fft equivalent to 10x oversampling
+ over=10
+ w = np.linspace(0,2-2./len(x),len(x))
+ y = fft(x)
+ wover = np.linspace(0,2-2./(over*len(x)),over*len(x))
+ yover = fft(x,over*len(x))
+
+ # Check that zoomfft is the equivalent of fft
+ y1 = zoomfft(x,0,2-2./len(y))
+
+ # Check that zoomfft with oversampling is equivalent to zero padding
+ y2 = zoomfft(x,0,2-2./len(yover), m=len(yover))
+
+ # Check that zoomfft works on a subrange
+ f1,f2 = w[3],w[6]
+ y3 = zoomfft(x,f1,f2,m=3*over+1)
+ w3 = np.linspace(f1,f2,len(y3))
+ idx3 = slice(3*over,6*over+1)
+
+ if not show: plots = []
+ if plots != []:
+ import pylab
+ if 0 in plots:
+ pylab.figure(0)
+ pylab.plot(x)
+ pylab.ylabel('Intensity')
+ if 1 in plots:
+ pylab.figure(1)
+ pylab.subplot(311)
+ pylab.plot(w,abs(y),'o',w,abs(y1))
+ pylab.legend(['fft','zoom'])
+ pylab.ylabel('Magnitude')
+ pylab.title('FFT equivalent')
+ pylab.subplot(312)
+ pylab.plot(w,np.angle(y),'o',w,np.angle(y1))
+ pylab.legend(['fft','zoom'])
+ pylab.ylabel('Phase (radians)')
+ pylab.subplot(313)
+ pylab.plot(w,abs(y)-abs(y1)) #,w,np.angle(y)-np.angle(y1))
+ #pylab.legend(['magnitude','phase'])
+ pylab.ylabel('Residuals')
+ if 2 in plots:
+ pylab.figure(2)
+ pylab.subplot(211)
+ pylab.plot(w,abs(y),'o',wover,abs(y2),wover,abs(yover))
+ pylab.ylabel('Magnitude')
+ pylab.title('Oversampled FFT')
+ pylab.legend(['fft','zoom','pad'])
+ pylab.subplot(212)
+ pylab.plot(wover,abs(yover)-abs(y2),
+ w,abs(y)-abs(y2[0::over]),'o',
+ w,abs(y)-abs(yover[0::over]),'x')
+ pylab.legend(['pad-zoom','fft-zoom','fft-pad'])
+ pylab.ylabel('Residuals')
+ if 3 in plots:
+ pylab.figure(3)
+ ax1=pylab.subplot(211)
+ pylab.plot(w,abs(y),'o',w3,abs(y3),wover,abs(yover),
+ w[3:7],abs(y3[::over]),'x')
+ pylab.title('Zoomed FFT')
+ pylab.ylabel('Magnitude')
+ pylab.legend(['fft','zoom','pad'])
+ pylab.plot(w3,abs(y3),'x')
+ ax1.set_xlim(f1,f2)
+ ax2=pylab.subplot(212)
+ pylab.plot(wover[idx3],abs(yover[idx3])-abs(y3),
+ w[3:7],abs(y[3:7])-abs(y3[::over]),'o',
+ w[3:7],abs(y[3:7])-abs(yover[3*over:6*over+1:over]),'x')
+ pylab.legend(['pad-zoom','fft-zoom','fft-pad'])
+ ax2.set_xlim(f1,f2)
+ pylab.ylabel('Residuals')
+ if plots != []:
+ pylab.show()
+
+ err = norm(y-y1)/norm(y)
+ #print "direct err %g"%err
+ assert err < 1e-10, "error for direct transform is %g"%(err,)
+ err = norm(yover-y2)/norm(yover)
+ #print "over err %g"%err
+ assert err < 1e-10, "error for oversampling is %g"%(err,)
+ err = norm(yover[idx3]-y3)/norm(yover[idx3])
+ #print "range err %g"%err
+ assert err < 1e-10, "error for subrange is %g"%(err,)
+
+def _testscaled(x):
+ n = len(x)
+ norm = np.linalg.norm
+ assert norm(fft(x)-scaledfft(x)) < 1e-10
+ assert norm(fftshift(fft(x))[n/4:3*n/4] - fftshift(scaledfft(x,scale=0.5,m=n/2))) < 1e-10
+
+def test(demo=None,plots=[1,2,3]):
+ # 0: Gauss
+ t = np.linspace(-2,2,128)
+ x = np.exp(-t**2/0.01)
+ _test1(x, show=(demo==0), plots=plots)
+
+ # 1: Linear
+ x=[1,2,3,4,5,6,7]
+ _test1(x, show=(demo==1), plots=plots)
+
+ # Check near powers of two
+ _test1(range(126-31), show=False)
+ _test1(range(127-31), show=False)
+ _test1(range(128-31), show=False)
+ _test1(range(129-31), show=False)
+ _test1(range(130-31), show=False)
+
+ # Check transform on n-D array input
+ x = np.reshape(np.arange(3*2*28),(3,2,28))
+ y1 = zoomfft(x,0,2-2./28)
+ y2 = zoomfft(x[2,0,:],0,2-2./28)
+ err = np.linalg.norm(y2-y1[2,0])
+ assert err < 1e-15, "error for n-D array is %g"%(err,)
+
+ # 2: Random (not a test condition)
+ if demo==2:
+ x = np.random.rand(101)
+ _test1(x, show=True, plots=plots)
+
+ # 3: Spikes
+ t=np.linspace(0,1,128)
+ x=np.sin(2*pi*t*5)+np.sin(2*pi*t*13)
+ _test1(x, show=(demo==3), plots=plots)
+
+ # 4: Sines
+ x=np.zeros(100)
+ x[[1,5,21]]=1
+ _test1(x, show=(demo==4), plots=plots)
+
+ # 5: Sines plus complex component
+ x += 1j*np.linspace(0,0.5,x.shape[0])
+ _test1(x, show=(demo==5), plots=plots)
+
+ # 6: Scaled FFT on complex sines
+ x += 1j*np.linspace(0,0.5,x.shape[0])
+ if demo == 6:
+ demo_scaledfft(x,0.25,200)
+ _testscaled(x)
+
+
+def demo_scaledfft(v, scale, m):
+ import pylab
+ shift = pylab.fftshift
+ n = len(v)
+ x = pylab.linspace(-0.5, 0.5 - 1./n, n)
+ xz = pylab.linspace(-scale*0.5, scale*0.5*(m-2.)/m, m)
+ pylab.figure()
+ pylab.plot(x, shift(abs(fft(v))), label='fft')
+ pylab.plot(x, shift(abs(scaledfft(v))),'ro', label='x1 scaled fft')
+ pylab.plot(xz, abs(zoomfft(v, -scale, scale*(m-2.)/m, m=m)),
+ 'bo',label='zoomfft')
+ pylab.plot(xz, shift(abs(scaledfft(v, m=m, scale=scale))),
+ 'gx', label='x'+str(scale)+' scaled fft')
+ pylab.gca().set_yscale('log')
+ pylab.legend()
+ pylab.show()
+
+if __name__ == "__main__":
+ # Choose demo in [0,4] to show plot, or None for testing only
+ test(demo=None)
+
diff --git a/python/fcch_burst_tagger.py b/python/fcch_burst_tagger.py
index 5142096..c14f7fb 100644
--- a/python/fcch_burst_tagger.py
+++ b/python/fcch_burst_tagger.py
@@ -23,7 +23,7 @@
from pylab import *
from gnuradio import gr
import pmt
-from scipy.signal.chirpz import ZoomFFT
+from gsm.chirpz import ZoomFFT
class fcch_burst_tagger(gr.sync_block):
"""