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SciPy Reference Guide, Release 0.8.dev Notes If method is ‘quadratic’, qshape specifies its shape. If f0 is an array, it forms the coefficients of a polynomial in t (see numpy.polval). The polynomial determines the waveform frequency change in time. In this case, the values of f1, t1, method, and qshape are ignored. 3.13.9 Window functions boxcar(M[, sym]) The M-point boxcar window. triang(M[, sym]) The M-point triangular window. parzen(M[, sym]) The M-point Parzen window. bohman(M[, sym]) The M-point Bohman window. blackman(M[, sym]) The M-point Blackman window. blackmanharris(M[, sym]) The M-point minimum 4-term Blackman-Harris window. nuttall(M[, sym]) A minimum 4-term Blackman-Harris window according to Nuttall. flattop(M[, sym]) The M-point Flat top window. bartlett(M[, sym]) The M-point Bartlett window. hann(M[, sym]) The M-point Hanning window. barthann(M[, sym]) Return the M-point modified Bartlett-Hann window. hamming(M[, sym]) The M-point Hamming window. kaiser(M, beta[, sym]) Return a Kaiser window of length M with shape parameter beta. gaussian(M, std[, sym]) Return a Gaussian window of length M with standard-deviation std. general_gaussian(M, p, sig[, sym]) Return a window with a generalized Gaussian shape. slepian(M, width[, sym]) Return the M-point slepian window. boxcar(M, sym=1) The M-point boxcar window. triang(M, sym=1) The M-point triangular window. parzen(M, sym=1) The M-point Parzen window. bohman(M, sym=1) The M-point Bohman window. blackman(M, sym=1) The M-point Blackman window. blackmanharris(M, sym=1) The M-point minimum 4-term Blackman-Harris window. nuttall(M, sym=1) A minimum 4-term Blackman-Harris window according to Nuttall. flattop(M, sym=1) The M-point Flat top window. bartlett(M, sym=1) The M-point Bartlett window. hann(M, sym=1) The M-point Hanning window. barthann(M, sym=1) Return the M-point modified Bartlett-Hann window. 346 Chapter 3. Reference
hamming(M, sym=1) The M-point Hamming window. kaiser(M, beta, sym=1) Return a Kaiser window of length M with shape parameter beta. gaussian(M, std, sym=1) Return a Gaussian window of length M with standard-deviation std. general_gaussian(M, p, sig, sym=1) Return a window with a generalized Gaussian shape. exp(-0.5*(x/sig)**(2*p)) half power point is at (2*log(2)))**(1/(2*p))*sig slepian(M, width, sym=1) Return the M-point slepian window. 3.13.10 Wavelets SciPy Reference Guide, Release 0.8.dev daub(p) The coefficients for the FIR low-pass filter producing Daubechies wavelets. qmf(hk) Return high-pass qmf filter from low-pass cascade(hk[, J]) (x,phi,psi) at dyadic points K/2**J from filter coefficients. daub(p) The coefficients for the FIR low-pass filter producing Daubechies wavelets. p>=1 gives the order of the zero at f=1/2. There are 2p filter coefficients. qmf(hk) Return high-pass qmf filter from low-pass cascade(hk, J=7) (x,phi,psi) at dyadic points K/2**J from filter coefficients. Inputs: hk – coefficients of low-pass filter J – values will be computed at grid points $K/2^J$ Outputs: Algorithm: x – the dyadic points $K/2^J$ for $K=0...N*(2^J)-1$ where len(hk)=len(gk)=N+1 phi – the scaling function phi(x) at x $phi(x) = sum_{k=0}^{N} h_k phi(2x-k)$ psi – the wavelet function psi(x) at x $psi(x) = sum_{k=0}^N g_k phi(2x-k)$ Only returned if gk is not None Uses the vector cascade algorithm described by Strang and Nguyen in “Wavelets and Filter Banks” Builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at then end 3.13. Signal processing (<strong>scipy</strong>.signal) 347
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