z = numpy.concatenate((numpy.flip(x[:l]),x))
    z = numpy.concatenate((z,numpy.flip(x[-l:])))

    fr =  planfftw.fft(z)
    ff = fr(z)

    # obtain the boundaries in the extend f
    bound2 = numpy.ceil(bounds*round(len(ff)/2)/numpy.pi).astype(dtype=int)
    #bound2 = numpy.concatenate((bound2,[8000]))
    efd = numpy.zeros(((len(bound2)-1,len(x))),dtype=numpy.float64)
    ft = numpy.zeros((efd.shape[0],len(ff)),dtype=numpy.cdouble)
    fz =  planfftw.ifft(ft[0,:])
    # define an ideal functions and extract components
    for k in range(efd.shape[0]):
        if bound2[k] == 0:
            ft[k,0:bound2[k+1]] = ff[0:bound2[k+1]]
            ft[k,len(ff)+2-bound2[k+1]:len(ff)] = ff[len(ff)+2-bound2[k+1]:len(ff)]
        else:
            ft[k,bound2[k]:bound2[k+1]] = ff[bound2[k]:bound2[k+1]]
            ft[k,len(ff)+2-bound2[k+1]:len(ff)+2-bound2[k]] = ff[len(ff)+2-bound2[k+1]:len(ff)+2-bound2[k]]
        rx = numpy.real(fz(ft[k,:]))
        efd[k,:] = rx[l:-l]