[FEATURE REQUEST] implement scipy.signal.lp2bp_zpk

[wired8]

Describe the solution you'd like

Please implement https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lp2bp_zpk.html

Additional context

Source:

def lp2bp_zpk(z, p, k, wo=1.0, bw=1.0):
    r"""
    Transform a lowpass filter prototype to a bandpass filter.
    Return an analog band-pass filter with center frequency `wo` and
    bandwidth `bw` from an analog low-pass filter prototype with unity
    cutoff frequency, using zeros, poles, and gain ('zpk') representation.
    Parameters
    ----------
    z : array_like
        Zeros of the analog filter transfer function.
    p : array_like
        Poles of the analog filter transfer function.
    k : float
        System gain of the analog filter transfer function.
    wo : float
        Desired passband center, as angular frequency (e.g., rad/s).
        Defaults to no change.
    bw : float
        Desired passband width, as angular frequency (e.g., rad/s).
        Defaults to 1.
    Returns
    -------
    z : ndarray
        Zeros of the transformed band-pass filter transfer function.
    p : ndarray
        Poles of the transformed band-pass filter transfer function.
    k : float
        System gain of the transformed band-pass filter.
    See Also
    --------
    lp2lp_zpk, lp2hp_zpk, lp2bs_zpk, bilinear
    lp2bp
    Notes
    -----
    This is derived from the s-plane substitution
    .. math:: s \rightarrow \frac{s^2 + {\omega_0}^2}{s \cdot \mathrm{BW}}
    This is the "wideband" transformation, producing a passband with
    geometric (log frequency) symmetry about `wo`.
    .. versionadded:: 1.1.0
    """
    z = atleast_1d(z)
    p = atleast_1d(p)
    wo = float(wo)
    bw = float(bw)

    degree = _relative_degree(z, p)

    # Scale poles and zeros to desired bandwidth
    z_lp = z * bw/2
    p_lp = p * bw/2

    # Square root needs to produce complex result, not NaN
    z_lp = z_lp.astype(complex)
    p_lp = p_lp.astype(complex)

    # Duplicate poles and zeros and shift from baseband to +wo and -wo
    z_bp = concatenate((z_lp + sqrt(z_lp**2 - wo**2),
                        z_lp - sqrt(z_lp**2 - wo**2)))
    p_bp = concatenate((p_lp + sqrt(p_lp**2 - wo**2),
                        p_lp - sqrt(p_lp**2 - wo**2)))

    # Move degree zeros to origin, leaving degree zeros at infinity for BPF
    z_bp = append(z_bp, zeros(degree))

    # Cancel out gain change from frequency scaling
    k_bp = k * bw**degree

    return z_bp, p_bp, k_bp