A practical loudspeaker frequency response interpolation model is developed using a modification of the Tuneable Approximate Piecewise Linear Regression (TAPLR) model that can provide a complete magnitude and phase response over the full frequency range of the loudspeaker. This is achieved by first taking standard one-twelfth octave frequency interval acoustic intensity measurements at a one meter distance in front of the loudspeaker. These measurements are inserted directly into the formulation, which then requires only minimal tuning to achieve a magnitude response model to better than +/- 1 dB error as compared with the magnitude of the Fourier transform of the impulse response for typical hi-fi loudspeakers. The Hilbert transform can then be used to compute the corresponding phase response directly from the resulting magnitude response. Even though it is initially based on consecutive piecewise linear sections this new model provides a continuous smooth interpolation between the measured values that is much more satisfactory than normal piecewise linear segment interpolation and much simpler to do than polynomial interpolation. It only requires the tuning of a single parameter to control the degree of smoothness from a stair step response at one extreme to a straight mean horizontal line at the other. It is easy to find the best tuning parameter value in between these two extremes by either trial and error or by the minimisation of a mean squared interpolation error
