Multi-channel light-emitting diode (LED) light sources have been developed for various applications in lighting, but especially for spectrum-tunable lighting. However, how to select the optimal combination of LEDs for these light sources is rarely discussed. Unlike the negative-pruning process which operates by removing LEDs from a set of available LEDs based on an unrealizable negativecoefficient criterion alone, the proposed pruning process removes LEDs so as to minimize the synthesis error. This method not only produces the same optimal set of LEDs as those identified by the full-search method but also suggests when using phosphor-converted LEDs is beneficial. It does this by investigating the trade-off between the full width half maximum of the LEDs and the number of LEDs.

To synthesise a spectrum with a given radiant flux by multi-channel light-emitting diodes, different light-emitting diodes should have different radiant fluxes to maximise the light-emitting diode flux utilisation rate defined by the radiant flux of the light-emitting diode's contribution to the synthesised spectrum divided by the rated radiant flux of this light-emitting diode. The optimal rating radiant flux algorithm for each light-emitting diode is achieved by applying the normreducing process and full-search method to the norm region of the spectra. As a result, light-emitting diodes with a broader full-width half maximum, such as phosphor-converted light-emitting diodes, are usually set at a high power level and the rest of the light-emitting diodes can be set to either medium or low power levels. Furthermore, the high-power light-emitting diode can be decomposed to some low-power light-emitting diodes to reduce both heat generated and lightemitting diode price.

Multi-LED colour mixing light sources are increasingly being used in lighting. The method used to set the dimming signal needs to accurately achieve and sustain the desired colour temperature and high colour rendering index (CRI). A pulse width modulation (PWM) signal is always used in LED colour mixing. But the PWM switch state creates a time delay in the multi-LED current regulator, resulting in a colour difference. A modified PWM signal to accurately maintain the desired colour temperature and a high CRI is derived from a parameterised LED current regulator switch state, using curve fitting. The modified PWM signal can be calculated from reconstructed coefficients of the illuminant spectrum.