High-Precision Fractional-Order Integrator for Generating Pink Noise from White Noise

For audio testing, a pink noise generator is a very useful and widely used tool for equalization of loudspeaker systems, room acoustics and crossovers. It can be built as a digital, analog or mixed circuit. The pink noise generator consists of a white noise source followed by a fractional order integrator (FOI) with a roll-off of 10 dB/decade. In this way, the obtained output power is constant in each decade, which is essential for testing audio devices within the entire audio frequency band. In this paper, an active realization of an FOI with an order 1/2 is presented, using an active-RC circuit that uses an operational amplifier as the active element. To build an FOI, we can use different approximation methods. We use our recently published Minimax method (MMX), with unequally (optimally) spaced singularities and compare it with a method proposed by other authors. The latter intuitively considers optimal singularities equally spaced on a logarithmic scale. We demonstrate the superiority of our proposed MMX approach.