Audio spectrum analyzer implemented with a minimum number of multiply operations

摘要

A spectrum analyzer that may be implemented by a simple microcontroller that does not have a hardware multiply function is disclosed. The spectrum analyzer of the present invention utilizes at least five frequency bins. The input signal is sampled at four times the bin frequency. The input signal is sampled at twice the Nyquist rate, which results in symmetries in the sin(wn) and cos(wn) functions. These symmetries allow the in-phase and quadrature components of the input signal to be calculated by add, ignore or subtract operations instead of the more complex multiplication and integration operations. Accordingly, the energy for each bin may be calculated with a minimum number of multiply operations. Because the number of multiply operations have been significantly reduced, these multiply operations may be performed by software instead of hardware. As a result, the spectrum analyzer may be implemented with a simple processor that does not have a hardware multiply. Another frequency bin is added by oversampling the highest frequency. A low pass filter is used to eliminate the effect of aliasing on the other frequency bins. A simple processor can still handle a bin that has been processed in this manner. As a result, at least five frequency bins may be processed by a spectrum analyzer implemented on a simple processor.