Extract frequencies from PCM signal
It is not clear if you want to visualize the signal or process/transform it ("graphic equalizer" is an effect/transformation adjusting the signal level independently in various frequency bands, not a visualization - a more correct term for the representation you posted an image of is "spectrum analyzer").

It is not clear if you are working in the analog domain or the digital domain, and what kind of technology you want to employ (analog electronics? computer code running on a DSP chip or microcontroller? on a desktop computer?).

Are your signals audio signals? In which case you have to be aware that a meaningful representation should display the 20 Hz .. 20kHz range (range of human hearing), and that it should be subdivided logarithmically.

To get this kind of visualization, there are two solutions:


A bunch of band-pass filters (and a low-pass + a high-pass for the lower and higher channels). You then measure the (log-) energy in each band to get the "height" of each bar. This can be done in the analog domain (a bunch of op-amps for the filter, a rectifier to measure the signal level, and a log-amplifier to get the energy on a log scale; or with dedicated ICs like the MSGEQ7); or in the digital domain with digital filters.
A FFT + some grouping of adjacent bins (which is more or less equivalent to computing the filter bank in the frequency domain). Note that this can only be used for digital signals.