Real Time Goertzel Algorithm
You can use forms of the Goertzel algorithm as a fixed length block filter, as a IIR filter with a very long impulse response, or as a fixed length running filter.

As a fixed length filter, a Goertzel results in a FIR filter similar (almost identical) to the result of 1 bin of a DFT or FFT of the same length.

As an IIR filter, a Goertzel filter is on the edge on instability (pole right on the unit circle), so you may need to bound the filter state and/or output externally, or reduce the gain slightly below 1.0.

As a fixed length running filter, you subtract the output of  2 offset (but stabilized) Goertzel IIR filters to get a FIR filter or 1 bin of a DFT (length equaling the offset) that updates every input sample, and with very few MACs per sample.