Logarithmically-spaced Dirac comb

Like the standard Dirac comb, the logarithmically-spaced Dirac comb consists of an infinite sequence of Dirac delta functions. In the case of the logarithmically-spaced comb, these are spaced in octave intervals, i.e., the delta functions are placed at positions $2^k\; f\_0$, for all integers $k$.

In musical applications, this type of Dirac comb can be used to create a 12-note scale that spans the infinite space of octaves. Such a log-spaced Dirac comb, with perhaps a Gaussian weighting, when ascending or descending, gives the well known Shepard tones effect of a sound which is perceived as though it is forever going up or down in pitch.