DFT/FFT in log frequency scale...?

I wonder if there is a convenient fast transform available to compute
the frequency spectrum with bins distributed in a logarithmic or near-
logarithmic frequency scale.

Here is the application background. In sound/acoustic/vibration signal
processing, it is common to use a so called fractional octave
analysis. Usually the cctave resolution is 1/1, 1/3, 1/6, 1/12, 1/24
or 1/48. a 1/3 octave filter bank means each octave will have 3
filters, which are all distributed evenly in the log frequency scale.
The existing technology to compute such a octave spectrum are:

1. Use multi-stages of decimation filters. In each stage of
decimation, IIR or FIR bandpass filters are applied. The output of
each filter is a 'bin"
2. Use multi-stages of decimation filters, in each stage of
decimation, FFT is used, after the FFT, filter banks are sythesized
using the FFT.
3. Use DFT, where frequencies can be well controlled but the speed of
computation is a big problem

it would be nice if somebody comes up a fast transform so that the
output of spectrum already takes the form of "log-distributed
frequency". it does not need to be exactly in log. The frequency of
each bins can be like this:

1Hz, 1Hz, ...1Hz, 2Hz, 2Hz, ...2Hz, 4Hz, 4Hz,.....4Hz, ......64Hz,
64Hz, ...64Hz

Any idea?

James
www.go-ci.com

>I wonder if there is a convenient fast transform available to compute
>the frequency spectrum with bins distributed in a logarithmic or near-
>logarithmic frequency scale.
>
>Here is the application background. In sound/acoustic/vibration signal
>processing, it is common to use a so called fractional octave
>analysis. Usually the cctave resolution is 1/1, 1/3, 1/6, 1/12, 1/24
>or 1/48. a 1/3 octave filter bank means each octave will have 3
>filters, which are all distributed evenly in the log frequency scale.
>The existing technology to compute such a octave spectrum are:
>
>1. Use multi-stages of decimation filters. In each stage of
>decimation, IIR or FIR bandpass filters are applied. The output of
>each filter is a 'bin"
>2. Use multi-stages of decimation filters, in each stage of
>decimation, FFT is used, after the FFT, filter banks are sythesized
>using the FFT.
>3. Use DFT, where frequencies can be well controlled but the speed of
>computation is a big problem
>
>it would be nice if somebody comes up a fast transform so that the
>output of spectrum already takes the form of "log-distributed
>frequency". it does not need to be exactly in log. The frequency of
>each bins can be like this:
>
>1Hz, 1Hz, ...1Hz, 2Hz, 2Hz, ...2Hz, 4Hz, 4Hz,.....4Hz, ......64Hz,
>64Hz, ...64Hz
>
>Any idea?
>
>James
>www.go-ci.com
>

Hi,

lookup constant-q spectrum or constant-q transform.

ida.first.fhg.de/publications/drafts/Bla_constQ.pdf 

maybe that could be of help.

gr.
Bjoern