Scipy : fourier transform of a few selected frequencies

Question

I am using scipy.fft on a signal, with a moving window to plot the amplitudes of frequencies changing with time (here is an example, time is on X, frequency on Y, and amplitude is the color).

However, only a few frequencies interest me (~3, 4 frequencies only). With FFTs it seems like I can't select only the frequencies I want (cause apparently the range of frequencies is determined by the algorithm), so I calculate a lot of useless stuff, and my program even crashes with a MemoryError if the signal is too long.

What should I do ? Do I have to use a custom Fourier transform - in which case, links of good implementations are welcome - , or is there a scipy way ?

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EDIT

After @jfaller answer, I decided to (try to) implement the Goertzel algorithm. I came up with this : https://gist.github.com/4128537 but it doesn't work (frequency 440 doesn't appear, nevermind the peaks, I didn't bother to apply a proper window). Any help !? I am bad with DSP.

Answer 1

You're really looking to use the Goertzel Algorithm: http://en.wikipedia.org/wiki/Goertzel_algorithm. Basically, it's an FFT at a single point, and efficient if you only need a limited number of frequencies in a signal. If you have trouble pulling apart the algorithm from Wikipedia, ping back, and I'll help you. Also if you google a few resources, there exist DTMF decoders (touch tone phone decoders) written in python. You could check out how they do it.