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I need to process an audio signal in an Android app. As shown in the two examples below, there is a 16kHz carrier signal and a lower frequency signal of varying frequency (0-4kHz). Does anyone know of an efficient algorithm to extract the lower frequecy signal in an Androd app?
http://mc.weatherflow.com.s3.amazonaws.com/media/IMG_03102014_135912.png
If you know your carrier is always exactly 16kHz (within a few percent or so), and you have sampled the audio at 48kHz, you can try a simple 3-tap FIR filter approach:
$$Smoothed(k) = \frac{1}{3}( Sig(k) + Sig(k-1) + Sig(k-2) )$$
This assumes your original signal is called $Sig()$, and it computes a new signal, $Smoothed()$.
The method exploits the fact that three sample periods equates to one entire cycle of a 16kHz sine wave, so an 16kHz component in the input signal will be cancelled (since summing all the samples of a full sine wave cycle will result in zero).
The resulting $Smoothed()$ signal should look like you original plots, with the furry 16kHz components gone.
If your sample rate is not 48kHz (let's call it $F_s$), or if your interfering sine wave is at some other frequency (let's call it $F_i$), you can craft the 3-tap filter as follows:
$$Smoothed(k) = \frac{1}{2-2\cos(\omega)}( Sig(k) - 2\cos(\omega) Sig(k-1) + Sig(k-2) )$$
where $\omega = 2\pi\frac{F_i}{F_s}$ (note that, if $F_i=16000$ and $F_s=48000$, we get $\omega=\frac{2\pi}{3}$ and hence $\cos(\omega)=-\frac{1}{2}$. If you substitute this into the second equation, you will simply get the first equation again.
This method is simply creating a $2^{nd}$ order FIR filter with zeros at $\pm F_i$, and with the gain at DC normalised to unity.
Similar to dave_mc's answer, the basic approach to do is to run the data through a low-pass filter that will eliminate the 16 kHz noise. The passband edge would be the highest frequency of your signal of interest- 4 kHz in this case. The stopband edge would be the lowest frequency of your noise.
If dave_mc's targeted FIR approach works, then great. If you want a more generalized low-pass filter that is computationally efficient than I would probably use an IIR filter.
Once the noise is removed I would search for local peaks and use them to determine where the cycles are repeating. You should then be able to determine the cycle frequency.
