DSP method to detect specific frequency which may not be the most dominant in the current sound

Question

I'm trying to determine the best DSP method for what I'm trying to accomplish, which is the following:

In real-time, detect the presence of a frequency from a set of different predefined frequencies (no more than 40 different frequencies all within a 1000Hz range). I need to be able to do this even when there are other frequencies (outside of this set or range) that are more dominant.

It is my understanding that FFT might not be the best method for this, because it tells you the most dominant frequency (magnitude) at any given time. This seems like it wouldn't work because if I'm trying to detect say a frequency at 1650Hz (which is present), but there's also a frequency at 500Hz which is stronger, then it's not going to tell me the current frequency is 1650Hz.

I've heard that maybe the Goertzel algorithm might be better for what I'm trying to do, which is to detect single frequencies or a set of frequencies in real-time, even within sounds that have more dominant frequencies than the ones trying to be detected .

Any guidance is greatly appreciated and please correct me if I'm wrong on these assumptions. Thanks!

Answer 1

In vague and somewhat inaccurate terms, the output of the FFT is the magnitude and phase of all[1] frequencies. That is, your statement, "[The FFT] tells you the most dominant frequency (magnitude) at any given time" is incorrect. The FFT is often used as a first step to determine the most dominant frequency, but that's not what it does. In fact, if you are interested in the most dominant frequency, you need to take extra steps over and beyond the FFT: you take the magnitude of all frequencies output by the FFT, and then find the maximum. The corresponding frequency is the dominant frequency.

For your application as I understand it, the FFT is the correct algorithm.

The Goertzel algorithm is closely related to the FFT. It allows for some optimization over the FFT if you are only interested in the magnitude and/or phase of a small subset of frequencies. It might be the right choice for your application depending on the number of frequencies in question, but only as an optimization -- other than performance, it won't solve any problems the FFT won't solve. Because there is more written about the FFT, I suggest you start there and use the Goertzel algorithm only if the FFT proves to not be fast enough and you can establish the Goertzel will be faster in your case.

[1] For practical purposes, what's most inaccurate about this statement is that the frequencies are grouped together in "bins". There's a limited resolution to the analysis which depends on a variety of factors.

Answer 2

I am leaving my other answer as-is because I think it stands on it's own.

Based on your comments and private email, the problem you are facing is most likely this: sounds, like speech, that are principally in one frequency range, have harmonics that stretch into higher frequency ranges. This problem is exacerbated by low quality microphones and electronics, but it is not caused by them and wouldn't go away even with perfect equipment. Once your signal is cluttered with noise in the same band, you can't really distinguish on from off in a simple and reliable way, because on could be caused by the noise. You could try to do some adaptive thresholding based on noise in other bands, and you'll probably get somewhere, but that's no way to build a robust system.

There are a number of ways to solve this problem, but they all involve modulating your signal and using error detection and correction. Basically, you are building a modem and/or radio. Ultimately, what I'm saying is this: you can't solve your problem on the detector alone. You need to build some redundancy into your signal, and you may need to think about other methods of detection. I know of three methods of sending complex signals:

• Amplitude modulation, which is what it sounds like you are doing now.
• Frequency modulation, which tends to be more robust in the face of ambient noise. (compare FM and AM radio)
• Phase modulation, which is more subtle and tricky.

These methods can be combined and multiplexed in various ways. Read about them on wikipedia. Moreover, once your base signal is transmitted, you can add error correction and detection on top.

I am not an expert in this area, but off the top of my head, I am not sure you'll be able to use PM silently, and AM is simply too sensitive to noise, as you've discovered, although it might work with the right kind of redundancy. FM is probably your best bet.