Can I get a higher resolution in the frequency domain with a stereo signal?

Question

Background

I admit that this issue is connected with the final lack of a deep understanding of basic mathematics related to digital signal processing; I am still studying.

I want to take a set of amplitude samples, for example 1024 (one channel), and bring them into the frequency domain. Obviously, this requires an FFT; no problem. The problem is that it only gives me frequencies up to the Nyquist frequency or 1024/2.

Question

If I have a stereo signal, can I combine the signals to create 2048 amplitude samples, thus returning 1024 frequency values? I want to get a higher resolution in the frequency domain.

So, is it possible to do this and return meaningful frequency data? Is there any other way to take a stereo signal and get higher resolutions in the frequency domain?

What i have found so far

I came across an article that suggested taking the left signal and making it the real value and the correct signal and making it the imaginary value of the complex value for the FFT. This does not make sense to me, perhaps because I do not understand math. I tried and it seemed to work, but I had a signal leak. Therefore, I applied the Hanning window, but after processing it received only 512 useful values.

Answer 1

If the signal you are analyzing has received from a physical signal, you cannot do anything. The merging of signals into one large array of 2048 samples will be sufficient to perform mathematics, but the result will be meaningless.

As an example, we make an array of 2048 cells and fill it as follows:

original = int [1024];
new = int [2048]
new [2 * n] = original [n];
new [2 * n + 1] = original [n];

This way you get a larger array and a higher frequency, but as your original data matches, the result you get will not be useful, it will be the same as the original FFT.

If you need only a higher-frequency analysis, you can do 2 things, change the sampling rate (I suppose you use the sound line in the jack) to the maximum that your sound card can use (mainly 48 kHz). Or, secondly, change the collection board to some specific equipment (any special usb assembly board can get up to 1 MHz easily).

Ps: frequency is 1024/2 times the sampling frequency. Remember to multiply the sampling rate.

Answer 2

In general, no. Your stereo signal is, of course, 2048 amplitude samples, but these are samples from two separate channels, each of which was filtered to remove all information above the Nyquest frequency before A / D conversion.

Two cases to consider turning on a 48 kHz channel pair:

• A signal with a frequency of 1000 Hz, recorded in the upper left corner, and a signal with a frequency of 2000 Hz, folded to the right. There is no relationship between them and none of the signals is present in the opposite channel, so combining them makes no sense.

• The 50 kHz signal took off to the left. There is nothing in the right channel, and if you accept the correct cutoff filter, nothing in the left channel. Without filtering, you have nonsense in the left channel.

However, you might think that if a pair of microphones recorded the surrounding signal in the room and you removed the cutoff filters, the phase differences between the two microphones could give you more information about the real signal. This would be a fascinating field of research, but, as far as I know, a long, long way from practical implementation at the moment.

Answer 3

Special occasion:

You can imagine a device with a single-point sound source, and the stereo input is designed to receive a half-wave offset between two channels.

Then you can combine the channels to receive high-frequency data.

You can do a nice demo, but this is not a practical application.

Answer 4

There is one possibility when you can get a higher speed from two channels. Often analog-to-digital systems are multiplexed, that is, they use one analog-to-digital converter for two channels alternating between them. If it was in your record, and two channels had an almost identical input, and the other variables were in your favor, then you could have twice the base sampling frequency.

It's a long shot, but maybe worth checking out. And if so, you can restore a higher frequency by simply interleaving the two channels in the correct order. (I see no reason for the idea of ​​turning one into a complex channel.)

To check if this is true, you can simply look at the alternating channel graph or plot the cross-correlation graph.

Answer 5

No, it cannot be done!

Left and right channels are combined into the imagination. number (left [i] + right [i] * j) form one signal, which contains two different audio channels. Such a signal can be mixed and transmitted through the medium (air, water, radio frequency). It is simply a means of multiplexing two real channels into one complex signal with similar bandwidth.