Embedded Music for low freq signals

[PAk-CatchFire]

Hello.
I am trying to implement a low memory Music algorithm to separate breathing and heart rate signals, which are 0.5Hz and 1-2Hz, on an ARM processor.

After some filtering I arrived to your implementation of Music, but I have seen that it is mostly prepared for 8kHz and 16 sample signals, and I am using 56 Hz as Fs and 200-500 sample points FFTs.

Would it be too difficult or memory dependant to adapt this library?
Thank you

[spinlockirqsave]

Hi, and many thanks for your question.

The libmusic will work with 56 Hz and 200-500 point FFT. The primary need addressed by this library was detection of DTMF frequencies in audio range, and this is why you can find lm_dtmf_detect function and other DTMF related things there, but library is meant to work with signals of other natures as well. The number of samples in a probe vector determines the accuracy of the detection, and depends on a number of frequencies (signal components) to be detected. It should be at least 8 times number of components, so for your 0.5 Hz and 1.2 Hz components it's at least 16 samples. The number of components should be known in advance for algorithm to give good results in the current implementation (limitation of MUSIC algorithm).

RAM

In your case of 2 signal components there will need to be at least this memory allocated(*):

• Array 'A': 9 * 8 * sizeof(double) = 9 * 8 * 8 (on x86 and x86_64) = 576 bytes
• Array A2: 9 * 8 * sizeof(double) = 9 * 8 * 8 (on x86 and x86_64) = 576 bytes
• Array S: 9 * 8 * sizeof(double) = 9 * 8 * 8 (on x86 and x86_64) = 576 bytes
• Array U: 9 * 9 * sizeof(double) = 9 * 9 * 8 (on x86 and x86_64) = 648 bytes
• Array VT: 8 * 8 * sizeof(double) = 8 * 8 * 8 (on x86 and x86_64) = 512 bytes
• Detections array: 0.5Fs * 10 = 40 kB
• Re Array: 8 * 8 = 64 bytes
• Im Array: 8 * 8 = 64 bytes
• LAPACK's output: 4544 bytes
• Other internal LAPACK memory: ? Test needed
• Other internal structures = ~300 bytes
• TOTAL RAM: (43.016 + 4.544 + ~0.3) kB + other LAPACK's internal mem = ~50.818 kB + other LAPACK's internal mem

(*) - on x86 and x86_64, but size of double may be different on your CPU/ALU

Library will reuse buffers (they are allocated once per all calls to lm_detect for a given detection session).

Please shout if you have any other questions.

[PAk-CatchFire]

Thank you!! That answer is quite helpful.
Right now we are working with a 57.6Hz sampling freq (Actually is a matrix of <4k points at 250kHz and then a sencond 2D FFT of 56.7Hz). The number of samples is not an issue, and we are using more than 200 hundred points for every MUSIC sliding window, we are searching for two frequencies.

What are the changes you would recommend to make the code work on this environment?

On the other hand, since I am trying to use it on a DSP, would it be possible to change the double variables to float?

Do you suggest an example for my test?

Thank you again

[spinlockirqsave]

Floats are possible. Which DSP you want to port this code for? Do you have SVD available on that processor?

[PAk-CatchFire]

Probably F28379D, or something in the family.

You can get a low cost board here:
http://www.ti.com/tool/LAUNCHXL-F28379D

BTW, why are you using the names: peak_697, etc?
As in:

if (f == 697) {
			d->info.peak_697 = peak;
		} else if (f == 770) {
			d->info.peak_770 = peak;
		} else if (f == 852) {
			d->info.peak_852 = peak;
		} else if (f == 941) {
			d->info.peak_941 = peak;
		}

```
if (f == 1209) {
		d->info.peak_1209 = peak;
	} else if (f == 1336) {
		d->info.peak_1336 = peak;
	} else if (f == 1477) {
		d->info.peak_1477 = peak;
	} else if (f == 1633) {
		d->info.peak_1633 = peak;
	}

``
Thank you again

[PAk-CatchFire]

Do you have SVD available on that processor?

You have some DSP and Math libraries, but probably not SVD per se. That's why I want to implement Music (or Burg) on it.

Both seem to work for this application (not for Yule Walker)

[spinlockirqsave]

Those peak_* variables are only for convenience of DTMF detection, they correspond to DTMF frequencies and are only used for quick access to frequencey detection results corresponding to DTMF.

Thank you for the link to the DSP board, I am having a look.

You have some DSP and Math libraries, but probably not SVD per se. That's why I want to implement Music (or Burg) on it

For MUSIC you need SVD to find eigenvectors corresponding to nullspace of correlation matrix.

[PAk-CatchFire]

For MUSIC you need SVD to find eigenvectors corresponding to nullspace of correlation matrix.

Where is the source code of your SVD function dgesvd?

Thank you

[piotrgregor]

dgesvd comes with LAPACK. It's definition can be found here

[PAk-CatchFire]

What are the minimum files I could use from the Laplace library to make it work on the DSP?
I am worried about memory size.
Regards

[spinlockirqsave]

Sorry, I am not sure what you mean by Laplace library? Did you mean LAPACK?