Spectogram - confusion

Hi,

As input I am using a 100ms audio fragment (44100 Hz).

So the Raw feature set consists of following 4410 numbers:

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The following Processed features are returned (54 numbers).

0.9453, 0.0000, 0.0264, 0.0241, 0.0407, 0.0009, 0.0856, 0.0078, 0.0011, 0.0262, 0.0934, 0.0814, 0.0793, 0.0049, 0.0204, 0.0989, 0.0086, 0.0059, 0.0191, 0.0124, 0.0104, 0.0220, 0.0223, 0.0227, 0.0286, 0.0041, 0.0284, 0.0137, 0.1771, 0.3029, 0.0029, 0.0029, 0.1414, 0.2703, 1.0000, 0.1793, 0.0122, 0.0050, 0.0667, 0.0331, 0.3692, 0.1990, 0.1903, 0.0176, 0.0229, 0.0179, 0.0557, 0.0065, 0.1181, 0.0187, 0.0037, 0.0036, 0.0145, 0.0776

The following 2 things are confusing:

  1. The spectogram diagram shows only 6 frequency bands while I have specified 10 Frequency bands in the spectogram parameter section.
  2. The spectogram diagram shows 9 time periods while I would expect 10 time periods (as my sample = 100 ms and frame length = 0.05 (= 50 ms) and frame stride = 0.005 (= 5 ms).

When I then open the NN Classifier it shows the following:

What is also confusing :
3. The input layer mentions 60 features while the spectogram block is apparently only outputting 54 features. So how is this mismatch explained ?

Hi @janvda,

We are going to add some documentation soon on the different DSP blocks.

In the meantime, here are some more details on the Spectrogram: the frequency bands corresponds to the number of FFT points. There is a correlation between the FFT size (number of FFT points) and the sample length.

In the FFT transformation documentation:

n: Number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

In your case you have 2205 samples in a subframe (50ms frame length @ 44.1kHz) so your input will be cropped as you set FFT size to 10. Also, it would be better to keep it as a power of 2 (128 to 512 are usual values).

For the output (number of frequency bins):

output: The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. If n is even, the length of the transformed axis is (n/2)+1. If n is odd, the length is (n+1)/2.

As FFT size is 10, you will have (10/2)+1 = 6 frequency bins.

Regarding the generated features, 60 should be the correct value. I’ll check why we display something different in the DSP block

Let me know if that clear things up,

Aurelien

1 Like

@aurel , thanks for your clear response.

  1. So in my example I have specified a Frame length of 0.05 sec but I could as well have specified 0.001 sec (=> this gives about 44 raw features for a 44.1 KHz input) as it is only considering the first 10 raw features within that frame as I had set Frequency bands to 10.

  2. So Frequency band parameter is not really the frequency band but the n parameter of the scipy.fft.fft function as specified in https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.rfft.html ?

@aurel, I have some follow up questions:

So I am assuming that the following algorithm is used to calculate the FFT : https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.fft.html#scipy.fft.fft

  1. The output of that algorithm is an array of complex numbers, while the edge impulse block is outputting an array of real numbers. So how do you get from the array of complex numbers to an array of real numbers ?
  2. The algorithm has also a norm input parameter. So is any normalization applied.

kr
Jan.

Hi @janvda,

The algorithm goes through those steps:

  • creating subframes
  • applying fft on subframes without normalization
  • compute power spectrum (this is based on the absolute value of the FFT -> output real numbers)
  • rescaling (min-max normalization)

Regarding your other questions:

  1. You could have specific a 0.001sec frame but it is most likely too short to extract meaningful features. It’s better to increase FFT length to 256 or 512.

  2. The spectrogram uses the scipy RFFT function underneath.

Aurelien

1 Like

It is still not exactly clear how you calculate the power spectrum.
I think RFFT is outputting complex numbers like

  • a + b.j

so did you calculate the power spectrum as

  • sqrt( a .a + b.b)

?

So is the rescaling happening per subframe only based on the power spectrum values calculated for that subframe ?

You’re right about power spectrum, the complete formula is:

1.0 / (FFT size) * (abs(fft) ^2)

with abs() being sqrt(a.a + b.b)

Rescaling is done over all the subframes -> input features to the NN are scaled to the [0; 1] interval

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I think that this might not be ideal for me.
The doorbell ring is not recorded that loudly by my device (device is in another room than doorbell). So if some other sound is rather loud for a specific frequency within a subframe of the 100 ms audio segment then this might scale down the relevant doorbell audio.
… but no issue: I will check this during testing.

Thanks a lot !

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