[Simon]

‘Sampling’ is indeed used to mean several things.

When talking about digital signals, sampling means the process of converting an analogue signal (in continuous-time) to a digital one (in discrete time): we take samples at regular intervals. A ‘sample’ here is a single number, stored in binary form (e.g., using 16 bits).

But we could also use the term ‘sample’ to describe a speech waveform taken from a larger one, perhaps for the purposes of speech synthesis. This use of ‘sampling’ is like in music production when someone ‘borrows’ a sample (e.g., a few notes, or a drum beat) from an existing track, and makes new music with it.

[Simon]

In your plot, make sure you know the difference between bins (all the red points) and the energy in the signal (in this case, the harmonics) which are only the red points with non-zero magnitude.

Earlier, we agreed that the lowest frequency basis function is the one with a single cycle in the analysis frame (e.g., 1 Hz for a 1 s analysis frame).

Your plot is consistent with that, except that there is also a bin at 0 Hz. We often disregard this because it doesn’t tell us about the frequency content of the signal, but about something else.

To understand why there is some energy at 0 Hz, and what that means, can you first describe what that 0 Hz basis function looks like?

[Simon]

That will work fine, or use ctrl-C in the Terminal to terminate the Jupyter process (it will prompt you if you really want to quit).

[Simon]

You are correct: “bins are then the discrete frequencies of the basis functions” – they are indexed by k in the DFT equation in the notebooks.

The DFT bins are determined only by the duration of the analysis frame and the sampling rate. They do not and cannot depend on the signal (e.g., on its fundamental frequency), because the DFT works for any signal and gives the same frequency resolution in all cases (for a particular sampling rate and analysis frame duration).

You correctly state that, for a 1 s analysis frame duration, the lowest frequency bin will be at 1 Hz. (We don’t even need to know the sampling rate to work this out.)

You are also correct in stating that when analysing a signal with energy at an “awkward” frequency (i.e., not an exact bin frequency), we will get leakage across several adjacent bins around that frequency.

Your final point is also correct: to construct a single impulse, we need to sum together all basis functions with equal amplitudes. The spectrum is flat, and there are no harmonics (because the single impulse is not a periodic signal).

Overall, your understanding looks pretty good!

[Simon]

Just to check – you posted this under “Remote Desktop” but you are actually using the Virtual Machine?

To solve the sound issue, try this and report back.

[Simon]

Yes, you’ve got it. k is indexing frequency – sometimes we say it is the DFT “bin”.

When plotting X[k] the axis will run from 0 to K (not from k to K). We could label that axis with the integers 0 to K (some of the notebooks do that), or we could convert k to Hz and label the axis with frequency.

How do we convert the integer k into a frequency in Hz ?

[Simon]

Your command

festival> (set! myutt "COVID19 is very dangerous")

sets the variable myutt to a string, which is not what you need to do. myutt should be a Festival Utterance object, so you need this (as in the instructions):

festival> (set! myutt (Utterance Text "COVID19 is very dangerous"))

which creates a new Utterance object and stores it in the variable myutt.

[Simon]

You might need to install ffmpeg. See this post and let us know if that solves it.

[Simon]

Are you connected to the VPN (on the host computer, i.e., your personal computer)?

[Simon]

The magnitude spectrum is not exactly the same thing as the spectral envelope.

The magnitude spectrum is something that can be obtained for any signal, such as speech, by taking the DFT of the signal (and discarding phase).

Looking at the magnitude spectrum of speech, we see two very different properties combined. One is the overall shape – the spectral envelope. The other is the fine structure.

For speech, the frequency response of the vocal tract filter is responsible for creating the spectral envelope of the speech signal.

For voiced speech, the fine structure will be a regular series of harmonics at multiples of F0, and this is created by the vocal folds.

[Simon]

Did you copy the files using rsync ?

[Simon]

Try rebooting the host machine too.

[Simon]

Sometimes the VM loses the network connection to the host computer. Can you reach any websites using a web browser in the VM? If not, then the network connection is definitely the problem.

First thing to try: restart the VM.

Let us know if this solves the problem, or if you need more help.

[Simon]

In the Linux VM, open Applications – System Tools – Settings (which you have open in your screenshot).

In Settings, look under Devices to find Displays, where you can change the resolution.

Report back to let others know if this works, or to let me know you need more help..

[Simon]

Did you complete Module 0, and was the sound working then?

Try Virtual Machine – Settings – Add Device (it’s a button on the Settings window, top right) and see if you can add a Sound Card. See screenshots attached.

You may need to do this when the virtual machine is shutdown, not running.

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