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I like your recipe analogy – let’s try using it: If we construct a recipe using the wrong phase, we’ll use the correct ingredients (i.e., sinusoids with the correct magnitudes), but in the wrong relationship to each other.
On the left of the attached picture (you may need to be logged in to see it) is a cake constructed with the correct phases of all the ingredients. On the right, the same ingredients with the wrong phases. Close your eyes and they will taste the same, but they look very different.
Note that the sinusoid basis functions in Fourier analysis can never cancel each other out though – because they are orthogonal.
Attachments:
You must be logged in to view attached files.The video Frequency domain will help you understand why phase is less important than magnitude, for human perception, and for speech technology.
The terms ‘pitch period’ and ‘fundamental period’ are used interchangeably in the field. You’re right that this is technically incorrect.
‘Register’ here just means ‘in a different frequency range’.
Don’t worry if you think you are only analysing these sounds in very simple terms: you are – that’s the point here: just get get our hands on some audio samples and inspect them. Do the readings as well as the exercises – they will help.
We are usually only concerned with taking the DFT of real-valued signals, such as speech waveforms. So, we will always see this mirroring.
Here are some further clues:
1) the mirroring is centred around the Nyquist frequency
2) the signal does not contain any information above the Nyquist frequency
3) aliasing !Fourier analysis only works for sinusoidal basis functions.
There are other forms of analysis that use different basis functions, but those are far less common (and far beyond the scope of Speech Processing). Even in those cases, the basis functions need to obey certain properties (e.g., arranged in a series like the sinusoids in Fourier analysis, orthogonal, etc).
Your two basis functions are actually identical (except for amplitude), so are definitely not a valid series of basis functions.
The VPN makes your personal computer become part of the University’s internal network. This enables access to certain parts of the University computing infrastructure that cannot be accessed from the outside world.
In general, you do not need to be connected to the VPN all the time. Just use it when instructed.
For Speech Processing, you’ll need the VPN at the start of the first assignment, when there will be some files to copy from the University filesystem to the Virtual Machine.
sp-m1-3-sampling-sinusoids notebook, section Magnitude and Phase Modifications
The unit circle is always centred at the origin (0,0).
A sinusoid with no phase shift starts on the unit circle at co-ordinates (1,0).
A sinusoid with a phase shift starts somewhere else on the same unit circle. The amount of phase shift specifies how far around the unit circle that starting point is. For example, a phase shift of pi/2 radians would mean moving that far around the unit circle and thus starting at (0,1).
Good – you are reading the tutorial carefully!
This is not significant – we can use any symbol we like in Euler’s formula (so long as we use the same one on the right and left-hand sides of the equation, of course!). theta and phi are popular choices for angles, in geometry.
(The Wikipedia page on Euler’s formula uses x in the text but phi in the diagram, for example).
The Speech Processing course prioritises conceptual understanding over mathematical ability.
If you can draw a diagram of a concept, and explain it in words, then you’ll do well on this course.
The SIGNALS tutorials at the start of this course involve maths that most students will find challenging. You won’t be directly examined on this maths: we’re using it as a tool to explain and understand the concepts.
Keep trying to understand the maths, and keep asking for help with it. But always remember that it’s the concepts that really matter.
You don’t need both, just the the VM.
Yes, there are some Hyper-V settings that may need to be different to run WSL vs VMWare, although the latest versions of VMWare on Windows claim to have solved this.
It looks like Fusion Player (which they only made free very recently) only exists in version 12. So your remaining options are:
Upgrade your Mac to 10.15 Catalina – if you were planning to upgrade anyway, now is the time (not mid-semester). Some very old software may no longer work, so check that first if you rely on this.
Use VirtualBox free host software instead of VMWare. It is not as good but should work.
Purchase either VMWare or Parallels Desktop 16 for Mac. Look for education discounts (Parallels is £35 for 1 year, for students). In either case, get a free trial license first to confirm it works on your Mac and with our VM image.
“Foundations of speech”, “Speech Synthesis” or “Automatic speech recognition” would all be relevant for this course.
If you’re not sure where to post, just guess! The main thing is to ask your question somewhere. We’ll move posts around to keep things organised.
The free license key is only for VMware Fusion Player, so the first thing to check is that you downloaded that, not the full version (which is not free). Check, and report back.
It’s possible to only use Notable – it just needs a decent internet connection.
To use the Jupyter Notebooks on your personal computer, simply follow the setup instructions: these will install all the necessary packages in a Python virtual environment.
Start up the Virtual Machine (VM), and inside that start a web browser (e.g. Chrome). Use that browser to follow the LinkedIn course, so that any files you download will be saved inside the VM.
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This is the new version. Still under construction.