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Simon November 23, 2014

The Gaussian probability density function: understanding the equation

slownormalfast

The equation for the Gaussian probability density function looks a little scary at first, but this video should help you understand what each of the terms is doing, and how they fit together.

After watching the video

download the spreadsheet which shows the calculations and plots from this video (tip: the Apple Numbers.app version includes images of the equations) – try changing the mean and variance and see what happens to the various plots
try this interactive demo to get a feel for how the mean and standard deviation affect the shape of the distribution

Filed Under: Probability Tagged With: equations, Gaussian, spreadsheet, video

Simon October 31, 2015

The speed of sound

At the Parque de las Ciencias in Granada, Spain there is this long tube, open at the end nearest you and closed at the far end. We can calculate the length of this tube just from the audio recording, because we know the speed of sound. Here’s the waveform of part of the recording, showing […]

Filed Under: Signals Tagged With: video, Wavesurfer

Simon February 1, 2015

Autocorrelation for estimating F0

Most methods for estimating F0 start from autocorrelation. The idea is pretty simple: we are just looking for a repeating pattern in the waveform, which corresponds to the periodic vocal fold activity. For some waveforms, it might be possible to do that directly in the time domain, but in general that doesn’t work very well. […]

Filed Under: Signals Tagged With: spreadsheet, video

Simon November 15, 2014

Token passing

Token passing is a really nice way to understand (and even to implement) Viterbi search for Hidden Markov Models. Here we see token passing in action, and you can look at the spreadsheet to see the calculations. To keep things simple, we are ignoring transition probabilities in this example. It would be simple to add them […]

Filed Under: Models, Recognition Tagged With: HMMs, spreadsheet, video

Simon October 11, 2014

Aliasing

In sampling and quantisation we saw that sampling a signal at a fixed rate means that there is an upper limit on the frequencies that can be represented. This limit is called the Nyquist frequency. Before sampling a signal, we must remove all energy above the Nyquist frequency, and here we will see what would […]

Filed Under: Signals Tagged With: Digital signal, video

Simon October 25, 2014

A super-simple speech recogniser

We make what is possibly the world’s simplest speech recognition system. It can only recognise two different words, but will help you understand the basic idea of pattern recognition using template matching. The templates are just pre-recorded words, with known labels. The features extracted are just two formant frequencies in the middle of the word, […]

Filed Under: Recognition Tagged With: Classification, equations, Wavesurfer

Simon October 30, 2015

Wave propagation on the surface of water

At the Alhambra (Granada, Spain) I saw this nice example of waves from a point source propagating in all directions at a fixed speed.

Filed Under: Signals Tagged With: video

Simon October 11, 2014

A simple synthetic vowel

Using Praat, we synthesise a simple vowel-like sound, starting with a pulse train, which we pass through a filter with resonant peaks.

Filed Under: Synthesis Tagged With: Harmonics, praat, Source-filter model, Spectral envelope, video

Simon October 11, 2014

Sampling and quantisation

Is digital better than analogue? Here we discover that there are limitations when storing waveforms digitally. We learn that the consequence of sampling at a fixed rate is an upper limit on the frequencies that can be represented, called the Nyquist frequency. In addition to the limitations of sampling, storing each sample of the waveform as a […]

Filed Under: Signals Tagged With: Digital signal, video, Wavesurfer

Simon October 12, 2014

Entropy: understanding the equation

The equation for entropy is very often presented in textbooks without much explanation, other than to say it has the desired properties. Here, I attempt an informal derivation of the equation starting from uniform probability distributions. A good way to think about information is in terms of sending messages. In the video, we send messages […]

Filed Under: Probability Tagged With: entropy, equations, video

Simon October 11, 2014

Pipeline architecture for TTS

Most text-to-speech systems split the problem into two main stages. The first stage is called the front end and contains many separate processes which gradually build up a linguistic specification from the input text. The second stage typically uses language-independent techniques (although they still require a language-specific speech corpus) to generate a waveform. Here we see those two […]

Filed Under: Synthesis Tagged With: front end, video, waveform generation

Simon January 2, 2016

Interactive unit selection

Just a toy demo, but should give you some idea of how unit selection waveform generation works. Click with your mouse to choose a candidate diphone from each column, then the corresponding synthesised waveform will appear. You can click on the synthesised waveform to hear it again. Try to obtain the most natural-sounding synthesis by […]

Filed Under: Synthesis Tagged With: interactive, waveform generation

The Gaussian probability density function: understanding the equation

The speed of sound

Autocorrelation for estimating F0

Token passing

Aliasing

A super-simple speech recogniser

Wave propagation on the surface of water

A simple synthetic vowel

Sampling and quantisation

Entropy: understanding the equation

Pipeline architecture for TTS

Interactive unit selection

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