Update README.md

README.md

@@ -2,13 +2,21 @@
 
 A project to model sinusoidal codec phase spectra with neural nets.
 
-Recent breakthroughs in NN speech synthesis (WaveNet, WaveRNN, LPCNet and friends) have resulted in exciting improvements in model based synthesised speech quality.  These algorithms typically use NNs to estimate the PDF of the next speech sample using a history of previous speech samples.  This PDF is then sampled.  As such, speech is generated on a sample by sample basis.  Computational complexity is high, although steadily being reduced.
+Recent breakthroughs in NN speech synthesis (WaveNet, WaveRNN, LPCNet and friends) have resulted in exciting improvements in model based synthesised speech quality.  These algorithms typically use NNs to estimate the PDF of the next speech sample conditioned on input features and a history of previously synthesised speech samples.  This PDF is then sampled to obtain the next output speech sample.  As the algorithms need all previous output speech samples, speech must be generated on a sample by sample basis.  Computational complexity is high, although steadily being reduced.
 
-Speech codecs employing frequency domain, block based techniques such as sinusoidal transform coding can deliver high quality speech using block based synthesis.  They typically synthesise speech in blocks of 10-20ms at a time (e.g. 160-320 samples at Fs=16kHz) using efficient overlap-add IDFT techniques.  Sinusoidal codecs use a similar parameter set to NN based synthesis systems (amplitude spectra and pitch information).
+Speech codecs employing frequency domain, block based techniques such as sinusoidal transform coding can deliver high quality speech using block based synthesis.  They typically synthesise speech in blocks of 10-20ms at a time (e.g. 160-320 samples at Fs=16kHz) using efficient overlap-add IDFT techniques.  Sinusoidal codecs use a similar parameter set to the features used for NN based synthesis systems (some form of amplitude spectra, pitch information, voicing).
 
-However for high quality speech, sinusoidal codecs require a suitable set of the sinusoidal harmonic phases for each frame that is synthesised. This work aims to generate the sinusoid phases from amplitude information using NNs, in order to develop a block based NN synthesis engine based on sinusoidal coding.
+For high quality speech, sinusoidal codecs require a suitable set of the sinusoidal harmonic phases for each frame that is synthesised. This work aims to generate the sinusoid phases from amplitude information using NNs, in order to develop a block based NN synthesis engine based on sinusoidal coding.
 
-## Status (Nov 2019)
+## Status (Dec 2019)
 
-Building up techniques for modelling phase using NNs and toy speech models (2nd order filters) in a series of tests.
+Building up techniques for modelling phase using NNs and toy speech models (cascades of 2nd order filters) in a series of tests.
+
+Here is the output from [phase_test11.py](phase_test11.py).  The first plot is a series of magnitude spectra of simulated speech frames.  The voiced frames have two fairly sharp peaks (formants) beneath Fs/2 with structured phase consisting of linear and dispersive terms.  Unvoiced frames have less sharp peaks above Fs/2, and random phases.
+
+![](example_mag.png "Magnitude Spectra")
+
+The next plot shows the original phase spectra (green), the phase spectra with an estimate of the linear phase term removed (red), and the NN ouput estimated phase (blue).  For voiced frames, we would like green (original) and blue (NN estimate) to match.  In particular we want to model the accurate phase shift across the peak of the amplitude spectra - this is the dispersive term that shifts the phase of high energy speech harmonics apart and reducing the buzzy/unnatural quality in synthsised speech.  For unvoiced speech, we want the NN output (blue) to be random.
+
+![](example_phase.png "Phase Spectra")