Sinewave Speech Analysis/Synthesis in Matlab

---

Introduction

The Haskins site includes several example analysis files that you can download.  These files contain, in a compact form, all the data you need to resynthesize the sinewave speech.  The Matlab routines below do this for you.

• README - usage details
• synthtrax.m - the main synthesis routine
• slinterp.m - subsidiary linear interpolation routine
• readswi.m - function to read the SWI-format data files into Matlab
• s1pars.swi, s6pars.swi - example paramters files from the Haskins site.

Sinewave analysis

I was developing some examples of LPC analysis for my speech and audio class, and to my surprise, crude translation of LPC pole positions does a pretty good job of extracting sinewave speech parameters. Thus, I am pleased to offer the following routines:

• Main routine: [F,M] = swsmodel(D,R,H) returns four sinusoids, with frequencies defined by rows of F and magnitudes defined by rows of M, tracking the formants in the speech sample D (of sampling rate R). Each column of F and M corresponds to H samples (so the analysis frame rate is R/H). Note: the sound is resampled to 8 kHz within the routine to focus the LPC on the main formant region, below 4 kHz.
• Support routine:
• [A,G,E] = lpcfit(D,P,H,W,O) fits P-th order LPC (all-pole, autoregressive) models to sound waveform D, using W-point windows advanced by H samples. Rows of A contain all-pole filter coefficiets [1 a1 a2 .. aP], with corresponding elements of G giving the frame gain (residual RMS). E is the actual excitation residual. Specifying OV as zero prevents overlap-add of the residual, for perfect reconstruction but a less useful E.
• Support routine: [F,M] = lpca2frq(A) factorizes the LPC polynomial defined in each row of A (as from lpcfit.m) and returns the sorted positive frequencies (up to P/2 of them) in columns of F, each with a corresponding approximate magnitude in M.
• Bonus routine: D = lpcsynth(A,G,E,H,OV) resynthesizes from LPC parameters returned by lpcfit, or using noise excitation if E is omitted.

An example use is shown below:

>> [d,r] = wavread('mpgr1_sx419.wav');
>> [F,M] = swsmodel(d,r);
>> plot(F'); % show all the frequencies
>> dr = synthtrax(F,M,r);
>> % Listen to it
>> sound(dr,r)
>> % Compare to noise-excited reconstruction of LPC analysis
>> [a,g] = lpcfit(d);
>> dl = lpcsynth(a,g);
>> sound(dl,r);
>> % The LPC reconstruction is based on more or less the same information 
>> % as the sinewave replica, but it sounds less 'weird'
>> % Compare the spectrograms
>> subplot(311)
>> specgram(d,256,r);
>> title('Original');
>> subplot(312)
>> specgram(dr,256,r);
>> title('Sine wave replica');
>> subplot(313)
>> specgram(dl,256,r);
>> title('Noise-excited LPC reconstruction');

Referencing

If you wish to reference this code in your publications, you can use the following citation:

    D. P. W. Ellis (2004) 
    "Sinewave Speech Analysis/Synthesis in Matlab", 
    Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/ .