Fill gaps using autoregressive modeling
fillgaps(___) with no output
arguments plots the original samples and the reconstructed signal.
This syntax accepts any input arguments from previous syntaxes.
Load a speech signal sampled at . The file contains a recording of a female voice saying the word "MATLAB®." Play the sound.
load mtlb % To hear, type soundsc(mtlb,Fs)
Simulate a situation in which a noisy transmission channel corrupts parts of the signal irretrievably. Introduce gaps of random length roughly every 500 samples. Reset the random number generator for reproducible results.
rng default gn = 3; mt = mtlb; gl = randi([300 600],gn,1); for kj = 1:gn mt(kj*1000+randi(100)+(1:gl(kj))) = NaN; end
Plot the original and corrupted signals. Offset the corrupted signal for ease of display. Play the signal with the gaps.
plot([mtlb mt+4]) legend('Original','Corrupted')
% To hear, type soundsc(mt,Fs)
Reconstruct the signal using an autoregressive process. Use
fillgaps with the default settings. Plot the original and reconstructed signals, again using an offset. Play the reconstructed signal.
lb = fillgaps(mt); plot([mtlb lb+4]) legend('Original','Reconstructed')
% To hear, type soundsc(lb,Fs)
Load a file that contains depth measurements of a mold used to mint a United States penny. The data, taken at the National Institute of Standards and Technology, are sampled on a 128-by-128 grid.
Draw a contour plot with 25 copper-colored contour lines.
nc = 25; contour(P,nc) colormap copper axis ij square
Introduce four 10-by-10 gaps into the data. Draw a contour plot of the corrupted signal.
P(50:60,80:90) = NaN; P(100:110,20:30) = NaN; P(100:110,100:110) = NaN; P(20:30,110:120) = NaN; contour(P,nc) colormap copper axis ij square
fillgaps to reconstruct the data, treating each column as an independent channel. Specify an 8th-order autoregressive model extrapolated from 30 samples at each end. Draw a contour plot of the reconstruction.
q = fillgaps(P,30,8); contour(q,nc) colormap copper axis ij square
Generate a function that consists of the sum of two sinusoids and a Lorentzian curve. The function is sampled at 200 Hz for 2 seconds. Plot the result.
x = -1:0.005:1; f = 1./(1+10*x.^2)+sin(2*pi*3*x)/10+cos(25*pi*x)/10; plot(x,f)
Insert gaps at intervals (-0.8,-0.6), (-0.2,0.1), and (0.4,0.7).
h = f; h(x>-0.8 & x<-0.6) = NaN; h(x>-0.2 & x< 0.1) = NaN; h(x> 0.4 & x< 0.7) = NaN;
Fill the gaps using the default settings of
fillgaps. Plot the original and reconstructed functions.
y = fillgaps(h); plot(x,f,'.',x,y) legend('Original','Reconstructed')
Repeat the computation, but now specify a maximum prediction-sequence length of 3 samples and a model order of 1. Plot the original and reconstructed functions. At its simplest,
fillgaps performs a linear fit.
y = fillgaps(h,3,1); plot(x,f,'.',x,y) legend('Original','Reconstructed')
Specify a maximum prediction-sequence length of 80 samples and a model order of 40. Plot the original and reconstructed functions.
y = fillgaps(h,80,40); plot(x,f,'.',x,y) legend('Original','Reconstructed')
Change the model order to 70. Plot the original and reconstructed functions.
y = fillgaps(h,80,70); plot(x,f,'.',x,y) legend('Original','Reconstructed')
The reconstruction is imperfect because very high model orders often have problems with finite precision.
Generate a multichannel signal consisting of two instances of a chirp sampled at 1 kHz for 1 second. The frequency of the chirp is zero at 0.3 seconds and increases linearly to reach a final value of 40 Hz. Each instance has a different DC value.
Fs = 1000; t = 0:1/Fs:1-1/Fs; r = chirp(t-0.3,0,0.7,40); f = 1.1; q = [r-f;r+f]';
Introduce gaps to the signal. One of the gaps covers the low-frequency region, and the other covers the high-frequency region.
gap = (460:720); q(gap-300,1) = NaN; q(gap+200,2) = NaN;
Fill the gaps using the default parameters. Plot the reconstructed signals.
y = fillgaps(q); plot(t,y)
Fill the gaps by fitting 14th-order autoregressive models to the signal. Limit the models to incorporate 15 samples on the end of each gap. Use the functionality of
fillgaps to plot the reconstructions.
Increase the number of samples to use in the estimation to 150. Increase the model order to 140.
x— Input signal
Input signal, specified as a vector or matrix. If
a matrix, then its columns are treated as independent channels.
to represent missing samples.
0 NaN 0],1,160) is a single-channel row-vector signal missing
40% of its samples.
NaN 0 NaN 0],160,2) is a two-channel signal with large gaps.
Complex Number Support: Yes
maxlen— Maximum length of prediction sequences
Maximum length of prediction sequences, specified as a positive
integer. If you leave
maxlen unspecified, then
fits autoregressive models using all previous points for forward estimation
and all future points for backward estimation.
order— Autoregressive model order
'aic'(default) | positive integer
Autoregressive model order, specified as
a positive integer. The order is truncated when
infinite or when there are not enough available samples. If you specify
or leave it unspecified, then
the order that minimizes the Akaike information criterion.
y— Reconstructed signal
Reconstructed signal, returned as a vector or matrix.
 Akaike, Hirotugu. "Fitting Autoregressive Models for Prediction." Annals of the Institute of Statistical Mathematics. Vol. 21, 1969, pp. 243–247.
 Kay, Steven M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice Hall, 1988.
 Orfanidis, Sophocles J. Optimum Signal Processing: An Introduction. 2nd Edition. New York: McGraw-Hill, 1996.