framesig

Create a matrix signal x and split each channel into frames of length 5 with 3 samples of overlap between consecutive frames.

x = reshape(1:24,12,2);

[xw,fc,fi] = framesig(x,5,OverlapLength=3)

xw = 
xw(:,:,1) =

     1     3     5     7
     2     4     6     8
     3     5     7     9
     4     6     8    10
     5     7     9    11


xw(:,:,2) =

    13    15    17    19
    14    16    18    20
    15    17    19    21
    16    18    20    22
    17    19    21    23

fc = 4×2

     9    21
    10    22
    11    23
    12    24

fi = 
1

Since x has two columns, xw results a 3-D matrix representing two channels of four frames and five samples per frame. The last three samples on any given frame are overlapped in the next one. fc contains the samples from the incomplete fifth frame in each channel, including the overlapping samples. fi is 1 due to the specified overlap length.

Compute the power spectral density of a signal by partitioning it into frames, windowing each frame, and applying the fast Fourier transform to each windowed frame.

Generate a signal x as 200-Hz cosine waveform with normally distributed noise. Set a sampling rate of 1000 samples per second and a time limit of 0.3 seconds.

fs = 1000;
t = 0:1/fs:0.3;
x = cos(2*pi*200*t)+randn(size(t));

Frame the signal using framesig with a frame length of 66 samples. Specify a Hamming window and 33 samples of overlap.

fl = 66;
ol = 33;
g = hamming(fl);

xw = framesig(x,fl,Window=g,OverlapLength=ol);

Compute the power spectral density. Use 256 points to compute the discrete Fourier transform for the framed signal.

NFFT = 256;
X = fft(xw,NFFT);
S = (diag(X*X')/(g'*g))/(size(xw,2)*fs);

Compare the computed power spectral density with Welch’s power spectral density estimate.

[p,f] = pwelch(x,fl,ol,NFFT,fs,"twosided");
plot(f,pow2db(p),f,pow2db(S),"--")
xlabel("Frequency (Hz)")
ylabel("Power/Frequency (dB/Hz)")
legend(["pwelch" "fft"])
grid

Create a multivariable single-channel timetable input signal and an initial condition timetable.

xTT = timetable(seconds((1:20)'),(1:20)',(41:60)');
icTT = timetable(seconds((-2:0)'),(-2:0)',(38:40)');

Split each variable into frames of length 4, using an underlap length of 3, an initial condition timetable, and setting the property IncompleteFrameRule to "zeropad".

xwTT = framesig(xTT,4,UnderlapLength=3, ...
  InitialCondition=icTT,IncompleteFrameRule="zeropad")

xwTT=4×2 timetable
      Time              Var1                    Var2        
    ________    ____________________    ____________________

    -0.5 sec    -2    -1     0     1    38    39    40    41
    6.5 sec      5     6     7     8    45    46    47    48
    13.5 sec    12    13    14    15    52    53    54    55
    20.5 sec    19    20     0     0    59    60     0     0

Generate a 3-D signal array, define a 3-D initial condition array, and partition the signal array along its third dimension.

Define a 3-D array with 30 elements from 1 to 30, distributed along two rows, three columns, and five pages.

x = reshape(1:30,[2 3 5]);

Set an initial-condition array as a 3-D array with 12 elements from –11 to 0, distributed along two rows, three columns, and two pages.

initCond = reshape(-11:0,[2,3,2]);

Partition the signal array along its third dimension. Display the first page of the framed signal output.

[xw,fc] = framesig(x,3,OverlapLength=2, ...
    InitialCondition=initCond,Dimension=3);
disp(xw(:,:,1,:))

(:,:,1,1) =

   -11    -5     1     7    13
    -5     1     7    13    19
     1     7    13    19    25


(:,:,1,2) =

    -9    -3     3     9    15
    -3     3     9    15    21
     3     9    15    21    27


(:,:,1,3) =

    -7    -1     5    11    17
    -1     5    11    17    23
     5    11    17    23    29

Define a multisegment data stream signal, perform successive framing for each segment, and compare with the framing of the entire stream.

Define a signal source stream data in two segments with a length of 7 samples per segment.

Ls = 7;
x0 = (1:2*Ls)';
x = reshape(x0,Ls,[]);

Split each segment into frames of length 4 with 3 samples of overlap between frames. Set the initial condition as an empty vector.

fl = 4;
ol = 3;
ic0 = [];

Perform successive framing of the data stream signal. Initialize the output frames and the initial condition array. Frame each segment with the specified frame length, overlap length, and initial condition. Keep the same amount of overlap among frames of consecutive segments. Accumulate the output frames after each iteration. Display the output frames and the final condition array.

xwa = [];
ici = ic0;
numSegments = size(x,2);
for i = 1:numSegments
    % Data streaming and framing
    xi = x(:,i);
    [xwi,fci] = framesig(xi,fl,OverlapLength=ol, ...
        InitialCondition=ici);
    % Settings for the next iteration
    xwa = [xwa xwi];
    ici = fci;
end
disp(xwa)

     1     2     3     4     5     6     7     8     9    10    11
     2     3     4     5     6     7     8     9    10    11    12
     3     4     5     6     7     8     9    10    11    12    13
     4     5     6     7     8     9    10    11    12    13    14

disp(fci)

    12
    13
    14

Frame the entire data stream with the specified frame length, overlap length, and initial condition. Observe that successive overlap framing yields the same result as when you feed all the segments at once.

[xwe,fce] = framesig(x0,fl,OverlapLength=ol, ...
    InitialCondition=ic0)

xwe = 4×11

     1     2     3     4     5     6     7     8     9    10    11
     2     3     4     5     6     7     8     9    10    11    12
     3     4     5     6     7     8     9    10    11    12    13
     4     5     6     7     8     9    10    11    12    13    14

fce = 3×1

    12
    13
    14

Use the framesig and chirp functions to generate a linearly swept-frequency cosine signal in each frame.

Specify a time vector representing five periods of 1 second, with a sample rate of 500 Hz.

Fs = 500;
T0 = 1;
t = (0:1/Fs:5*T0-1/Fs)';

Define the frame length as the number of samples in one single period.

fl = round(T0*Fs);

Partition a time vector into frames.

tf = framesig(t,fl);

Generate a linear swept-frequency cosine signal at the time instances defined in each frame. Set the reference frequencies so that the chirp instantaneous frequency starts at 0 Hz and crosses 25 Hz at the end of the period T0. Specify the sweep method option as "linear". Alternate the signs for all even frames.

f0 = 0;
f1 = 25;
numFrames = size(tf,2);
y = zeros(fl,numFrames);

for i = 1:numFrames
    tfi = mod(tf(:,i),T0);
    y(:,i) = chirp(tfi,f0,T0,f1,"linear")*(-1)^(i-1);
end

Plot the chirp signal frames in time domain. Plot the spectrogram of the entire stream. Use a 144-sample Blackman window, an overlap of 128 samples, 1024 sampling points to calculate the discrete Fourier transform, the signal sampling frequency Fs, and set the frequency display axis property to "yaxis".

tiledlayout flow

nexttile
plot(tf,y)
title("Chirp Frames in Time Domain")
xlabel("Time (s)")
ylabel("Voltage (V)")
grid

nexttile
spectrogram(y(:),blackman(144),128,1024,Fs,"yaxis")
title("Spectrogram")
xlabel("Time (s)")
ylabel("Frequency (Hz)")
ylim([f0 1.2*f1])

Partition a data stream signal into segments using overlap. Perform successive framing and joint framing of the signal segments with underlap.

Load a data file with a 73113-sample signal y sampled at a rate Fs of 8192 Hz.

load handel

sl = 25000;
ol = 5000;

yfs = framesig(y,sl,OverlapLength=ol, ...
        IncompleteFrameRule="zeropad", ...
        InitialCondition=zeros(ol,1));
ns = size(yfs,2);

strips(yfs)
patch([0 sl]+[1 -1].*[0 0 ol ol]',2*([-1 0]+[1 ns ns 1]')-1, ...
    "r",EdgeColor="none",FaceAlpha=0.1)
grid
xlabel("Sample Number")
ylabel("Segment Number")
yticklabels(ns:-1:1)

fl = 256;
ul = 112;
yfa = [];
ic0 = [];
ii0 = 1;

ica = ic0;
iia = ii0;
for i = 1:ns
    % Data streaming and framing
    yi = yfs(:,i);
    [yfi,fci,fii] = framesig(yi,fl,UnderlapLength=ul, ...
        InitialCondition=ica,InitialIndex=iia);
    disp("i = "+i+", fii = "+fii)
    % Settings for the next iteration
    yfa = [yfa yfi];
    ica = fci;
    iia = fii;
end

i = 1, fii = 25
i = 2, fii = 49
i = 3, fii = 73
i = 4, fii = 97

[yfe,fce,fie] = framesig(yfs(:),fl,UnderlapLength=ul, ...
    InitialCondition=ic0,InitialIndex=ii0);

nf = size(yfe,2);
figure
tiledlayout vertical
for i = [20 floor(nf/2) nf-20]
    nexttile
    plot(yfa(:,i))
    hold on
    plot(yfe(:,i),":")
    hold off
    grid
    xlabel("Sample number")
    title("Frame "+i)
    legend(["Successive" "Joint"]+" framing",Location="eastoutside")
end