Adds gaussian case

experiments_music.m

@@ -0,0 +1,42 @@
+%% Parameters data
+clear all
+close all
+clc
+tic
+%diary('/Users/Code/Desktop/hello_diary')
+%diary on
+data_options = struct();
+data_options.type = 'gaussian';
+data_options.noise_level = 0.1;
+data_options.mu = [-0.5, 0, 0.9];
+data_options.n = 5000;
+data_options.D = 200;
+data_options.gain = 'on';
+data_options.circular = 'on';
+data_options.width = 0.1;
+
+data_options.neigh = 1000;
+data_options.tries = 50;
+%% Parameters algo
+radius_options = struct('it',5,'it_end',2,'it_start',5,'it_mid',4);
+
+%% Subsampling options 
+sub_options = struct('state',true,'nb',round(sqrt(data_options.n)));
+
+%% Plotting options
+plt_options = struct('sample',true,'avg',true,'msvd',true,'rmsvd',true);
+
+%% Generating dataset of pulses 
+noisy_data = generate_music_data(data_options);
+%% plot
+I = linspace(-1,1,data_options.D);
+close all
+for i=50:55
+plot(I,noisy_data(i,:))
+hold on
+end
+
+%% MUSIC
+
+pmusic(noisy_data, length(data_options.mu))
+

functions/generate_music_data.m

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+
+% this function wraps all data generating functions for the project
+% badly coded from generate_data
+function [data] = generate_music_data(data_options)
+
+% set default values for empty fields
+% elementary signal
+if ~isfield(data_options,'type') data_options.type = 'gaussian'; end
+if ~isfield(data_options,'width') data_options.width = 0.1; end
+if ~isfield(data_options,'noise_level') data_options.width = 0.1; end
+
+%dataset
+if ~isfield(data_options,'n') data_options.n = 1000; end
+if ~isfield(data_options,'D') data_options.D = 50; end
+%if ~isfield(data_options,'k') data_options.k = 2; end
+if ~isfield(data_options,'mu') data_options.mu = [0.25, 0.75]; end
+if ~isfield(data_options,'circular') data_options.circular = 'on'; end
+
+data_options.gain = 'on';
+
+if ~isfield(data_options,'seed') data_options.seed = 555; end
+
+switch data_options.type
+    case 'gaussian'
+        data = generate_music_gaussian(data_options);
+    case 'triangle'
+        data = generate_music_triangle(data_options);
+    case 'stair'
+        data = generate_music_stair(data_options);
+
+end        
+% adding gaussian noise on data
+if data_options.noise_level > 0
+    data = data + data_options.noise_level * randn(data_options.n, data_options.D);
+end
+
+end

functions/generate_music_gaussian.m

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+% badly coded from generate gaussian
+function [ data ] = generate_music_gaussian(data_options)
+% this function generates a dataset of gaussian signals given the data_options
+% parameters :
+%   n - size of the dataset
+%   D - num of sample points in the range [-1,1]
+%   mu - delay parameters
+%   width - the std parameter given to the normalpdf function
+%   circular : 'on' means the interval is circular and so overlap
+%   gain : add rayleigh gain
+
+data = zeros(data_options.n,data_options.D);
+I = linspace(-1,1,data_options.D);
+
+if strcmpi(data_options.circular,'on')
+    %case circular
+    half_width = norminv(0.99,0,data_options.width); % disclaimer, in the gaussian case, half width is not witdh/2
+    half_width_sample = round(0.5*half_width * data_options.D);
+    I_extended = linspace(-1 - half_width , 1 + half_width , data_options.D + 2*half_width_sample);
+    data_extended = zeros(data_options.n, data_options.D + 2*half_width_sample);
+    for mu = data_options.mu
+        for j = 1:data_options.n
+            gain = raylrnd(sqrt(2/pi));
+            data_extended(j,:) = data_extended(j,:) + gain * normpdf(I_extended, mu, data_options.width);
+        end
+    end
+
+    data = data_extended(:,half_width_sample+1:data_options.D + half_width_sample);
+    data(:,1:half_width_sample) = data(:,1:half_width_sample) + data_extended(:,data_options.D + half_width_sample+1 : data_options.D + 2*half_width_sample);
+    data(:, data_options.D - half_width_sample + 1 : data_options.D ) = data(:, data_options.D - half_width_sample + 1 : data_options.D ) + data_extended(:, 1 : half_width_sample );
+
+else
+
+    for mu = data_options.mu
+        for j = 1:data_options.n
+            gain = raylrnd(sqrt(2/pi));
+            data(j,:) = data(j,:) + gain * normpdf(I, mu, data_options.width);
+        end
+    end
+
+end
+
+end

functions/generate_music_stair.m

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+%badly coded from generate_stair.m
+function [ data ] = generate_stair(data_options)
+% this function generates a dataset of stair signals given the data_options 
+% parameters :
+%   n - size of the dataset
+%   D - num of sample points in the range [-1,1]
+%   mu - 
+%   width - the half width of a stair
+%   circular : 'on' means the interval is circular and so overlap
+%   gain : 'on' means we add rayleigh gain
+
+data = zeros(data_options.n,data_options.D);
+I = linspace(-1,1,data_options.D);
+
+if strcmpi(data_options.circular,'on')
+    %case circular
+    half_width = data_options.width / 2 ;
+    half_width_sample = round( 0.5* half_width * data_options.D)+1; % convert number of sample points
+    I_extended = linspace(-1 - half_width , 1 + half_width , data_options.D + 2*half_width_sample);
+    data_extended = zeros(data_options.n, data_options.D + 2*half_width_sample);
+    for start_point = data_options.mu
+        for j = 1:data_options.n
+
+            gain = raylrnd(sqrt(2/pi));
+
+            start_point_idx = find(I_extended > start_point,1);
+            end_point_idx = find(I_extended > start_point+data_options.width,1);
+
+            data_extended(j,start_point_idx:end_point_idx) = data_extended(j,start_point_idx:end_point_idx) + gain / data_options.width;
+
+        end
+    end
+
+    data = data_extended(:,half_width_sample+1:data_options.D + half_width_sample);
+    data(:,1:half_width_sample) = data(:,1:half_width_sample) + data_extended(:,data_options.D + half_width_sample+1 : data_options.D + 2*half_width_sample);
+    data(:, data_options.D - half_width_sample + 1 : data_options.D ) = data(:, data_options.D - half_width_sample + 1 : data_options.D ) + data_extended(:, 1 : half_width_sample );
+else
+
+    for start_point = data_options.mu
+        for j = 1:data_options.n
+
+            gain = raylrnd(sqrt(2/pi));
+
+            start_point_idx = find(I > start_point,1);
+            end_point_idx = find(I>start_point+data_options.width,1);
+
+            data(j,start_point_idx:end_point_idx) = data(j,start_point_idx:end_point_idx) + gain / data_options.width;
+        end
+    end
+
+end
+
+
+end   

functions/generate_music_triangle.m

@@ -0,0 +1,56 @@
+function [ data ] = generate_music_triangle(data_options)
+% this function generates a dataset of triangle signals given the data_options
+% parameters :
+%   n - size of the dataset
+%   D - num of sample points in the range [-1,1]
+%   k - num of triangle summed
+%   width - the half width of a triangle
+%   circular : 'on' means the interval is circular and so overlap
+%   gain : 'on' means we add rayleigh gain
+
+data = zeros(data_options.n,data_options.D);
+I = linspace(-1,1,data_options.D);
+
+if strcmpi(data_options.circular,'on')
+    %case circular
+    half_width = data_options.width; % disclaimer, in the triangle case, half width is not witdh/2
+    half_width_sample = round( 0.5* half_width * data_options.D)+1; % convert number of sample points
+    I_extended = linspace(-1 - half_width , 1 + half_width , data_options.D + 2*half_width_sample);
+    data_extended = zeros(data_options.n, data_options.D + 2*half_width_sample);
+    for middle_point = data_options.mu
+        for j = 1:data_options.n
+            gain = raylrnd(sqrt(2/pi));
+
+            middle_point_idx =  find(I_extended > middle_point,1);
+            start_point_idx = find(I_extended > middle_point - data_options.width,1);
+            end_point_idx = find(I_extended > middle_point + data_options.width,1)-1;
+
+            data_extended(j,start_point_idx:middle_point_idx) = data_extended(j,start_point_idx:middle_point_idx) + (gain/data_options.width^2)*(I_extended(start_point_idx:middle_point_idx) - I_extended(start_point_idx));
+
+            data_extended(j,middle_point_idx+1:end_point_idx) = data_extended(j,middle_point_idx+1:end_point_idx) - (gain/data_options.width^2)*(I_extended(middle_point_idx+1:end_point_idx) - I_extended(end_point_idx));
+        end
+    end
+
+    data = data_extended(:,half_width_sample+1:data_options.D + half_width_sample);
+    data(:,1:half_width_sample) = data(:,1:half_width_sample) + data_extended(:,data_options.D + half_width_sample+1 : data_options.D + 2*half_width_sample);
+    data(:, data_options.D - half_width_sample + 1 : data_options.D ) = data(:, data_options.D - half_width_sample + 1 : data_options.D ) + data_extended(:, 1 : half_width_sample );
+else
+
+    for middle_point = data_options.mu
+        for j = 1:data_options.n
+
+            gain = raylrnd(sqrt(2/pi));
+
+            middle_point_idx =  find(I > middle_point,1);
+            start_point_idx = find(I > middle_point - data_options.width,1);
+            end_point_idx = find(I>middle_point + data_options.width,1)-1;
+
+            data(j,start_point_idx:middle_point_idx) = data(j,start_point_idx:middle_point_idx) +  (gain/data_options.width^2)*(I(start_point_idx:middle_point_idx) - I(start_point_idx));
+            data(j,middle_point_idx+1:end_point_idx) =  data(j,middle_point_idx+1:end_point_idx)  - (gain/data_options.width^2)*(I(middle_point_idx+1:end_point_idx) - I(end_point_idx));
+        end
+    end
+
+end
+
+
+end