From 76d5f3bebdbf02c7c5a415455665913f230b5025 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Gi=C3=B9=20Marcer?= Date: Fri, 22 May 2020 15:27:16 +0200 Subject: [PATCH] ex-6: wrote something about ex-6 in the readme file and put in order ex.6/plots ex-6/plots/emd-round.py renamed into ex-6/plots/emd.py and made interactive. --- README.md | 39 +++++++++--- ex-6/dist-plot.py | 4 +- ex-6/plot.py | 3 +- ex-6/plots/emd-noiseless.txt | 75 +++++++++++++++++++++++ ex-6/plots/emd-noisy.txt | 64 ++++++++++++++++++++ ex-6/plots/emd-round-conv.txt | 75 ----------------------- ex-6/plots/emd-round-noise.txt | 92 ----------------------------- ex-6/plots/{emd-round.py => emd.py} | 30 +++++----- notes/sections/6.md | 49 ++++++++------- 9 files changed, 210 insertions(+), 221 deletions(-) create mode 100644 ex-6/plots/emd-noiseless.txt create mode 100644 ex-6/plots/emd-noisy.txt delete mode 100644 ex-6/plots/emd-round-conv.txt delete mode 100644 ex-6/plots/emd-round-noise.txt rename ex-6/plots/{emd-round.py => emd.py} (57%) mode change 100644 => 100755 diff --git a/README.md b/README.md index 3c33f27..9a18b77 100644 --- a/README.md +++ b/README.md @@ -162,19 +162,42 @@ To plot the results do: `ex-6/bin/main` simulates a Fraunhöfer diffraction experiment. The program prints to `stdout` the bin counts of the intensity as a function of the -diffraction angle. To plot a histogram simply pipe the output to the -program `ex-6/plot.py`. +diffraction angle. To plot a histogram do: + + $ ex-6/bin/main | ex-6/plot.py The program convolves the original signal with a Gaussian kernel (`-s` to -change the σ), optionally adds a Poisson noise (`-m` to change the mean μ) and -performs either a naive deconvolution by a FFT (`-m fft` mode) or applying the -Richard-Lucy deconvolution algorithm (`-m rl` mode), which is expected to -perform optimally in this case. +change the kernel σ), optionally adds a Gaussian noise (`-n` to change the +noise σ) and performs either a naive deconvolution by a FFT (`-m fft` mode) +or applying the Richardson-Lucy deconvolution algorithm (`-m rl` mode). -The `-c` and `-d` options control whether the convolved or deconvolved -histogram counts should be printed to `stdout`. For more options +The `-o`, `-c` and `-d` options control whether the original, convolved or +deconvolved histogram counts should be printed to `stdout`. For more options run the program with `-h` to see the usage screen. +`ex-6/bin/test` simulates a customizable number of experiments and prints +to `stdout` the histograms of the distribution of the EMD of the convolved +signal together with the deconvolved signal EMD histograms with both FFT and +Richardson-Lucy procedures. It also prints to `stderr` the average, standard +deviation and skewness of the histograms. To plot the results, do: + + $ ex-6/bin/test | ex-6/dist-plot.py + +The program accepts some parameters to control the histogram and number of +events, run it with `-h` to see their usage. + +`ex-6/plots/emd.py` plots the content of the files `ex-6/plots/emd-noisy.txt` +and `ex-6/plots/emd-noiseless.txt` depending on the argument passed to it from +stdin. Do: + + $ ex-6/plots/emd.py 'noisy' + +to plot the content of the first file and do: + + $ ex-6/plots/emd.py 'noiseless' + +to plot the content of the second file. + ### Exercise 7 diff --git a/ex-6/dist-plot.py b/ex-6/dist-plot.py index 4a774b4..ee8b2f3 100755 --- a/ex-6/dist-plot.py +++ b/ex-6/dist-plot.py @@ -30,6 +30,4 @@ hist(a[2*n:], insert(b[2*n:], 0, a[2*n]), weights=f[2*n:], ticklabel_format(style='sci', axis='x', scilimits=(0, 0), useMathText=True) tight_layout() - -name = (sys.argv[1] if len(sys.argv) > 1 else "prova") -savefig('notes/images/' + name + '.pdf' ) +show() diff --git a/ex-6/plot.py b/ex-6/plot.py index 0bdbe8a..f40135c 100755 --- a/ex-6/plot.py +++ b/ex-6/plot.py @@ -14,5 +14,4 @@ xlabel(r'$\theta$ (radians)') ylabel(r'$I(\theta)$ (a.u.)') tight_layout() -name = sys.argv[2] if len(sys.argv) > 2 else "prova" -savefig('notes/images/' + name + '.pdf' ) +show() diff --git a/ex-6/plots/emd-noiseless.txt b/ex-6/plots/emd-noiseless.txt new file mode 100644 index 0000000..af0c6da --- /dev/null +++ b/ex-6/plots/emd-noiseless.txt @@ -0,0 +1,75 @@ +#rounds mean stddev +#σ = 1 + 1 1.88e-04 1.4e-05 + 2 3.17e-04 1.4e-05 + 3 1.80e-04 1.4e-05 + 4 2.02e-04 1.5e-05 + 5 1.70e-04 1.4e-05 + 6 1.64e-04 1.4e-05 + 7 1.75e-04 1.4e-05 + 8 1.67e-04 1.4e-05 + 9 1.61e-04 1.4e-05 + 10 1.57e-04 1.4e-05 + 11 1.59e-04 1.4e-05 + 12 1.56e-04 1.4e-05 + 13 1.54e-04 1.4e-05 + 14 1.53e-04 1.4e-05 + 15 1.51e-04 1.4e-05 + 16 1.50e-04 1.3e-05 + 17 1.49e-04 1.3e-05 + 18 1.48e-04 1.3e-05 + 19 1.46e-04 1.3e-05 + 20 1.47e-04 1.3e-05 + 40 1.35e-04 1.3e-05 + 60 1.28e-04 1.3e-05 + 80 1.24e-04 1.3e-05 + 100 1.21e-04 1.3e-05 + 400 1.02e-04 1.2e-05 + 800 9.37e-05 1.1e-05 + 1600 8.61e-05 1.0e-05 + 3800 7.98e-05 9.2e-06 + 7600 7.97e-05 9.2e-06 + 10000 8.06e-05 9.2e-06 + 15000 8.16e-05 9.2e-06 +#σ = 0.5 + 1 1.17e-04 8.0e-06 + 2 2.47e-05 3.0e-06 + 3 3.65e-05 3.8e-06 + 4 5.85e-05 5.4e-06 + 5 1.48e-05 3.3e-06 + 6 1.82e-05 3.0e-06 + 7 1.22e-05 3.8e-06 + 8 1.31e-05 3.6e-06 + 9 1.19e-05 3.9e-06 + 10 1.17e-05 3.9e-06 + 11 1.16e-05 4.0e-06 + 12 1.16e-05 4.0e-06 + 13 1.16e-05 4.0e-06 + 14 1.16e-05 4.0e-06 + 15 1.16e-05 4.0e-06 + 16 1.16e-05 4.0e-06 + 17 1.16e-05 4.0e-06 + 18 1.16e-05 4.0e-06 + 19 1.16e-05 4.0e-06 + 20 1.16e-05 4.0e-06 +#σ = 0.1 + 1 4.23e-16 3.1e-16 + 2 4.23e-16 3.2e-16 + 3 4.24e-16 3.1e-16 + 4 4.24e-16 3.1e-16 + 5 4.25e-16 3.2e-16 + 6 4.25e-16 3.2e-16 + 7 4.24e-16 3.1e-16 + 8 4.24e-16 3.1e-16 + 9 4.24e-16 3.1e-16 + 10 4.25e-16 3.2e-16 + 11 4.25e-16 3.2e-16 + 12 4.24e-16 3.1e-16 + 13 4.25e-16 3.2e-16 + 14 4.24e-16 3.1e-16 + 15 4.25e-16 3.2e-16 + 16 4.24e-16 3.1e-16 + 17 4.25e-16 3.2e-16 + 18 4.24e-16 3.1e-16 + 19 4.25e-16 3.2e-16 + 20 4.24e-16 3.1e-16 diff --git a/ex-6/plots/emd-noisy.txt b/ex-6/plots/emd-noisy.txt new file mode 100644 index 0000000..556c956 --- /dev/null +++ b/ex-6/plots/emd-noisy.txt @@ -0,0 +1,64 @@ +#rounds mean stddev +#σ=0.005 + 1 2.92e-04 4.7e-05 + 2 2.18e-04 4.7e-05 + 3 2.28e-04 4.5e-05 + 4 2.12e-04 4.8e-05 + 5 2.08e-04 4.8e-05 + 6 2.02e-04 4.9e-05 + 7 2.05e-04 4.9e-05 + 8 2.00e-04 4.9e-05 + 9 1.98e-04 5.0e-05 + 10 1.95e-04 5.0e-05 + 11 1.97e-04 5.0e-05 + 12 1.94e-04 5.0e-05 + 13 1.93e-04 5.0e-05 + 14 1.92e-04 5.0e-05 + 15 1.91e-04 5.1e-05 + 16 1.90e-04 5.1e-05 + 17 1.90e-04 5.1e-05 + 18 1.89e-04 5.1e-05 + 19 1.88e-04 5.1e-05 + 20 1.88e-04 5.1e-05 +#σ = 0.01 + 1 3.47e-04 1.0e-04 + 2 3.96e-04 1.1e-04 + 3 3.39e-04 1.1e-04 + 4 3.42e-04 1.1e-04 + 5 3.34e-04 1.1e-04 + 6 3.35e-04 1.1e-04 + 7 3.37e-04 1.1e-04 + 8 3.33e-04 1.1e-04 + 9 3.33e-04 1.1e-04 + 10 3.32e-04 1.1e-04 + 11 3.32e-04 1.1e-04 + 12 3.31e-04 1.1e-04 + 13 3.31e-04 1.1e-04 + 14 3.31e-04 1.1e-04 + 15 3.31e-04 1.1e-04 + 16 3.31e-04 1.1e-04 + 17 3.31e-04 1.1e-04 + 18 3.31e-04 1.1e-04 + 19 3.31e-04 1.1e-04 + 20 3.31e-04 1.1e-04 +#σ=0.05 + 1 1.49e-03 5.7e-04 + 2 1.51e-03 5.6e-04 + 3 1.50e-03 5.7e-04 + 4 1.50e-03 5.6e-04 + 5 1.52e-03 5.6e-04 + 6 1.53e-03 5.6e-04 + 7 1.52e-03 5.6e-04 + 8 1.51e-03 5.6e-04 + 9 1.54e-03 5.5e-04 + 10 1.53e-03 5.5e-04 + 11 1.53e-03 5.5e-04 + 12 1.54e-03 5.5e-04 + 13 1.54e-03 5.5e-04 + 14 1.54e-03 5.5e-04 + 15 1.55e-03 5.5e-04 + 16 1.55e-03 5.5e-04 + 17 1.55e-03 5.5e-04 + 18 1.56e-03 5.5e-04 + 19 1.56e-03 5.4e-04 + 20 1.56e-03 5.4e-04 diff --git a/ex-6/plots/emd-round-conv.txt b/ex-6/plots/emd-round-conv.txt deleted file mode 100644 index 40768ec..0000000 --- a/ex-6/plots/emd-round-conv.txt +++ /dev/null @@ -1,75 +0,0 @@ -#rounds mean stddev skew -#σ = 1 - 1 1.88e-04 1.4e-05 0.26 - 2 3.17e-04 1.4e-05 0.19 - 3 1.80e-04 1.4e-05 0.27 - 4 2.02e-04 1.5e-05 0.21 - 5 1.70e-04 1.4e-05 0.27 - 6 1.64e-04 1.4e-05 0.27 - 7 1.75e-04 1.4e-05 0.27 - 8 1.67e-04 1.4e-05 0.27 - 9 1.61e-04 1.4e-05 0.26 - 10 1.57e-04 1.4e-05 0.25 - 11 1.59e-04 1.4e-05 0.26 - 12 1.56e-04 1.4e-05 0.25 - 13 1.54e-04 1.4e-05 0.25 - 14 1.53e-04 1.4e-05 0.25 - 15 1.51e-04 1.4e-05 0.25 - 16 1.50e-04 1.3e-05 0.25 - 17 1.49e-04 1.3e-05 0.25 - 18 1.48e-04 1.3e-05 0.25 - 19 1.46e-04 1.3e-05 0.25 - 20 1.47e-04 1.3e-05 0.25 - 40 1.35e-04 1.3e-05 0.29 - 60 1.28e-04 1.3e-05 0.31 - 80 1.24e-04 1.3e-05 0.33 - 100 1.21e-04 1.3e-05 0.35 - 400 1.02e-04 1.2e-05 0.40 - 800 9.37e-05 1.1e-05 0.36 - 1600 8.61e-05 1.0e-05 0.27 - 3800 7.98e-05 9.2e-06 0.26 - 7600 7.97e-05 9.2e-06 0.28 -10000 8.06e-05 9.2e-06 0.26 -15000 8.16e-05 9.2e-06 0.25 -#σ = 0.5 - 1 1.17e-04 8.0e-06 0.25 - 2 2.47e-05 3.0e-06 0.32 - 3 3.65e-05 3.8e-06 0.35 - 4 5.85e-05 5.4e-06 0.34 - 5 1.48e-05 3.3e-06 0.51 - 6 1.82e-05 3.0e-06 0.44 - 7 1.22e-05 3.8e-06 0.42 - 8 1.31e-05 3.6e-06 0.47 - 9 1.19e-05 3.9e-06 0.38 -10 1.17e-05 3.9e-06 0.36 -11 1.16e-05 4.0e-06 0.35 -12 1.16e-05 4.0e-06 0.34 -13 1.16e-05 4.0e-06 0.34 -14 1.16e-05 4.0e-06 0.34 -15 1.16e-05 4.0e-06 0.34 -16 1.16e-05 4.0e-06 0.34 -17 1.16e-05 4.0e-06 0.34 -18 1.16e-05 4.0e-06 0.34 -19 1.16e-05 4.0e-06 0.34 -20 1.16e-05 4.0e-06 0.34 -#σ = 0.1 - 1 4.23e-16 3.1e-16 0.81 - 2 4.23e-16 3.2e-16 0.85 - 3 4.24e-16 3.1e-16 0.87 - 4 4.24e-16 3.1e-16 0.88 - 5 4.25e-16 3.2e-16 0.82 - 6 4.25e-16 3.2e-16 0.82 - 7 4.24e-16 3.1e-16 0.87 - 8 4.24e-16 3.1e-16 0.87 - 9 4.24e-16 3.1e-16 0.87 -10 4.25e-16 3.2e-16 0.82 -11 4.25e-16 3.2e-16 0.82 -12 4.24e-16 3.1e-16 0.87 -13 4.25e-16 3.2e-16 0.82 -14 4.24e-16 3.1e-16 0.87 -15 4.25e-16 3.2e-16 0.82 -16 4.24e-16 3.1e-16 0.87 -17 4.25e-16 3.2e-16 0.82 -18 4.24e-16 3.1e-16 0.87 -19 4.25e-16 3.2e-16 0.82 -20 4.24e-16 3.1e-16 0.87 diff --git a/ex-6/plots/emd-round-noise.txt b/ex-6/plots/emd-round-noise.txt deleted file mode 100644 index 06b8178..0000000 --- a/ex-6/plots/emd-round-noise.txt +++ /dev/null @@ -1,92 +0,0 @@ -#rounds mean stddev skew -#σ = 0 - 1 2.43e-4 1.3e-5 0.22 - 2 1.67e-4 1.3e-5 0.27 - 3 1.52e-4 1.3e-5 0.29 - 4 1.43e-4 1.3e-5 0.29 - 5 1.36e-4 1.2e-5 0.28 - 6 1.31e-4 1.2e-5 0.29 - 7 1.26e-4 1.2e-5 0.29 - 8 1.22e-4 1.2e-5 0.30 - 9 1.19e-4 1.2e-5 0.31 - 10 1.16e-4 1.2e-5 0.33 - 11 1.13e-4 1.2e-5 0.34 - 12 1.11e-4 1.2e-5 0.34 - 13 1.09e-4 1.2e-5 0.36 - 14 1.07e-4 1.1e-5 0.36 - 15 1.05e-4 1.1e-5 0.36 - 16 1.03e-4 1.1e-5 0.37 - 17 1.01e-4 1.1e-5 0.37 - 18 9.97e-5 1.1e-5 0.37 - 19 9.82e-5 1.1e-5 0.37 - 20 9.68e-5 1.1e-5 0.37 - 40 7.74e-5 1.0e-5 0.35 - 60 6.57e-5 9.4e-6 0.32 - 80 5.78e-5 9.1e-6 0.30 - 100 5.20e-5 9.0e-6 0.30 - 400 3.61e-5 1.0e-5 0.33 - 800 3.60e-5 1.0e-5 0.33 -1600 3.60e-5 1.0e-5 0.33 -#σ=0.005 - 1 2.92e-04 4.7e-05 1.43 - 2 2.18e-04 4.7e-05 1.72 - 3 2.28e-04 4.5e-05 1.73 - 4 2.12e-04 4.8e-05 1.72 - 5 2.08e-04 4.8e-05 1.71 - 6 2.02e-04 4.9e-05 1.69 - 7 2.05e-04 4.9e-05 1.70 - 8 2.00e-04 4.9e-05 1.69 - 9 1.98e-04 5.0e-05 1.68 -10 1.95e-04 5.0e-05 1.67 -11 1.97e-04 5.0e-05 1.68 -12 1.94e-04 5.0e-05 1.67 -13 1.93e-04 5.0e-05 1.67 -14 1.92e-04 5.0e-05 1.67 -15 1.91e-04 5.1e-05 1.66 -16 1.90e-04 5.1e-05 1.66 -17 1.90e-04 5.1e-05 1.66 -18 1.89e-04 5.1e-05 1.66 -19 1.88e-04 5.1e-05 1.66 -20 1.88e-04 5.1e-05 1.66 -#σ = 0.01 - 1 3.47e-04 1.0e-04 1.58 - 2 3.96e-04 1.1e-04 1.53 - 3 3.39e-04 1.1e-04 1.56 - 4 3.42e-04 1.1e-04 1.57 - 5 3.34e-04 1.1e-04 1.55 - 6 3.35e-04 1.1e-04 1.55 - 7 3.37e-04 1.1e-04 1.55 - 8 3.33e-04 1.1e-04 1.55 - 9 3.33e-04 1.1e-04 1.55 -10 3.32e-04 1.1e-04 1.55 -11 3.32e-04 1.1e-04 1.54 -12 3.31e-04 1.1e-04 1.54 -13 3.31e-04 1.1e-04 1.54 -14 3.31e-04 1.1e-04 1.54 -15 3.31e-04 1.1e-04 1.55 -16 3.31e-04 1.1e-04 1.55 -17 3.31e-04 1.1e-04 1.55 -18 3.31e-04 1.1e-04 1.55 -19 3.31e-04 1.1e-04 1.55 -20 3.31e-04 1.1e-04 1.55 -#σ=0.05 - 1 1.49e-03 5.7e-04 1.38 - 2 1.51e-03 5.6e-04 1.41 - 3 1.50e-03 5.7e-04 1.39 - 4 1.50e-03 5.6e-04 1.40 - 5 1.52e-03 5.6e-04 1.42 - 6 1.53e-03 5.6e-04 1.43 - 7 1.52e-03 5.6e-04 1.43 - 8 1.51e-03 5.6e-04 1.42 - 9 1.54e-03 5.5e-04 1.45 -10 1.53e-03 5.5e-04 1.44 -11 1.53e-03 5.5e-04 1.44 -12 1.54e-03 5.5e-04 1.45 -13 1.54e-03 5.5e-04 1.45 -14 1.54e-03 5.5e-04 1.46 -15 1.55e-03 5.5e-04 1.46 -16 1.55e-03 5.5e-04 1.46 -17 1.55e-03 5.5e-04 1.47 -18 1.56e-03 5.5e-04 1.47 -19 1.56e-03 5.4e-04 1.47 -20 1.56e-03 5.4e-04 1.48 diff --git a/ex-6/plots/emd-round.py b/ex-6/plots/emd.py old mode 100644 new mode 100755 similarity index 57% rename from ex-6/plots/emd-round.py rename to ex-6/plots/emd.py index 2db2b64..f681a3f --- a/ex-6/plots/emd-round.py +++ b/ex-6/plots/emd.py @@ -1,5 +1,8 @@ +#!/usr/bin/env python + import numpy as np import matplotlib.pyplot as plt +import sys def plot(table, title='', log=False): @@ -24,23 +27,18 @@ def plot(table, title='', log=False): twin.set_ylabel('standard deviation', color='gray') twin.ticklabel_format(style='sci', axis='y', scilimits=(0, 0), useMathText=True) - - # plt.subplot(212) - # if log: - # plt.xscale('log') - # plt.title('skewness', loc='right') - # plt.xlabel('RL rounds') - # plt.plot(table[0], table[3], color='xkcd:gray') - plt.tight_layout() -table = np.loadtxt('ex-6/plots/emd-round-noise.txt') +file = sys.argv[1] if len(sys.argv) > 1 else 'noiseless' +table = np.loadtxt('ex-6/plots/emd-' + file + '.txt') +if file == 'noiseless': + plot(table[:31].T, title=r'noise at $\sigma_N = 0.005$') + plot(table[31:51].T, title=r'noise at $\sigma_N = 0.005$') + plot(table[51:].T, title=r'noise at $\sigma_N = 0.01$') +else: + plot(table[:20].T, title=r'noise at $\sigma_N = 0.005$') + plot(table[20:40].T, title=r'noise at $\sigma_N = 0.005$') + plot(table[40:].T, title=r'noise at $\sigma_N = 0.01$') +plt.show() -# plot(table[:27].T, title='noiseless', log=True) -plot(table[27:47].T, title=r'noise at $\sigma_N = 0.005$') -plt.savefig('notes/images/6-rounds-noise-0.005.pdf') -plot(table[47:67].T, title=r'noise at $\sigma_N = 0.01$') -plt.savefig('notes/images/6-rounds-noise-0.01.pdf') -plot(table[67:].T, title=r'noise at $\sigma_N = 0.05$') -plt.savefig('notes/images/6-rounds-noise-0.05.pdf') diff --git a/notes/sections/6.md b/notes/sections/6.md index 647d739..32d3b8f 100644 --- a/notes/sections/6.md +++ b/notes/sections/6.md @@ -647,31 +647,6 @@ histogram as follow. ![Example of Noisy histogram, $\sigma_N = 0.05$.](images/6-noisy.pdf){#fig:noisy} -
- ![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005} - - ![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01} - - ![](images/6-noise-rounds-0.05.pdf){#fig:rnoise-0.05} - -EMD as a function of RL rounds for different noise $\sigma_N$ values with the -kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the -standard deviation in grey. Noisy results. -
- -
- ![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005} - - ![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01} - - ![$\sigma_N = 0.05$](images/6-noise-emd-0.05.pdf){#fig:enoise-0.05} - -EMD distributions for different noise $\sigma_N$ values. The plots on the left -show the results for the FFT deconvolution, the central column the results for -the RL deconvolution and the third one shows the EMD for the convolved signal. -Noisy results. -
- For each bin, once the convolved histogram was computed, a value $v_N$ was randomly sampled from a Gaussian distribution with standard deviation $\sigma_N$, and the value $v_n \cdot b$ was added to the bin itself, where $b$ @@ -724,4 +699,28 @@ noise. When the kernel is not known a-priori, either of them turns out to be as good as the FFT in the aforementioned situation: only a poor approximation of the original signal can be derived. +
+ ![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005} + + ![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01} + + ![](images/6-noise-rounds-0.05.pdf){#fig:rnoise-0.05} + +EMD as a function of RL rounds for different noise $\sigma_N$ values with the +kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the +standard deviation in grey. Noisy results. +
+ +
+ ![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005} + + ![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01} + + ![$\sigma_N = 0.05$](images/6-noise-emd-0.05.pdf){#fig:enoise-0.05} + +EMD distributions for different noise $\sigma_N$ values. The plots on the left +show the results for the FFT deconvolution, the central column the results for +the RL deconvolution and the third one shows the EMD for the convolved signal. +Noisy results. +