From 947a198f9a1f5fe0fab5f378390af7fdf7a651ad Mon Sep 17 00:00:00 2001 From: Andrew Gait Date: Fri, 13 Nov 2026 10:28:46 +0000 Subject: [PATCH 1/3] Add visuals to explain signal vs noise --- episodes/03-numpy_essential.md | 44 ++++++++++++++++------------ episodes/fig/gauss_curve_signal.png | Bin 27211 -> 13642 bytes 2 files changed, 26 insertions(+), 18 deletions(-) diff --git a/episodes/03-numpy_essential.md b/episodes/03-numpy_essential.md index 5300e01e..de618e7d 100644 --- a/episodes/03-numpy_essential.md +++ b/episodes/03-numpy_essential.md @@ -244,14 +244,31 @@ plt.show() ## Noisy Signal -Now we are going to add some random noise to that curve. To do this we need to create a Random Number Generator (RNG), which we can then use with the function `normal` from the module `random` provided by the NumPy library. We create an array of zeros of the same length as the array for our curve `g` as the mean values for the random noise, and then scale the magnitude of the noise so it is (roughly) a 10th of the magnitude of the Gaussian maximum. Finally, we then plot the result of adding the noise to the original curve: +Now we are going to add some random noise to that curve. To do this we need to create a Random Number Generator (RNG), which we can then use with the function `normal` from the module `random` provided by the NumPy library. We create an array of zeros of the same length as the array for our curve `g` as the mean values for the random noise, and then scale the magnitude of the noise so it is (roughly) a 10th of the magnitude of the Gaussian maximum. ```python rng = np.random.default_rng() zeros = np.zeros(len(g)) noise = rng.normal(zeros, g.max() / 10) noisy = g + noise +``` + +To identify any signal in the data we can use the standard deviation as an estimate of the noise around the mean value of the data: + +```python +stddev_noisy = np.std(noisy) +mean_noisy = np.mean(noisy) +print(f'standard deviation is: {stddev_noisy:.5f}') +print(f'mean value is: {mean_noisy:.5f}') +``` + +Finally, we then plot the result of adding the noise to the original curve, alongside some guides to show the mean and standard deviation of the noise: + +```python plt.plot(x, noisy) +plt.plot(x, [mean_noisy]*len(x), 'g-') # Plot a green line to show the mean of the noise +plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r-') # Plot red lines to show mean +/- stddev +plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r-') plt.show() ``` @@ -269,20 +286,7 @@ it each time it is required. :::::::::::::::::::::::::::::::::::::::::::::::::: -To identify any signal in the data we can use the standard deviation as an estimate of the noise around the mean value of the data. - -```python -stddev_noisy = np.std(noisy) -mean_noisy = np.mean(noisy) -print(f'standard deviation is: {stddev_noisy:.5f}') -print(f'mean value is: {mean_noisy:.5f}') -``` -```output -standard deviation is: 0.01159 -mean value is: 0.00505 -``` - -We will create a mask for the data, by selecting all data points below this threshold value (we'll assume here that any signal we might be interested in is positive): +Now we will create a mask for the data, by selecting all data points below this threshold value (we'll assume here that any signal we might be interested in is positive): ```python mask = noisy < (stddev_noisy + mean_noisy) @@ -290,11 +294,15 @@ mask = noisy < (stddev_noisy + mean_noisy) This creates an array of boolean values, the same shape as our original data, with `True` values where the conditional statement has been met. -The mask and noisy data can now be combined using the `array` function of the NumPy masked arrays module (`np.ma`). Any `True` value in the mask will exclude the corresponding element from subsequent computation or plotting: +The mask and noisy data can now be combined using the `array` function of the NumPy masked arrays module (`np.ma`). Any `True` value in the mask will exclude the corresponding element from subsequent computation or plotting. Again, we plot the green and red lines to give a visual indication of what our computation is doing: ```python -noisy_ma = np.ma.array(noisy, mask=mask) -plt.plot(noisy_ma) +noisy_masked = np.ma.array(noisy, mask=mask) +plt.plot(x, noisy_masked) +plt.xlim(-100,100) +plt.plot(x, [mean_noisy]*len(x), 'g-') +plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r-') +plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r-') plt.show() ``` diff --git a/episodes/fig/gauss_curve_signal.png b/episodes/fig/gauss_curve_signal.png index 87cf8104e8c9ca34d0fed7ad5a3756c3be075695..c5fa8e5451e16eaea6ae72a6542d45780e449b5c 100644 GIT binary patch literal 13642 zcmeIYXH=72+by~hItZwUC`eHR6c7|C(t}8oCW7=TARy9vkBagr2ndSOQBXj7?*uDC zq?gb;(ui*t ztc=nHpV%fI{?T2HMSbD(YkJ%x_1g3C!(#3OT#Bt zImZH*cgAj!G#~ys^PW~v@Hi76`X`@8_4T;a@#(8}38QVR_x#ERQwP_U_WbiT?m4*g zmnDX*%>`*C*qbE4^)#ItTo^;Z|74v+9EBe*Q=;I9uSWs=?uas=1mNequ^Xt$S7{cpNA^wIR9f>%}@#{9DP7k5X&PxTtI$+#zbrR_G6OpVs!>)K_m 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15:12:11 +0000 Subject: [PATCH 2/3] Updates based on review - add output for SD and mean - change line type for SD plots --- episodes/03-numpy_essential.md | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/episodes/03-numpy_essential.md b/episodes/03-numpy_essential.md index de618e7d..70bff6ac 100644 --- a/episodes/03-numpy_essential.md +++ b/episodes/03-numpy_essential.md @@ -261,14 +261,18 @@ mean_noisy = np.mean(noisy) print(f'standard deviation is: {stddev_noisy:.5f}') print(f'mean value is: {mean_noisy:.5f}') ``` +```output +standard deviation is: 0.01159 +mean value is: 0.00505 +``` Finally, we then plot the result of adding the noise to the original curve, alongside some guides to show the mean and standard deviation of the noise: ```python plt.plot(x, noisy) plt.plot(x, [mean_noisy]*len(x), 'g-') # Plot a green line to show the mean of the noise -plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r-') # Plot red lines to show mean +/- stddev -plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r-') +plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r--') # Plot red lines to show mean +/- stddev +plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r--') plt.show() ``` @@ -301,8 +305,8 @@ noisy_masked = np.ma.array(noisy, mask=mask) plt.plot(x, noisy_masked) plt.xlim(-100,100) plt.plot(x, [mean_noisy]*len(x), 'g-') -plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r-') -plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r-') +plt.plot(x, [mean_noisy+stddev_noisy]*len(x), 'r--') +plt.plot(x, [mean_noisy-stddev_noisy]*len(x), 'r--') plt.show() ``` From 2a76f1ff6b035ff1a1076d21678387557dafcdc9 Mon Sep 17 00:00:00 2001 From: Andrew Gait Date: Fri, 13 Nov 2026 15:34:06 +0000 Subject: [PATCH 3/3] Update figures with dashed lines --- episodes/fig/gauss_curve_noisy.png | Bin 23866 -> 33724 bytes episodes/fig/gauss_curve_signal.png | Bin 13642 -> 14374 bytes 2 files changed, 0 insertions(+), 0 deletions(-) diff --git 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