Downsampling strategies in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of simple downsampling with slicing

What is the output plot's number of points after downsampling the data by slicing every 3rd point?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(0, 30)
y = np.sin(x)

x_downsampled = x[::3]
y_downsampled = y[::3]

plt.plot(x_downsampled, y_downsampled, 'o-')
plt.title(f'Downsampled points: {len(x_downsampled)}')
plt.show()

print(len(x_downsampled))

A 30

B 9

C 11

D 10

💡 Hint

Remember slicing with step 3 picks every third element starting from index 0.

The original array has 30 points (0 to 29). Slicing with step 3 picks indices 0, 3, 6, ..., 27, which is 10 points total.

❓ data_output

intermediate

Resulting data after averaging downsampling

Given a 1D numpy array of 12 values, what is the resulting array after downsampling by averaging every 4 points?

Matplotlib

import numpy as np

data = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24])

# Downsample by averaging every 4 points
downsampled = data.reshape(-1, 4).mean(axis=1)

print(downsampled)

A [5.0, 13.0, 21.0]

B [4.0, 12.0, 20.0]

C [6.0, 14.0, 22.0]

D [5.0, 14.0, 23.0]

💡 Hint

Calculate the mean of each group of 4 consecutive numbers.

The groups are [2,4,6,8], [10,12,14,16], and [18,20,22,24]. Their means are 5.0, 13.0, and 21.0 respectively.

❓ visualization

advanced

Visual difference between no downsampling and decimation

Which plot correctly shows the effect of decimation downsampling by factor 5 on a noisy sine wave?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 4 * np.pi, 500)
y = np.sin(x) + np.random.normal(0, 0.1, 500)

y_decimated = y[::5]
x_decimated = x[::5]

plt.figure(figsize=(10, 4))
plt.plot(x, y, label='Original')
plt.plot(x_decimated, y_decimated, 'o-', label='Decimated (factor 5)')
plt.legend()
plt.title('Decimation Downsampling')
plt.show()

A Plot with original smooth sine and fewer noisy points connected by lines every 5th point

B Plot with original sine wave but decimated points are random unrelated points

C Plot with only noisy points and no sine wave visible

D Plot with original sine and all points connected with no difference

💡 Hint

Decimation picks every nth point, so the decimated plot should have fewer points but follow the original shape.

Decimation reduces points by picking every 5th point, so the decimated plot shows fewer points connected, preserving the sine shape but with less detail.

🧠 Conceptual

advanced

Effect of downsampling on signal frequency content

What is the main risk when downsampling a signal without applying a low-pass filter first?

A The signal will become longer and harder to process

B The signal may lose high-frequency details causing aliasing artifacts

C The signal will automatically become smoother without any artifacts

D The signal's amplitude will increase causing distortion

💡 Hint

Think about what happens to frequencies higher than half the new sampling rate.

Without low-pass filtering, high-frequency components fold back into lower frequencies causing aliasing, which distorts the signal.

🔧 Debug

expert

Identify the error in downsampling code using pandas resample

What error will this code raise when trying to downsample a time series by 2 minutes using pandas resample?

Matplotlib

import pandas as pd
import numpy as np

rng = pd.date_range('2024-01-01', periods=5, freq='T')
data = pd.Series(np.arange(5), index=rng)

# Attempt to downsample by 2 minutes
result = data.resample('2min').mean()
print(result)

A TypeError: resample() missing required argument

B ValueError: Invalid frequency string

C No error, outputs mean values for 2-minute bins

D KeyError: '2min' not found in index

💡 Hint

Check if '2min' is a valid frequency string for pandas resample.

The code correctly uses '2min' frequency string and resample with mean works without error, producing averaged values over 2-minute intervals.