Sample rate conversion basics in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a new sample rate by doubling the original sample rate.

Signal Processing

new_sample_rate = original_sample_rate [1] 2

Drag options to blanks, or click blank then click option'

A*

B+

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' adds 2 to the sample rate instead of doubling it.

Using '/' divides the sample rate, which reduces it.

Multiplying the original sample rate by 2 doubles it, which is a common way to increase sample rate.

2fill in blank

medium

Complete the code to downsample a signal by keeping every {{BLANK_1}}-th sample.

Signal Processing

downsampled_signal = original_signal[::[1]]

Drag options to blanks, or click blank then click option'

A3

B0

C2

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 as step causes an error.

Using -1 reverses the signal instead of downsampling.

Using a step of 2 in slicing keeps every second sample, effectively downsampling by 2.

3fill in blank

hard

Fix the error in the code to correctly upsample a signal by inserting zeros between samples.

Signal Processing

upsampled_signal = [original_signal[i // [1]] if i % [1] == 0 else 0 for i in range(len(original_signal) * [1])]

Drag options to blanks, or click blank then click option'

A1

B2

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 places original samples everywhere, no zeros inserted.

Using 0 causes division by zero error.

Using 2 inserts a zero between each original sample, doubling the length and upsampling by 2.

4fill in blank

hard

Fill both blanks to create a dictionary mapping each sample index to its value only if the value is greater than 0.

Signal Processing

filtered_samples = {i: sample for i, sample in enumerate(original_signal) if sample [1] 0 and i [2] 10}

Drag options to blanks, or click blank then click option'

A>

B<

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' instead of '>' filters only zeros.

Using '!=' does not filter properly.

The code keeps samples greater than 0 and with index less than 10.

5fill in blank

hard

Fill both blanks to create a dictionary of squared sample values for samples with index less than 5 and value greater than 0.

Signal Processing

squared_samples = {i: sample[1] for i, sample in enumerate(original_signal) if i [2] 5 and sample > 0}

Drag options to blanks, or click blank then click option'

B**2

C<

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Adding extra characters after 'i' in the key.

Using '==' instead of '<' for index filtering.

The dictionary comprehension keeps index as key, squares the sample value, and filters by index less than 5 and positive samples.

Practice

1. What does sample rate conversion do in signal processing?

easy

A. Changes how often a signal is measured

B. Changes the signal's amplitude

C. Changes the signal's frequency content

D. Changes the signal's phase

Solution

1. Step 1: Understand sample rate meaning

   Sample rate is how many times per second a signal is measured or sampled.

2. Step 2: Define sample rate conversion

   Sample rate conversion changes this measurement rate, either increasing or decreasing it.

3. Final Answer:

   Changes how often a signal is measured -> Option A

4. Quick Check:

   Sample rate conversion = Changes measurement rate [OK]

Hint: Sample rate conversion changes measurement frequency [OK]

Common Mistakes:

• Confusing sample rate with signal amplitude
• Thinking it changes signal frequency content
• Mixing phase changes with sample rate changes

2. Which of the following is the correct Python syntax to upsample a signal by a factor of 2 using scipy.signal.resample_poly?

easy

A. resample_poly(signal, up=1, down=2)

B. resample_poly(signal, up=2, down=1)

C. resample_poly(signal, rate=2)

D. resample_poly(signal, down=2)

Solution

1. Step 1: Recall resample_poly parameters

   The function uses 'up' to increase sample rate and 'down' to decrease it.

2. Step 2: Identify upsampling by 2

   To upsample by 2, set up=2 and down=1 to keep original rate multiplied by 2.

3. Final Answer:

   resample_poly(signal, up=2, down=1) -> Option B

4. Quick Check:

   Upsample factor = up=2, down=1 [OK]

Hint: Upsample means up>down, so up=2, down=1 [OK]

Common Mistakes:

• Swapping up and down values
• Omitting required parameters
• Using only up or down without the other

3. Given a signal sampled at 1000 Hz, what will be the new sample rate after applying resample_poly(signal, up=3, down=2)?

medium

A. 1500 Hz

B. 2000 Hz

C. 500 Hz

D. 3000 Hz

Solution

1. Step 1: Understand resample_poly rate change

   The new sample rate = original rate * (up / down).

2. Step 2: Calculate new sample rate

   1000 Hz * (3 / 2) = 1500 Hz.

3. Final Answer:

   1500 Hz -> Option A

4. Quick Check:

   1000 * 3/2 = 1500 Hz [OK]

Hint: Multiply original rate by up/down ratio [OK]

Common Mistakes:

• Multiplying by down/up instead of up/down
• Forgetting to multiply by original rate
• Confusing sample rate with signal length

4. What is wrong with this code snippet for downsampling a signal by 4?

from scipy.signal import resample_poly
new_signal = resample_poly(signal, up=1, down=4)

medium

A. It will cause a syntax error due to missing import

B. The up parameter should be 4, not 1

C. It may cause aliasing without proper filtering

D. The down parameter should be 1, not 4

Solution

1. Step 1: Check code correctness

   The code syntax is correct and imports resample_poly properly.

2. Step 2: Understand downsampling risks

   Downsampling by 4 reduces sample rate, which can cause aliasing if signal is not filtered.

3. Final Answer:

   It may cause aliasing without proper filtering -> Option C

4. Quick Check:

   Downsampling needs filtering to avoid aliasing [OK]

Hint: Downsampling needs filtering to prevent aliasing [OK]

Common Mistakes:

• Assuming code syntax error
• Confusing up and down parameters
• Ignoring aliasing effects

5. You have a 44100 Hz audio signal and want to convert it to 16000 Hz for a speech recognition system. Which combination of up and down factors correctly resamples the signal using resample_poly?

hard

A. up=1600, down=441

B. up=44100, down=16000

C. up=160, down=4410

D. up=160, down=441

Solution

1. Step 1: Calculate ratio for resampling

   The ratio is new_rate / old_rate = 16000 / 44100 ≈ 0.3628.

2. Step 2: Find integer up/down factors

   Scaling both by 1000 gives up=160, down=441, which approximates the ratio well.

3. Final Answer:

   up=160, down=441 -> Option D

4. Quick Check:

   160/441 ≈ 0.3628 matches 16000/44100 [OK]

Hint: Simplify ratio new_rate/old_rate to small integers [OK]

Common Mistakes:

• Using raw sample rates as up/down without simplification
• Swapping up and down values
• Choosing factors that don't approximate ratio