Sample rate conversion basics in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the purpose of sample rate conversion

Why do we perform sample rate conversion in digital signal processing?

A To change the sampling frequency of a signal to match another system's requirements

B To increase the amplitude of the signal without changing its frequency

C To convert an analog signal directly into a digital signal

D To remove noise from the signal by filtering

💡 Hint

Think about why two devices with different sampling rates need to communicate.

Sample rate conversion changes the sampling frequency of a digital signal so it can be processed or played back on systems with different sampling rates.

❓ Predict Output

intermediate

Output of upsampling by 2

What is the output array after upsampling the input signal by a factor of 2?

Input signal: [1, 2, 3]

Upsampling means inserting zeros between samples.

Signal Processing

input_signal = [1, 2, 3]
upsample_factor = 2
output_signal = []
for sample in input_signal:
    output_signal.append(sample)
    output_signal.append(0)
print(output_signal)

A [1, 2, 3, 0, 0, 0]

B [0, 1, 0, 2, 0, 3]

C [1, 0, 2, 0, 3, 0]

D [1, 0, 0, 2, 0, 0, 3, 0, 0]

💡 Hint

Upsampling by 2 inserts one zero after each original sample.

Upsampling by 2 inserts one zero after each sample, doubling the length of the signal.

❓ data_output

advanced

Length of signal after downsampling

Given a signal of length 1000 samples, what is the length after downsampling by a factor of 4?

A 1004

B 4000

C 996

D 250

💡 Hint

Downsampling by 4 keeps every 4th sample.

Downsampling by 4 reduces the number of samples to one fourth, so 1000 / 4 = 250.

❓ visualization

advanced

Effect of interpolation filter on upsampled signal

Which plot best shows the effect of applying an interpolation low-pass filter after upsampling a signal by 2?

The original signal is a sine wave sampled at 10 Hz.

A Plot showing a noisy signal with random spikes after filtering

B Plot showing the upsampled signal with zero-inserted samples and smooth sine wave after filtering

C Plot showing a sine wave with doubled frequency without zero samples

D Plot showing only the original sine wave without any zero samples

💡 Hint

Interpolation filters smooth the zero-inserted samples to reconstruct the signal.

After upsampling by inserting zeros, the interpolation filter smooths the signal to approximate the original waveform at a higher sample rate.

🔧 Debug

expert

Identify error in sample rate conversion code

What error will this Python code raise when trying to downsample a signal by 3?

signal = [10, 20, 30, 40, 50]
downsample_factor = 3
result = [signal[i] for i in range(0, len(signal), downsample_factor + 1)]
print(result)

A The output is [10, 50] which is incorrect downsampling

B The code runs without error and outputs [10, 40]

C IndexError because the range step is incorrect

D The code runs but outputs [10, 20, 30, 40, 50] without downsampling

💡 Hint

Check how the step size in range affects the indices selected.

The code uses step = downsample_factor + 1 = 4, so it picks indices 0 and 4, outputting [10, 50]. The code is incorrect because it should use step = downsample_factor = 3 to pick every 3rd sample.

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