Audio compression basics in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

What is the main goal of audio compression?

Audio compression is used to reduce the size of audio files. What is the main goal of this process?

A To reduce file size while keeping sound quality as high as possible

B To increase the file size for better sound quality

C To convert audio files into text format

D To remove all background noise from the audio

💡 Hint

Think about why we want smaller audio files but still want them to sound good.

The main goal of audio compression is to reduce the file size so it takes less space and bandwidth, but still keep the sound quality as close to the original as possible.

❓ Predict Output

intermediate

What is the output of this Python code simulating audio compression ratio?

Consider this simple Python code that calculates the compression ratio of an audio file:

original_size = 5000  # in KB
compressed_size = 1250  # in KB
compression_ratio = original_size / compressed_size
print(round(compression_ratio, 2))

What will be printed?

Signal Processing

original_size = 5000  # in KB
compressed_size = 1250  # in KB
compression_ratio = original_size / compressed_size
print(round(compression_ratio, 2))

A 3750

B 0.25

C 6250

D 4.0

💡 Hint

Compression ratio is original size divided by compressed size.

The compression ratio is 5000 divided by 1250, which equals 4.0.

❓ data_output

advanced

What is the shape of the compressed audio data array?

Given a numpy array representing raw audio data with shape (44100, 2) for 1 second stereo audio sampled at 44.1kHz, after compression the data is downsampled by a factor of 4 and converted to mono by averaging channels.

What is the shape of the compressed audio data array?

Signal Processing

import numpy as np
raw_audio = np.random.rand(44100, 2)
compressed_audio = raw_audio[::4].mean(axis=1)
print(compressed_audio.shape)

A (11025, 2)

B (11025,)

C (44100,)

D (44100, 2)

💡 Hint

Downsampling by 4 reduces samples by 4 times. Averaging channels reduces 2 channels to 1.

Downsampling reduces 44100 samples to 11025 (44100/4). Averaging the 2 channels results in a single channel, so shape is (11025,).

❓ visualization

advanced

Which plot shows the effect of lossy audio compression on frequency spectrum?

You have two frequency spectrum plots of the same audio: one original and one after lossy compression. Which plot likely shows the compressed audio?

A Plot with completely flat line at zero

B Plot with more high-frequency spikes and noise

C Plot with fewer high-frequency components and smoother curve

D Plot with random spikes across all frequencies

💡 Hint

Lossy compression often removes high-frequency details to save space.

Lossy compression reduces or removes some high-frequency sounds, so the compressed audio spectrum looks smoother with fewer high-frequency spikes.

🔧 Debug

expert

What error does this audio compression code raise?

Consider this Python code snippet that attempts to compress audio data by quantization:

import numpy as np
audio = np.array([0.1, 0.5, 0.9])
quantized = audio // 0.5
print(quantized)

What error will this code produce when run?

Signal Processing

import numpy as np
audio = np.array([0.1, 0.5, 0.9])
quantized = audio // 0.5
print(quantized)

A No error, output: [0. 1. 1.]

B ValueError: operands could not be broadcast together

C TypeError: unsupported operand type(s) for //: 'numpy.ndarray' and 'float'

D SyntaxError: invalid syntax

💡 Hint

Check if floor division (//) works with float operands in numpy arrays.

NumPy supports the floor division operator (//) for float NumPy arrays and float scalars. It computes the floor of the division element-wise: 0.1//0.5 = floor(0.2) = 0.0, 0.5//0.5 = floor(1.0) = 1.0, 0.9//0.5 = floor(1.8) = 1.0. Thus, no error, output: [0. 1. 1.].

Practice

1. What is the main goal of audio compression?

easy

A. To reduce the file size while keeping sound quality acceptable

B. To increase the file size for better quality

C. To convert audio files into video files

D. To remove all background noise completely

Solution

1. Step 1: Understand the purpose of audio compression

   Audio compression aims to make audio files smaller so they use less space and bandwidth.

2. Step 2: Identify the correct goal

   The goal is to reduce size but keep the sound quality good enough for listening.

3. Final Answer:

   To reduce the file size while keeping sound quality acceptable -> Option A

4. Quick Check:

   Audio compression = smaller files with good quality [OK]

Hint: Compression means smaller size, not bigger [OK]

Common Mistakes:

• Thinking compression increases file size
• Confusing audio with video conversion
• Assuming all noise is removed

2. Which of the following is a correct statement about lossy audio compression?

easy

A. It keeps all original audio data intact

B. It removes some audio data permanently to reduce size

C. It converts audio to text format

D. It increases the audio file size

Solution

1. Step 1: Define lossy compression

   Lossy compression removes some audio data permanently to save space.

2. Step 2: Compare options

   Only It removes some audio data permanently to reduce size correctly describes lossy compression; others are incorrect or unrelated.

3. Final Answer:

   It removes some audio data permanently to reduce size -> Option B

4. Quick Check:

   Lossy = data removed permanently [OK]

Hint: Lossy means some data is lost forever [OK]

Common Mistakes:

• Confusing lossy with lossless compression
• Thinking lossy keeps all data
• Believing audio is converted to text

3. Consider this Python code snippet simulating audio compression bitrate calculation:

original_bitrate = 1411  # in kbps for CD quality
compression_ratio = 0.1
compressed_bitrate = original_bitrate * compression_ratio
print(int(compressed_bitrate))

What is the output of this code?

medium

A. 1411

B. 14

C. 141

D. 0

Solution

1. Step 1: Calculate compressed bitrate

   Multiply original bitrate 1411 kbps by compression ratio 0.1: 1411 * 0.1 = 141.1

2. Step 2: Convert to integer and print

   int(141.1) is 141, so the output is 141.

3. Final Answer:

   141 -> Option C

4. Quick Check:

   1411 * 0.1 = 141 [OK]

Hint: Multiply bitrate by ratio, then convert to int [OK]

Common Mistakes:

• Forgetting to multiply by compression ratio
• Confusing int conversion rounding
• Printing original bitrate instead

4. This code tries to calculate compressed audio size but has an error:

file_size_mb = 50
compression_rate = 0.2
compressed_size = file_size_mb / compression_rate
print(compressed_size)

What is the error in this code?

medium

A. Division by zero error

B. Variable names are invalid

C. Missing import statement

D. It should multiply, not divide, by compression_rate

Solution

1. Step 1: Understand compression calculation

   Compressed size should be original size multiplied by compression rate (fraction less than 1).

2. Step 2: Identify the error in code

   The code divides file_size_mb by compression_rate, which increases size incorrectly.

3. Final Answer:

   It should multiply, not divide, by compression_rate -> Option D

4. Quick Check:

   Compression size = original size * rate [OK]

Hint: Compression reduces size, so multiply by rate [OK]

Common Mistakes:

• Using division instead of multiplication
• Assuming variable names cause error
• Expecting import needed for math

5. You have a 100 MB audio file and want to compress it to about 25% of its size using lossy compression. Which bitrate should you choose if the original bitrate is 160 kbps?

Options:
A) 40 kbps
B) 80 kbps
C) 120 kbps
D) 160 kbps

hard

A. 40 kbps

B. 80 kbps

C. 120 kbps

D. 160 kbps

Solution

1. Step 1: Calculate target bitrate for 25% size

   25% means 0.25 times original bitrate: 160 kbps * 0.25 = 40 kbps.

2. Step 2: Choose bitrate matching target

   40 kbps is 40 kbps, which matches the target bitrate for 25% size.

3. Final Answer:

   40 kbps -> Option A

4. Quick Check:

   160 * 0.25 = 40 kbps [OK]

Hint: Multiply original bitrate by compression fraction [OK]

Common Mistakes:

• Choosing bitrate higher than target size
• Confusing percentage with absolute value
• Ignoring lossy compression effect