Real-time DSP processing pipeline in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple real-time filter code

What is the output array after applying this simple moving average filter on the input signal?

Signal Processing

import numpy as np

def moving_average(signal, window_size=3):
    filtered = []
    for i in range(len(signal)):
        window = signal[max(0, i - window_size + 1):i + 1]
        filtered.append(sum(window) / len(window))
    return np.array(filtered)

input_signal = np.array([1, 2, 3, 4, 5])
output_signal = moving_average(input_signal)
print(output_signal)

A [1.0, 1.5, 2.0, 2.5, 3.0]

B [1.0, 1.5, 2.0, 3.0, 4.0]

C [1.0, 2.0, 3.0, 4.0, 5.0]

D [2.0, 3.0, 4.0, 5.0, 6.0]

💡 Hint

Think about how the moving average window grows at the start of the signal.

The moving average at each point is the average of the current and previous samples up to the window size. For the first element, only one sample is available, so average is 1.0. For the second, average of [1,2] = 1.5, and so on.

❓ data_output

intermediate

Number of samples after downsampling

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

A 1000

B 4000

C 996

D 250

💡 Hint

Downsampling by 4 means keeping every 4th sample.

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

❓ visualization

advanced

Identify the correct frequency spectrum plot

Which plot correctly shows the frequency spectrum of a 5 Hz sine wave sampled at 50 Hz?

Signal Processing

import numpy as np
import matplotlib.pyplot as plt

fs = 50  # Sampling frequency
f = 5    # Signal frequency

t = np.arange(0, 1, 1/fs)
signal = np.sin(2 * np.pi * f * t)

fft_vals = np.fft.fft(signal)
fft_freq = np.fft.fftfreq(len(signal), 1/fs)

plt.plot(fft_freq[:len(signal)//2], np.abs(fft_vals)[:len(signal)//2])
plt.xlabel('Frequency (Hz)')
plt.ylabel('Magnitude')
plt.title('Frequency Spectrum')
plt.show()

A Multiple peaks at 0 Hz and 50 Hz

B No peaks, flat spectrum

C A single peak at 5 Hz

D A peak at 25 Hz

💡 Hint

The sine wave frequency should appear as a peak in the spectrum.

A pure sine wave at 5 Hz sampled at 50 Hz will show a single peak at 5 Hz in the frequency spectrum.

🔧 Debug

advanced

Identify the error in this real-time filter code snippet

What error will this code raise when run?

Signal Processing

def real_time_filter(signal):
    filtered = []
    for i in range(len(signal)):
        filtered[i] = signal[i] * 0.5
    return filtered

print(real_time_filter([1, 2, 3]))

A IndexError: list assignment index out of range

B TypeError: unsupported operand type(s) for *: 'list' and 'float'

C NameError: name 'filtered' is not defined

D No error, outputs [0.5, 1.0, 1.5]

💡 Hint

Look at how the list 'filtered' is used before any elements are added.

The code tries to assign to filtered[i] but filtered is empty, so this causes an IndexError.

🚀 Application

expert

Choosing the best approach for real-time DSP latency reduction

Which approach best reduces latency in a real-time DSP pipeline processing audio signals?

A Use smaller buffer sizes and optimize filter algorithms

B Increase buffer sizes to process more samples at once

C Add more complex filters to improve signal quality

D Use batch processing after recording all audio

💡 Hint

Lower latency means processing data faster with less delay.

Smaller buffers reduce delay before processing starts, and optimized filters run faster, both reducing latency.

Practice

1. What is the main purpose of a real-time DSP processing pipeline?

easy

A. To process signals step-by-step as data arrives

B. To store large amounts of data for later analysis

C. To generate random signals for testing

D. To visualize signals after processing is complete

Solution

1. Step 1: Understand real-time processing

   Real-time DSP means processing data immediately as it comes in, not storing for later.

2. Step 2: Identify pipeline purpose

   The pipeline processes signals step-by-step to analyze or clean them on the fly.

3. Final Answer:

   To process signals step-by-step as data arrives -> Option A

4. Quick Check:

   Real-time DSP = step-by-step processing [OK]

Hint: Real-time means processing data immediately as it arrives [OK]

Common Mistakes:

• Confusing real-time with batch processing
• Thinking pipeline stores data only
• Assuming visualization is the main goal

2. Which of the following is the correct syntax to apply a moving average filter on a signal array data in Python using a window size of 3?

easy

A. filtered = [sum(data[i:i+3])*3 for i in range(len(data)-2)]

B. filtered = [sum(data[i:i+3])/3 for i in range(len(data)-2)]

C. filtered = [sum(data[i:i+3])/3 for i in range(len(data)+2)]

D. filtered = sum(data[i:i+3])/3 for i in range(len(data)-2)

Solution

1. Step 1: Understand moving average filter

   It averages each group of 3 consecutive elements in the data.

2. Step 2: Check syntax correctness

   filtered = [sum(data[i:i+3])/3 for i in range(len(data)-2)] correctly uses list comprehension with range(len(data)-2) and divides sum by 3.

3. Final Answer:

   filtered = [sum(data[i:i+3])/3 for i in range(len(data)-2)] -> Option B

4. Quick Check:

   Correct list comprehension with proper range and division [OK]

Hint: Use range(len(data)-window+1) for correct slicing [OK]

Common Mistakes:

• Missing brackets for list comprehension
• Using wrong range length causing index errors
• Multiplying instead of dividing for average

3. Given the Python code below for a simple real-time DSP pipeline, what is the output of print(filtered_signal)?

signal = [1, 3, 5, 7, 9]
window_size = 2
filtered_signal = [ (signal[i] + signal[i+1]) / 2 for i in range(len(signal)-1) ]
print(filtered_signal)

medium

A. [1.0, 4.0, 6.0, 8.0]

B. [1.0, 3.0, 5.0, 7.0, 9.0]

C. [2.0, 4.0, 6.0, 8.0]

D. [3.0, 5.0, 7.0, 9.0]

Solution

1. Step 1: Understand the list comprehension

   It averages each pair of consecutive elements: (signal[i] + signal[i+1]) / 2.

2. Step 2: Calculate each average

   Pairs: (1+3)/2=2.0, (3+5)/2=4.0, (5+7)/2=6.0, (7+9)/2=8.0.

3. Final Answer:

   [2.0, 4.0, 6.0, 8.0] -> Option C

4. Quick Check:

   Pairwise averages = [2.0, 4.0, 6.0, 8.0] [OK]

Hint: Calculate pair averages step-by-step [OK]

Common Mistakes:

• Including last element without pair
• Confusing sum with average
• Wrong range causing index error

4. The following code attempts to implement a moving average filter but raises an error. What is the error and how to fix it?

data = [2, 4, 6, 8]
window = 3
filtered = []
for i in range(len(data)):
    avg = (data[i] + data[i+1] + data[i+2]) / window
    filtered.append(avg)
print(filtered)

medium

A. IndexError because indexing goes beyond list end; fix by using range(len(data)-window+1)

B. ZeroDivisionError because window is zero; fix by setting window to 1

C. TypeError because sum cannot add list slices; fix by converting slice to list

D. No error; code runs correctly

Solution

1. Step 1: Identify the error cause

   Loop runs till len(data), but indexing data[i+2] exceeds list length at end.

2. Step 2: Fix the loop range

   Change loop to range(len(data)-window+1) to avoid out-of-range indexing.

3. Final Answer:

   IndexError because indexing goes beyond list end; fix by using range(len(data)-window+1) -> Option A

4. Quick Check:

   Loop range must prevent out-of-bound indexing [OK]

Hint: Loop till len(data)-window+1 for safe indexing [OK]

Common Mistakes:

• Ignoring index bounds causing IndexError
• Changing window size incorrectly
• Assuming no error occurs

5. You want to build a real-time DSP pipeline that filters noise from a sensor signal using a moving average filter of window size 4, but the sensor sometimes sends fewer than 4 samples at once. How should you adapt your pipeline to handle this situation correctly?

hard

A. Use a fixed window size of 1 to avoid buffering

B. Apply the filter on whatever samples arrive, even if fewer than 4, without buffering

C. Discard any samples fewer than 4 and wait for a full batch

D. Process only when at least 4 samples are available; buffer incoming data until then

Solution

1. Step 1: Understand window size requirement

   Moving average with window 4 needs 4 samples to compute an average.

2. Step 2: Handle fewer samples in real-time

   Buffer incoming samples until at least 4 are collected, then apply filter.

3. Step 3: Avoid incorrect averages

   Processing fewer samples without buffering gives wrong results; discarding loses data.

4. Final Answer:

   Process only when at least 4 samples are available; buffer incoming data until then -> Option D

5. Quick Check:

   Buffering ensures correct window size for filtering [OK]

Hint: Buffer data until window size reached before filtering [OK]

Common Mistakes:

• Filtering with incomplete windows causing errors
• Discarding useful data
• Using window size 1 losing noise reduction benefits