Project 2: The Moving Average Filter (Removing the Noise)

Build a moving average filter that smooths noisy signals and reveals the underlying trend.

Project Overview

Attribute	Value
Difficulty	Level 1: Beginner
Time Estimate	1 evening
Main Language	C
Alternative Languages	Python, Rust, C++
Knowledge Area	Time-domain filtering
Tools	Audacity or CSV plotting tool
Main Book	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith

What you’ll build: A filter that replaces each sample with the average of the last N samples.

Why it teaches DSP: This is the simplest real filter. It shows how smoothing is just a sliding window sum.

Core challenges you’ll face:

Choosing window size and understanding its tradeoffs
Managing sample history in a fixed buffer
Measuring how smoothing affects sharp transitions

Real World Outcome

You will feed a noisy signal in and get a smoother signal out. You should be able to visualize how spikes are reduced and how the signal lags behind sudden changes.

Example Output:

$ ./moving_avg --window 8 --input noisy.csv --output smooth.csv
Input samples: 2000
Window size: 8
Wrote smoothed output to smooth.csv

Verification steps:

Plot input and output on the same chart
Confirm noise is reduced and peaks are rounded

The Core Question You’re Answering

“How does a simple average become a filter, and what do I lose when I smooth a signal?”

This project makes the cost of smoothing obvious: less noise but also less detail and added delay.

Concepts You Must Understand First

Stop and research these before coding:

Sliding windows
- How do you update a rolling average without recomputing the whole sum?
- Book Reference: “The Scientist and Engineer’s Guide to DSP” Ch. 15
Filter delay
- Why does a moving average introduce a lag?
- Book Reference: “Understanding Digital Signal Processing” by Richard G. Lyons, Ch. 6
Noise vs. signal
- What counts as noise and what counts as signal?
- Book Reference: “The Scientist and Engineer’s Guide to DSP” Ch. 2

Questions to Guide Your Design

Window size selection
- How will you choose the window size for different noise levels?
- How will you quantify the smoothing effect?
Streaming vs. batch
- Can your filter work in streaming mode, one sample at a time?
- What state must be stored between samples?

Thinking Exercise

Manual Windowing

Take the sample sequence below and compute the moving average with window size 4:

Sequence: 2, 4, 8, 4, 2, 0, 2, 4

Questions while working:

Where does the output begin (after how many samples)?
Which features are smoothed out completely?
What happens if the window size is 2 vs 8?

The Interview Questions They’ll Ask

Prepare to answer these:

“Why does a moving average act as a low-pass filter?”
“How does window size affect frequency response?”
“What is filter delay and why does it happen?”
“How can you compute a running average efficiently?”
“When would you avoid a moving average filter?”

Hints in Layers

Hint 1: Starting Point Keep a fixed-size queue of recent samples.

Hint 2: Next Level Maintain a running sum so each new sample is O(1).

Hint 3: Technical Details When a new sample arrives, add it to the sum and subtract the oldest sample.

Hint 4: Tools/Debugging Plot the filtered output over the noisy input to verify smoothing and delay.

Books That Will Help

Topic	Book	Chapter
Moving average filters	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith	Ch. 15
Filter delay	“Understanding Digital Signal Processing” by Richard G. Lyons	Ch. 6
Noise fundamentals	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith	Ch. 2

Implementation Hints

Use a circular buffer to store the last N samples.
Document the effective delay so users interpret results correctly.
Keep numeric types stable to avoid accumulating error.

Learning Milestones

First milestone: You can smooth a noisy sequence with a fixed window.
Second milestone: You can explain how window size changes the output.
Final milestone: You can describe why this filter attenuates high frequencies.