Project 8: Spectrogram Visualizer (Seeing in 3D)

Build a spectrogram tool that shows how frequency content changes over time.

Project Overview

Attribute	Value
Difficulty	Level 2: Intermediate
Time Estimate	1-2 weeks
Main Language	C
Alternative Languages	Python, Rust, C++
Knowledge Area	Time-frequency analysis
Tools	Plotting tool, image writer
Main Book	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith

What you’ll build: A tool that slices audio into windows, runs the FFT, and renders a spectrogram image.

Why it teaches DSP: It forces you to understand windowing, overlap, and the time-frequency tradeoff.

Core challenges you’ll face:

Choosing window size and overlap
Mapping magnitude to color or intensity
Balancing time and frequency resolution

Real World Outcome

You will generate a spectrogram image where vertical axis is frequency, horizontal axis is time, and color indicates magnitude. Spoken words and tones should appear as distinct patterns.

Example Output:

$ ./spectrogram --input speech.wav --window 1024 --overlap 512 --output spec.png
Frames: 172
Wrote spectrogram to spec.png

Verification steps:

Check for horizontal bands for steady tones
Confirm transient sounds appear as vertical streaks

The Core Question You’re Answering

“How can I see frequency content evolve over time without losing too much detail?”

This is the practical face of the uncertainty principle in DSP.

Concepts You Must Understand First

Stop and research these before coding:

Short-time Fourier transform
- Why do we analyze windows rather than the entire signal?
- Book Reference: “The Scientist and Engineer’s Guide to DSP” by Steven W. Smith, Ch. 10
Window functions
- How do Hann and Hamming windows reduce leakage?
- Book Reference: “Understanding Digital Signal Processing” by Richard G. Lyons, Ch. 9
Time-frequency tradeoff
- Why do smaller windows give better time resolution but worse frequency resolution?
- Book Reference: “The Scientist and Engineer’s Guide to DSP” by Steven W. Smith, Ch. 10

Questions to Guide Your Design

Visualization mapping
- Will you use grayscale or a color palette?
- How will you scale magnitudes to avoid washed-out images?
Windowing strategy
- What overlap percentage gives a smooth spectrogram?
- How will you handle partial windows at the end?

Thinking Exercise

Window Tradeoff

Consider a 1-second signal. Compare using a 256-sample window vs a 2048-sample window at 44.1kHz.

Questions while working:

Which window gives better frequency resolution?
Which window captures fast transients better?

The Interview Questions They’ll Ask

Prepare to answer these:

“What is a spectrogram and how is it computed?”
“Why does window size change time and frequency resolution?”
“How does overlap affect the spectrogram?”
“Why do we use logarithmic magnitude scales for audio?”
“What artifacts appear if you choose a poor window function?”

Hints in Layers

Hint 1: Starting Point Split the signal into overlapping windows and apply the FFT.

Hint 2: Next Level Convert magnitude values to a log scale before mapping to pixels.

Hint 3: Technical Details Use a consistent window function and overlap to stabilize the image.

Hint 4: Tools/Debugging Start with a simple tone that sweeps upward to validate your display.

Books That Will Help

Topic	Book	Chapter
Short-time Fourier transform	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith	Ch. 10
Window functions	“Understanding Digital Signal Processing” by Richard G. Lyons	Ch. 9
Spectrogram interpretation	“The Scientist and Engineer’s Guide to DSP” by Steven W. Smith	Ch. 10

Implementation Hints

Start with a simple grayscale image output to validate correctness.
Use a log magnitude scale so quiet details are visible.
Keep window parameters configurable for experimentation.

Learning Milestones

First milestone: You can create a spectrogram that shows clear bands.
Second milestone: You can explain time-frequency tradeoffs.
Final milestone: You can tune windowing to highlight different features.