[Leejohnston]

Thread 9 — Digital Signal Processing (DSP) 
How Electronics Interpret Sound, Light, Motion & Data 

Digital Signal Processing (DSP) is the science of converting real-world signals 
— audio, images, vibration, radio waves, sensor data — 
into digital form so computers and microcontrollers can analyze them.

DSP powers:
• microphones and speakers 
• phone cameras 
• medical scanners 
• seismographs 
• satellite communication 
• robotics and self-driving systems 
• image stabilization 
• noise suppression 

This thread builds a strong foundation for understanding how DSP works.

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1. What Is a Signal?

A signal is any quantity that varies over time — 
voltage, sound pressure, vibration, light intensity, etc.

Analog signal examples:
• voice picked up by a microphone 
• ECG heartbeat waveform 
• accelerometer vibration 
• light captured by a camera sensor 

DSP converts these analog waveforms into numbers 
so computers can process them.

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2. Sampling — Turning Signals Into Numbers

A microcontroller or ADC takes “samples” of a signal at regular intervals.

Sampling frequency (Fs): 
how many samples per second are recorded.

Examples:
• CD audio: 44,100 Hz 
• Phone microphones: ~8,000–48,000 Hz 
• Seismometers: 100–500 Hz 
• Camera video: 30–240 samples (frames) per second 

Nyquist Rule: 
To capture a frequency f, you must sample at least 2f.

So to capture 10 kHz audio → sample ≥ 20 kHz.

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3. Quantisation — Turning Each Sample Into a Number

Each analog sample is mapped to a digital value.

Bit depth determines accuracy: 
• 8-bit → 256 levels 
• 12-bit → 4096 levels 
• 16-bit → 65,536 levels 
• 24-bit → 16.7 million levels 

Higher bit depth = more detail & less noise.

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4. Filters — Removing Unwanted Parts of a Signal

Filters reshape signals.

Low-pass filter (LPF): 
lets low frequencies through (remove hiss, jitter).

High-pass filter (HPF): 
lets high frequencies through (remove hum, DC offset).

Band-pass filter: 
keeps only a selected range.

Band-stop / notch filter: 
removes a specific frequency (e.g., 50/60 Hz mains hum).

Filters exist in:
• analog circuits 
• digital algorithms (DSP) 

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5. Fourier Transform — The Heart of DSP

The Fourier Transform converts a time-domain signal 
into its frequency components.

Instead of seeing the waveform itself, 
we see *which frequencies* are present.

Example: A guitar chord 
→ time-domain: complex waveform 
→ frequency-domain: peaks at musical notes

Digital version used in DSP:
Fast Fourier Transform (FFT)

Applications:
• audio analysis 
• vibration monitoring 
• RF communication 
• astronomy (spectral analysis) 
• image compression 

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6. Convolution — How Filters Work Internally

Convolution slides a filter “kernel” across the signal.

Used for:
• blurring or sharpening images 
• edge detection 
• smoothing sensor data 
• motion tracking 
• machine learning 

Convolution is at the heart of:
CNNs (Convolutional Neural Networks)

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7. DSP in Microcontrollers

Modern MCUs (ARM Cortex-M series, ESP32) include DSP instructions.

Microcontrollers can perform:
• FFTs 
• filtering 
• decimation 
• interpolation 
• noise reduction 

Common sensor applications:
• accelerometers (vibration analysis) 
• gyroscopes (orientation) 
• microphones (audio processing) 
• motor control (current wave shaping) 

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8. Example: Real-Time Low-Pass Filter in Code

Simple digital smoothing filter:

Code:

float smooth(float prev, float input, float alpha) {
  return alpha * input + (1 - alpha) * prev;
}

Where:
• alpha = smoothing factor (0.0 to 1.0) 
• smaller alpha = more smoothing 
• larger alpha = more responsiveness 

Used for:
• stabilizing sensor readings 
• removing noise 
• making robotics more reliable 

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9. Example: Detecting Frequency with FFT

Pseudo-code:

Code:

// collect samples into array
for (int i = 0; i < N; i++) {
    samples[i] = analogRead(micPin);
}

// run FFT
runFFT(samples);

// find the strongest frequency peak
float peak = findDominantFrequency();

This is how apps detect pitch — and how machines detect vibration problems.

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10. What You Can Build With DSP

Here are real project ideas users can build:

• digital oscilloscope 
• vibration analyzer 
• spectrum analyser 
• audio visualizer 
• noise gate for microphones 
• step detection (accelerometer DSP) 
• seismic monitor 
• motor vibration health monitor 
• heart-rate detection from IR sensor 
• remote sensing & signal decoding 

DSP unlocks the real world.

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11. Recommended Next Threads

• Thread 10 — Build a Simple DSP-Based Spectrum Analyzer 
• Thread 11 — Real-Time Sensor Fusion (Kalman Filters) 
• Thread 12 — Introduction to Control Theory 

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End of Thread — Digital Signal Processing (DSP)