DSP Basics - Part 1

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DSP Basics - Part 1

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Hey, what’s DSP anyway?

If you’re like me, the first time you hear Digital Signal Processing your brain probably goes:

“Uhh… that sounds like NASA-level math. Not for me.”

But hold on. DSP is actually just a fancy name for something pretty simple:
it’s about taking signals (things that change over time) and playing with them using math.

  • A song on Spotify? → It’s a signal of air pressure over time.
  • Your heartbeat on a smartwatch? → A signal of voltage in your body.
  • Even the temperature throughout the day? → Yep, also a signal.

So basically: if it changes over time and you can measure it → it’s a signal. DSP is how we make sense of it.

Why Digital?

Okay, so signals in real life are smooth and continuous. Like drawing a curve.
But computers don’t do curves. They only do dots.

Think of it like this:

  • A beautiful painting (continuous) → you take a photo of it (discrete).
  • Or, a smooth circle → made out of LEGO blocks.

That process of turning a smooth signal into dots is called sampling. And that’s step 1 in DSP.

The Big Ideas

Here are the core tools we’ll eventually use (don’t worry, we’ll go one by one):

  • Sampling → Take snapshots of the signal.
  • Frequency → How often something repeats (heartbeat vs. mosquito buzz).
  • Fourier Transform → The “X-ray vision” of signals; it shows the hidden ingredients (frequencies).
  • Filtering → Turn the bass up, kill the noise, boost the treble. Basically EQ for any signal.

Let’s Code a Baby Step 🐣

Enough theory, let’s actually see something.
We’ll make the simplest signal ever: a sine wave. This is the “hello world” of DSP.

import numpy as np
import matplotlib.pyplot as plt

# Imagine a clock ticking 1000 times per second
fs = 1000  # samples per second
t = np.linspace(0, 1, fs, endpoint=False)

# Let's create a 5 Hz sine wave (5 cycles per second)
f = 5
x = np.sin(2 * np.pi * f * t)

plt.plot(t, x)
plt.title("5 Hz Sine Wave")
plt.xlabel("Time [s]")
plt.ylabel("Amplitude")
plt.show()

Run this, and boom—you just made your first digital signal. It looks like a smooth wave because we sampled it fast enough. Pretty cool, right?

Cooking Analogy 🍳

Think of DSP like cooking (yes, really):

  • The signal is your raw ingredient.
  • The Fourier transform is the recipe: it tells you what’s inside.
  • Filtering is like choosing which spices to keep or throw away.
  • Sampling is chopping things into small, equal pieces.

Suddenly, DSP is not rocket science—it’s just kitchen science.

Where We’re Headed

This was just the “getting to know each other” part. In the next posts, I’ll walk through:

  • Mixing multiple sine waves (like making chords in music 🎵)
  • Seeing signals in frequency land (with FFT)
  • Building simple filters in Python
  • Cleaning up real-world noisy data

DSP is everywhere: music apps, medical devices, video streaming, even the camera on your phone. And trust me—once you see how it works, you’ll start recognizing DSP tricks everywhere in daily life.

So… ready to keep going? 🚀