Ahhh yes, welcome to the “why are we multiplying things?” club 😄 — this is actually the heart of how a radio works.
Short answer:
You multiply the incoming RF signal by a fixed signal source (a local oscillator) to shift it down in frequency so you can actually process it.
Now let’s unpack that properly.
📡 What’s Coming In
Your antenna is picking up an AM station sitting at something like:
1,000,000 Hz (1 MHz)
But the audio you care about (voice/music) is only:
~0–5 kHz
The audio is riding on that big 1 MHz carrier.
You can’t realistically filter audio directly at 1 MHz — that would require an insanely sharp, ultra-high-Q filter. Not fun.
🔄 What Multiplying Does (The Magic Bit)
When you multiply two signals together, something very useful happens:
If you multiply:
Incoming RF signal at f₁
×
Local oscillator at f₂
You get new signals at:
f₁ + f₂
f₁ - f₂
This is called mixing.
So if your station is at 1 MHz and your LO is also at 1 MHz:
1 MHz - 1 MHz = 0 Hz ← this is baseband (the audio!)
1 MHz + 1 MHz = 2 MHz ← unwanted, we’ll filter it out
Boom. You’ve just shifted the station down to baseband.
🎯 Why Not Just Filter First?
Because the signal is still sitting at RF.
Filtering works best when the thing you want is separated in frequency from the thing you don’t want.
If you tried to low-pass filter before mixing, you’d just kill everything — the audio isn’t sitting at low frequency yet. It’s riding around 1 MHz.
The mixer step moves the signal so filtering becomes easy.
🧠 In GNU Radio Terms
Your flowgraph usually looks like:
Source (RF)
→ Multiply (with Signal Source = LO)
→ Low Pass Filter
→ (Optional: AM envelope detection or just take real part)
→ Audio sink
The multiply block is your digital mixer.
Without it, you’re trying to extract audio from a signal still parked at RF.
🎵 But Wait — Isn’t AM Simple?
Good catch.
There is another way: envelope detection.
If the signal is already tuned and narrowband enough, you can just:
Bandpass filter
→ Complex to Mag
→ Low pass filter
That works too.
But in SDR land, mixing down to baseband is the standard superheterodyne / direct conversion approach. It gives you much more control and flexibility.
🛰 Big Picture
Multiplying is necessary because:
- Radios don’t directly process RF
- We shift RF down to baseband
- Filtering is much easier at low frequencies
- This is how essentially all modern SDRs work