DSP — How Your Radio Thinks Digitally - Digital Modes & SDR

DSP — How Your Radio Thinks Digitally

What is DSP and Why Should You Care?

Digital Signal Processing (DSP) has revolutionised amateur radio. Modern transceivers convert the RF signal to digital data, process it mathematically, then convert it back. This allows:

Adjustable filter bandwidth (change from 2.4 kHz SSB to 500 Hz CW at the press of a button)
Noise reduction that actually works
Notch filters that automatically find and remove interfering carriers
All modulation/demodulation done in software

Sampling — Turning Analogue into Digital

To process a signal digitally, you first need to convert it from continuous (analogue) to discrete samples (digital). The critical rule is the Nyquist theorem:

\( f_{sample} \geq 2 \times f_{max} \)

In plain English: You must sample at least twice as fast as the highest frequency in the signal. If your audio goes up to 3 kHz, you need at least 6,000 samples per second.

What happens if you don't? Aliasing! Higher frequencies "fold back" and appear as false lower frequencies in the digital signal. It sounds terrible. This is why every ADC has an anti-aliasing filter in front of it — a low-pass filter that removes any frequencies above half the sample rate.

Quantisation — How Many Bits?

Each sample is assigned a digital value. More bits = finer resolution = wider dynamic range:

\( \text{Dynamic range} \approx 6 \times n \text{ dB} \)

Where n = number of bits. So:

12-bit ADC → ~72 dB dynamic range
16-bit ADC → ~96 dB dynamic range (CD quality)
24-bit ADC → ~144 dB dynamic range (high-end audio/radio)

Shannon's Channel Capacity

How much data can you squeeze through a noisy channel? Claude Shannon gave us the answer:

\( C = B \log_2(1 + SNR) \)

C = maximum bits per second, B = bandwidth in Hz, SNR = signal-to-noise ratio (linear).

Why this matters for amateur radio: Modern digital modes like FT8 approach the Shannon limit by using clever coding and long integration times. FT8 can decode signals at −24 dB SNR — that's signals buried 250× below the noise! This is why FT8 can work when you can't even hear the signal by ear.