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Digital signal processing
Filtering and demodulating with maths instead of components.
Filtering and demodulating with maths instead of components.
Digital signal processing (DSP) is doing the work of filters, mixers and demodulators with arithmetic on a stream of numbers instead of with coils, capacitors and crystals. An ADC turns the signal into samples, a processor does the maths, and a DAC (or the screen) turns the result back into something you can hear or see. See ADCs and DACs.
The simplest digital filter averages the last few samples. Random noise changes sign from sample to sample and tends to cancel, while a slow signal barely changes, so it survives. Averaging N samples cuts random noise by about 10 × log₁₀(N) dB.
A general FIR (finite impulse response) filter does the same with a different weight for each sample. Choosing the weights shapes the response: low-pass, band-pass, or the very steep "brick-wall" edges that make a 300 Hz CW filter or a narrow SSB passband possible. Doing that with real components would need many precisely matched parts. In DSP, changing a bandwidth is just loading new numbers, which is why a modern radio can offer adjustable filter widths and shifts at the press of a button.
The cost is delay: a symmetrical FIR filter (which has linear phase, so every frequency is delayed equally) of N taps delays the signal by (N − 1) ÷ 2 samples. A 255-tap filter at 48 kHz delays it 127 samples, which is 2.65 ms. An IIR filter feeds its output back, needing far fewer calculations for a given steepness, but it can behave less predictably.
The FFT (fast Fourier transform) turns a block of samples into a spectrum, one line per frequency "bin". Bin width is the sample rate divided by the number of points: at 48 kHz with 4096 points, about 11.7 Hz. Narrower bins need more samples, so they take longer to collect. This is the engine behind waterfalls, band scopes and decoders for modes like FT8. See Time domain, frequency domain and Fourier.
Once a signal is a stream of numbers, mixing it is multiplying and demodulating it is arithmetic. SDR receivers keep two copies of the signal 90° apart (I and Q); the maths then separates the upper sideband from the lower, cancels the unwanted one, and recovers AM, FM or SSB audio without any hardware change. Noise reduction, notch filters that automatically follow a whistle, and automatic gain control are all programs running on the sample stream.