Also known as: digital filter
A digital filter passes some frequencies and attenuates others by performing arithmetic on a stream of samples — no physical components, just multiply-and-add.1 The two main families are FIR (finite impulse response) and IIR (infinite impulse response), and both are defined entirely by a small table of coefficients.
How it works
A filter computes each output sample as a weighted sum of input samples — a convolution of the signal with the filter’s impulse response. An FIR filter weights a finite window of past inputs (its “taps”); more taps give a sharper transition between passband and stopband but cost more arithmetic per sample. An IIR filter also feeds back past outputs, so a short recursion can mimic a very long impulse response — cheap and steep, at the price of possible instability and non-linear phase. The coefficient table is the filter: change the numbers and the same code becomes a low-pass, a band-pass, or a pulse shaper.
The frequency response and the impulse response are a Fourier-transform pair, so filter design is the art of choosing an impulse response whose transform has the passband and stopband you want. A window function is often applied to trade transition sharpness against stopband ripple.
Variants
- FIR — always stable, can be made exactly linear-phase (no group-delay distortion, vital for digital modulation); the default in SDR channelisers. Includes the root-raised-cosine and matched filters used for pulse shaping.
- IIR — Butterworth, Chebyshev, elliptic responses; steep for few coefficients, used for audio and control loops where phase linearity matters less.
- CIC — a multiplierless integrator-comb structure for large decimation factors in hardware.
- Adaptive filters — coefficients that update themselves, as in equalisers that cancel multipath.
In practice
By response shape, a low-pass keeps frequencies below a cutoff, a band-pass keeps a chosen range, and a notch removes a narrow interferer. In an SDR the workhorse is the narrow channel filter that isolates one signal from a wide capture, almost always paired with decimation so the two run as a single efficient stage (a polyphase decimating FIR). Filters also appear as the pulse-shaping and matched filters that maximise signal-to-noise at the symbol decision, and as the loop filters inside timing and carrier recovery.
Relevance to SDR
Filtering is fundamental to channelising the IQ stream and to pulse shaping. GopherTrunk uses low-pass FIR filters inside its down-converters to isolate each control and voice channel, and matched/root-raised-cosine filtering in the demodulator to recover symbols cleanly.
Sources
-
Digital filter — Wikipedia, on FIR/IIR families and frequency response. ↩