A radio works at baseband and transmits at carrier frequency, and something has to move the signal between them. Doing it digitally is now standard, which turns a mixer problem into a multirate filtering problem — and the filter chain, not the mixer, is where the logic and the power go.
Baseband is generated at a low sample rate because the information bandwidth is narrow. The converter runs far faster, because it has to represent the carrier. Digital up conversion bridges the two: interpolate the signal up to the converter rate, then mix it to the carrier with a numerically controlled oscillator.
Down conversion is the same sequence reversed. Mix the received signal down to baseband, then decimate to the rate the demodulator needs.
The mixing is arithmetically trivial; the rate change is not. Every interpolation stage creates images and every decimation stage risks aliasing, so each is paired with a filter. That chain — not the multiplier — is what consumes the logic and the power.
| Stage | What it does | Why it is placed there |
|---|---|---|
| CIC | Large rate change with no multipliers, using only integrators and combs | Cheapest way to move a big ratio, placed at the high-rate end where multipliers would be most expensive |
| CIC compensation | A short FIR correcting the CIC's droop across the passband | The CIC is cheap because it is a crude filter; this repairs its response |
| Half-band | Rate change of exactly two, with almost half the coefficients zero | Nearly free arithmetic, so cascading several beats one large filter |
| Shaping FIR | Final pulse shaping and out-of-band rejection | Placed at the low-rate end where each tap costs the least |
| NCO and mixer | Generates the carrier phase and translates the signal | Its spurious performance sets the noise floor; phase word width matters more than the multiplier |
The staging exists for one reason: multipliers cost far more at a high sample rate than at a low one, so the crude cheap filters go where the rate is highest and the precise expensive ones go where it is lowest.
Interpolating a baseband signal up to the converter's sample rate and mixing it to the carrier frequency using a numerically controlled oscillator. It replaces analog mixing stages with arithmetic, which makes the design a multirate filtering problem rather than an RF one.
Direction. DUC interpolates baseband up to the converter rate and mixes to carrier for transmit. DDC mixes the received signal down to baseband and decimates to the rate the demodulator needs. The filter structures are the same, reversed.
Because it changes rate by a large factor using only integrators and combs, with no multipliers at all. That makes it the cheapest option at the high-rate end of the chain. The cost is a droopy passband, which a short compensating FIR then corrects.
A filter that changes rate by exactly two, in which almost half the coefficients are zero. The zero taps cost nothing, so the arithmetic is close to half price — which is why three cascaded half-bands usually cost less than one filter performing the same total decimation.
Phase truncation. Reducing the accumulator width to save logic produces spurious tones whose frequencies depend on the tuning word, and those can land in band. A larger accumulator or added dither trades logic against spur level.
Because multiplication by a complex exponential is arithmetically trivial, while every rate change needs a filter to suppress images or aliases. In a multi-carrier radio that chain frequently dominates the digital front end's logic area and power.
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The filters themselves.
PRODUCTWhere DUC and DDC sit.
PRODUCTMany channels at once.
TECHNOLOGYThe chain around it.
KNOWLEDGEThe budget these stages spend.
KNOWLEDGEThe other half of the DFE.
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