Side-by-side comparison
| Parameter | Decimation | Interpolation in DSP |
|---|---|---|
| Operation | Reduce sample rate by factor M (downsample) | Increase sample rate by factor L (upsample) |
| Process | Lowpass filter → keep every M-th sample | Insert L−1 zeros between samples → lowpass filter |
| Filter Role | Anti-aliasing: remove energy above new Nyquist | Anti-imaging: remove spectral images above original Nyquist |
| Typical Factor | M = 2, 4, 8, 64 (PDM mic to PCM) | L = 2, 4 (CD 44.1 kHz → 176.4 kHz) |
| Effect on Spectrum | Spectrum compressed; images fold if not filtered | Spectrum stretched; images appear at multiples of original fs |
| Computational Load | Filter at high rate, then downsample — polyphase reduces ops | Upsample first, then filter — polyphase reduces ops |
| Nyquist Frequency After | fs_new/2 = fs_old/(2M) | fs_new/2 = L×fs_old/2 |
| Risk if Filter Omitted | Aliasing — high-freq content folds into baseband | Imaging — spectral copies appear in output |
| Common DSP ICs | ADAU1777 decimation filter, CIC decimators in sigma-delta ADCs | Interpolation filter in CS43L22 audio DAC |
| Cascade Structure | Multistage: decimate by 2 three times rather than once by 8 | Multistage: interpolate by 2 repeatedly for efficiency |
Key differences
Decimation by M keeps one sample out of every M, but without lowpass filtering first, any signal component above fs/(2M) folds back as aliasing — permanently corrupting the decimated signal. Interpolation by L inserts L−1 zeros and then filters to remove spectral images at multiples of the original fs; omitting the filter leaves images that sound like harmonic distortion. The key asymmetry: decimation's anti-aliasing filter operates at the original high sample rate (expensive), while interpolation's anti-imaging filter operates after upsampling (also at high rate). Polyphase decomposition reduces both to filtering at the lower rate, saving computation by a factor of M or L.
When to use Decimation
Use decimation when interfacing high-rate digital sensors (PDM microphones, sigma-delta ADCs outputting at 3 MHz) to low-rate digital processors. CIC (Cascaded Integrator-Comb) filters are the standard decimation structure in these paths.
When to use Interpolation in DSP
Use interpolation when a DAC requires a higher sample rate than the digital source provides, such as driving the CS43L22 at 176.4 kHz from a 44.1 kHz I²S stream, or in digital upconversion before RF transmission in SDR systems.
Recommendation
Understand both as a pair — real systems chain them. Choose decimation after oversampled ADCs and interpolation before DACs or RF upconverters. Always implement the anti-aliasing or anti-imaging lowpass filter; skipping it is the single most common error in multirate design.
Exam tip: Examiners ask you to draw the decimation block diagram showing the order of lowpass filter then down-sampler, and interpolation as up-sampler then lowpass filter — reversing the order is a common wrong answer.
Interview tip: Interviewers at audio IC companies and modem designers ask why multistage decimation (e.g., ÷2 three times) is more efficient than a single ÷8 stage — the answer is that the FIR filter in each stage operates at a progressively lower rate, reducing total multiply-accumulate operations.