fractionaldecimation

Fractional decimation is a signal processing operation that reduces the sampling rate of a discrete-time signal by a non-integer factor. In practice, non-integer rate changes are achieved as a rational resampling factor L/M, where L and M are integers. The common implementation sequence is to upsample by L, apply a low-pass filter to limit spectral images, and then downsample by M, yielding an output sampling rate of Fs_out = Fs_in × L / M. An equivalent approach uses a polyphase finite impulse response (FIR) filter to realize the same rational rate change in a single structured operation, often with greater efficiency. This technique is a core part of fractional (or rational) resampling in multirate digital signal processing.

Implementation aspects: Up-sampling introduces spectral replicas that must be suppressed by an anti-imaging filter prior to down-sampling. A well-designed polyphase resampler minimizes computations by distributing filtering across the polyphase components corresponding to the L and M factors. The resulting system can be viewed as a bank of filters that interpolates and then decimates, achieving the desired non-integer rate change.

Design considerations: Key factors include preserving the signal’s passband, suppressing aliasing and imaging, and managing computational load and latency. Filter design trade-offs affect phase response, group delay, and numerical precision, particularly in fixed-point implementations.

Applications: Fractional decimation is used in audio and communications systems for non-integer sample-rate conversion, software-defined radio, and sensor data processing where exact integer decimation is insufficient.

See also: resampling, fractional resampling, polyphase filter, multirate signal processing, upsampling, downsampling.