I/Q Resampling

Resampling is achieved by a rational factor L/M, where L is the interpolation factor and M is the decimation factor. The process typically involves:

• Upsampling by L: Inserting L-1 zeros between original samples
• Anti-imaging filtering: Applying a low-pass filter to remove spectral images created by zero-insertion
• Downsampling by M: Keeping every M-th sample from the filtered output
• Anti-aliasing filtering: Ensuring the signal bandwidth does not exceed the new Nyquist frequency before decimation This cascaded operation allows conversion between arbitrary sample rates, such as adapting a 30.72 MHz LTE capture to a 20 MHz classifier input requirement.

Efficient resampling is implemented using polyphase decomposition, which restructures the interpolation/decimation filter into parallel sub-filters operating at the lower input rate. Key advantages include:

• Computational efficiency: Filtering occurs at the lower of the two sample rates, not the upsampled rate
• No wasted multiply-adds: Zero-valued inserted samples are never explicitly processed
• Parallel architecture: Naturally maps to FPGA and GPU hardware for real-time streaming
• Commutation structure: A rotating switch model distributes samples across filter phases This technique is essential for high-throughput IQ pipelines where resampling must occur at line rate without buffering bottlenecks.

When the conversion factor is not a simple rational ratio, a Farrow structure provides continuously variable delay and sample rate conversion using polynomial interpolation. The architecture consists of:

• Fixed FIR sub-filters: Computing polynomial coefficients from the input samples
• Fractional delay parameter μ: Controlling the exact interpolation point between samples
• Cubic or Lagrange interpolation: Typically 3rd or 5th order polynomials for sufficient accuracy
• Continuous adaptation: Enables symbol timing recovery loops and Doppler compensation This method is critical for software-defined radios where the ADC clock and the desired output rate are derived from independent, non-synchronized oscillators.

The primary design constraint in resampling is Nyquist compliance—ensuring no aliasing occurs during decimation. Critical specifications include:

• Passband ripple: Typically < 0.1 dB to preserve modulation fidelity
• Stopband attenuation: > 80 dB to suppress adjacent channel interference
• Transition bandwidth: The guard band between the signal of interest and the decimated Nyquist boundary
• Filter order: Determined by the sharpness of the transition band, often requiring hundreds of taps Improper filter design introduces spectral inversion or foldover artifacts that distort the IQ constellation and catastrophically degrade classifier accuracy.

Deep learning classifiers require fixed-size input tensors, making resampling a mandatory preprocessing step. The operation ensures:

• Fixed sample count per inference window: e.g., 1024 or 2048 IQ samples regardless of source bandwidth
• Consistent symbol rate representation: Normalizing the number of samples per symbol across different modulation types
• Bandwidth decimation: Reducing wideband captures to the specific sub-band containing the signal of interest
• Dataset homogenization: Enabling mixed-source training data to share identical dimensionalities Without resampling, a classifier trained on 20 MHz captures cannot process a 40 MHz or 15.36 MHz IQ stream without architectural modification.

Simple integer-factor decimation (M) is used to reduce the sample rate when the signal of interest occupies only a fraction of the captured bandwidth. Benefits include:

• Reduced inference latency: Fewer samples per classification window
• Lower memory footprint: Smaller input tensors require less GPU VRAM
• Power savings on edge devices: Directly proportional to the reduction in multiply-accumulate operations
• Simplified anti-alias design: Integer decimation allows efficient half-band and CIC filter structures The trade-off is the processing gain lost from the narrower noise bandwidth, which can be mitigated by ensuring the decimation filter's passband fully encompasses the target signal.