What is an interpolation factor?

The interpolation factor L is the integer by which you upsample a signal — insert L−1 zeros between each input sample and then apply a lowpass anti-imaging filter. The output rate becomes Fin × L Hz.

What if the ratio Fout/Fin is not a whole number?

Most real-world rate pairs (e.g. 44100 → 48000) are rational, not integer. The tool reduces Fout/Fin to the irreducible fraction L/M. You upsample by L, apply the filter, then downsample by M (decimation).

What is the GCD reduction used for?

Dividing both rates by their GCD gives the smallest possible L and M, which minimizes the number of filter taps and multiply-accumulate operations in a polyphase realization.

What cutoff should the anti-imaging filter use?

The lowpass filter after upsampling should have a cutoff of min(Fin, Fout) / 2 normalized to the interpolated rate Fin × L. This simultaneously prevents imaging and acts as the anti-aliasing filter for the subsequent decimation.

Why does the tool show an intermediate rate?

In a rational L/M converter, the signal temporarily lives at Fin × L before decimation. Knowing this rate helps you size internal buffers and choose a practical FFT length for frequency-domain filtering.

Can I use non-integer sample rates?

Yes — the tool accepts decimal inputs (e.g. 22050.5 Hz). It converts them to integers by multiplying both rates by a power of 10 that clears the fractional part before computing the GCD.

Interpolation Rate Calculator

Enter DSP input and output sample rates to compute the integer interpolation factor L and reduced L/M ratio for sample rate conversion.

Sample Rate Inputs

Input Sample Rate (Fin)

Target Output Rate (Fout)

Common Conversions

Enter rates above and press Calculate.

Summary

This calculator determines the DSP upsampling (interpolation) factor L required to convert a digital signal between sample rates (not linear or interest rate interpolation). It computes the greatest common divisor (GCD) of the two rates, derives the reduced rational ratio, and reports whether exact integer interpolation is possible. For sample rate conversion involving both upsampling and downsampling, it also shows the combined L/M ratio.

How it works

Enter the input sample rate (Fin) in Hz — for example 44100 for CD audio.
Enter the desired output sample rate (Fout) in Hz — for example 48000.
The calculator finds GCD(Fin, Fout) and reduces the ratio Fout/Fin to lowest terms L/M.
L is the interpolation (upsampling) factor; M is the decimation (downsampling) factor.
The intermediate rate after upsampling equals Fin × L; the final rate after decimation equals Fin × L / M.
If L = 1, no upsampling is needed; if M = 1, no decimation is needed (pure interpolation).

Use cases

Determine L and M for a polyphase sample rate converter between two audio standards.
Plan the intermediate buffer size when upsampling before decimation in a DSP chain.
Verify that two sample rates share a common integer ratio before designing a filter bank.
Check whether a simple integer-L FIR upsample is sufficient or a rational L/M SRC is needed.
Calculate the anti-imaging filter cutoff relative to the interpolated rate.
Compare multiple target rates to find the one requiring the lowest L for hardware cost.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu