Decimation and Interpolation Factor Calculator
Find the resulting sampling rate and required filter cutoff when decimating or interpolating a signal by an integer factor.
🔀 What is Decimation and Interpolation?
Decimation and interpolation are the two basic operations for changing a digital signal's sampling rate by an integer factor. Decimation reduces the sampling rate by keeping only every Mth sample and discarding the rest. Interpolation increases the sampling rate by inserting new samples between the existing ones, typically starting with zero-value samples that are then smoothed by a filter.
Audio engineers use decimation and interpolation constantly when converting between sample rates, such as downsampling a 96 kHz studio recording to 44.1 kHz for CD release, or upsampling audio for a digital-to-analog converter that requires a higher rate. Software-defined radio engineers use decimation heavily to reduce a wideband ADC's very high sample rate down to a manageable rate for a narrow channel of interest. Multirate filter banks, used in image compression and wavelet transforms, build on the same decimation and interpolation building blocks.
A common misconception is that decimation is just "throwing away samples" with no other consideration needed. In practice, dropping samples without first removing high-frequency content above the new, lower Nyquist frequency causes aliasing, permanently corrupting the signal. Likewise, interpolation by zero-stuffing alone does not produce a genuinely higher-resolution signal; it creates spectral images that must be removed by a low-pass filter before the result is usable.
This calculator finds the resulting output sampling rate for either operation, along with the anti-alias filter cutoff required before decimating, or the anti-imaging filter cutoff required after interpolating.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Downsampling a Studio Recording
Decimate 48,000 Hz by a factor of 4
Example 2 — SDR Wideband-to-Narrowband Decimation
Decimate 192,000 Hz by a factor of 8
Example 3 — Upsampling for a DAC
Interpolate 44,100 Hz by a factor of 2
❓ Frequently Asked Questions
🔗 Related Calculators
What is decimation in digital signal processing?
Decimation reduces a signal's sampling rate by an integer factor M, keeping every Mth sample and discarding the rest. The output sampling rate is fs_out = fs_in / M, and an anti-alias low-pass filter must remove content above the new, lower Nyquist frequency (fs_out / 2) before the samples are dropped.
What is interpolation in digital signal processing?
Interpolation increases a signal's sampling rate by an integer factor L, typically by inserting L-1 zero samples between each original sample (zero-stuffing) and then applying a low-pass filter to smooth out the result. The output sampling rate is fs_out = fs_in x L.
Why does decimation need an anti-alias filter?
Dropping samples effectively lowers the sampling rate, which lowers the Nyquist frequency too. Any signal content that was previously valid but now exceeds the new, lower Nyquist frequency will fold back (alias) into the decimated output unless it is filtered out beforehand, corrupting the result permanently.
Why does interpolation need an anti-imaging filter after zero-stuffing?
Zero-stuffing raises the sample rate but does not add any real information between samples, and it creates unwanted spectral copies (images) of the original signal at multiples of the original sampling rate. A low-pass filter with cutoff at the original Nyquist frequency removes these images, leaving a smooth, correctly interpolated signal.
How do you convert between two sample rates that aren't an integer ratio, like 44.1 kHz to 48 kHz?
Express the ratio as a fraction in lowest terms (48000/44100 = 160/147), then interpolate by L=160, low-pass filter, and decimate by M=147. This rational (L/M) resampling chain is the standard way to convert between sample rates that don't divide evenly into each other.
What is the output sampling rate after decimating by 4?
Decimating by a factor of M=4 divides the sampling rate by 4: fs_out = fs_in / 4. For example, decimating a 48,000 Hz signal by 4 gives an output rate of 12,000 Hz, with a new Nyquist frequency of 6,000 Hz.
What is the output sampling rate after interpolating by 2?
Interpolating by a factor of L=2 multiplies the sampling rate by 2: fs_out = fs_in x 2. For example, interpolating a 44,100 Hz signal by 2 gives an output rate of 88,200 Hz, with the anti-imaging filter cutoff set at the original Nyquist frequency of 22,050 Hz.
Why use multi-stage decimation instead of one large decimation factor?
A single large decimation factor requires an anti-alias filter with a very narrow, computationally expensive transition band relative to the final low output rate. Splitting the same total decimation factor into several smaller cascaded stages usually needs far less total filter computation, since each stage's transition band is proportionally wider relative to its own, still-higher sampling rate.
Does decimation lose information?
Decimation itself only discards samples, but with the required anti-alias filter applied first, no information is lost that could not already be represented at the new, lower sampling rate. Without the anti-alias filter, decimation does lose information permanently, since aliased high-frequency content becomes indistinguishable from real low-frequency content.
Can decimation and interpolation factors be non-integer?
The individual decimation factor M and interpolation factor L are always positive integers by definition, since they describe discrete operations (keeping every Mth sample, inserting L-1 zeros). Any non-integer, or rational, overall rate change is achieved by combining an interpolation stage and a decimation stage together.