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Multiple vs. Non-Multiple Resampling Audio [Article]

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Audio Basis - educational articles

Resampling (upsampling, downsampling, oversampling) is sample rate altering of audio stream or file.

Standard sample rates audio are based on 44100 and 48000 Hz.

Somebody think that multiple resampling (integer sampling rate multiplication/division) have lesser distortions than non-multiple one.

Read below about difference between both resampling kinds.

Multiple vs. non-multiple resampling

 

How to work resampling

Resampling may be performed via audio sample rate converter software (Mac, Windows, Linux).

The altering may be real-time or offline.

As rule, used for adjusting sound files to optimal playback as DAC. Read more >

 

Upsampling, oversampling

Multiple upsampling is provided by adding "virtual" samples between original signal's ones.

Upsampling audio

Upsampling musical signal

These samples can be added via interpolator. Interpolator can be implemented as spline function, that can cause harmonic distortions.

Spline interpoplation like a steel-edge ruler that filxed in points of real point sample values.

 

But in the audio resampling zero-level samples are inserted as "virtual". However it distort musical signal. Appear aliases - spectrum periodically mirrored to range above Nyquist frequency (half of discretization frequency).

Oversampled musical record spectrum

Oversampling spectrum

To keep initial spectrum the aliases are eliminated by digital filter. Digital filtration cause ringing artifacts, some small oscillations of amplitude-frequency response. If minimal-phase filter is used, its phase-frequency response is non-linear.

Multiple upsampler audio

Multiple upsampler

 

Low frequency filter work at frequency [input sample rate] x [oversampling coefficient].

Low frequency filtering should cut all frequencies above half of minimal sample rate (input or output).

Example:

If input 44100 Hz and output 88200 Hz, filter cut frequency is 22050 Hz = 44100/2

Low frequency filtration work at 88200 Hz = 44100 x 2.

 

In general, non-multiple upsampling implemented via interpolator only.

But for frequencies 44.1 kHz and 48 kHz integer coefficients 160 and 147 are exists:

44100 Hz * 160 / 147 = 48000 Hz

44100 Hz * 320 / 147 = 96000 Hz

etc.

Non-multiple upsampling

Non-multiple upsampling

 

Example:

If input 44100 Hz and output 48000 Hz, filter cut frequency is 22050 Hz = 44100/2

Low frequency filtering work at 7056000 Hz = 44100 x 160.

 

Sometimes may be implementation difference between multiple and non-multiple resampling audio standard sample rates.
Because digital low frequency filters for both cases may be designed for different sample rates and have different features.

 

 

Downsampling

Multiple downsampling applied via decimation (removing samples between output samples).

Multiple downsampling

Multiple downsampling

 

Demands to filtering like oversampling.

Non-multiple downsampling may be implemented via interpolator.

But for sample rates based on 44.1 kHz and 48 kHz integer coefficients 160 and 147 may be applied:

48000 Hz * 147 / 160 = 44100 Hz

96000 Hz * 147 / 320 = 44100 Hz

etc.

Non-multiple downsampling

Non-multiple downsampling

 

Input signal is multiple oversampled and downsampled and filtered once.

 

 

Conclusion

For standard sample rates, based on 44.1 kHz and 48 kHz, multiple and non-multiple resampling audio performed same way.

But there are may be difference by digital filter implementation.

As rule, professional sample rate conversion software have the minimal difference.

 

So for proper sample rate converter software multiple or non-multiple resampling ratio is not matter.

 

 

References

Sample rate converter comparison

 

 


Read about sample rate issues

 

 


Read articles