Unfortunately, the answer is not quite obvious, especially because some of the effects suffered from serveral implementation flaws in older versions (before sox 12.16). The resample effect had some trouble with calculating the correct cut-off frequency, which lead to aliasing when downsampling and excessive low pass filtering when upsampling. This problem has been removed in the version used here. The polyphase effect has been improved, too, which gives much better results than previous versions.
To address the signal-processing issues, I performed a series of experiments using Sox 12.17.3 and Matlab under Linux. The script of these experiments is available, should you wish to recreate them.
These experiments are intended to find the effects of these differing techniques on the spectrum of the signal processed, and what drawbacks (if any) exist.
Table of Contents:
Sample-rate conversion from a higher sampling rate to a lower sampling rate removes signal energy from Fnew / 2 to Forig / 2, thereby reducing the signal content, and creates a new signal at the new sampling rate.
To evaluate different sample-rate conversion techniques, the output of each is compared to this ideal. The key features for up-conversion are:
The signal source is originally at 8 kHz sampling rate, and written to a 16-bit, single channel .WAV file (PCM encoding). Sox is used to perform sample rate conversion to 44.1 kHz using each of the sample-rate conversion algorithms.
Each of the resulting up-sampled files is loaded into Matlab using a function that reads the binary format into memory, and then a 64k-point FFT is performed. The resulting spectrum is plotted in dB against the new sampling rate.
The upper limit of data at an 8 kHz sampling rate is 4 kHz, which is shown by the green line. Each method leaves some amount of signal energy above 4 kHz, which is improper as the original signal had no energy at these frequencies. On the other hand, the truncation error when reducing the sample values to 16-bit integers produces a noise floor which is about -40 dB. No method could ever become better than that, of course, if testing with wave files.
Looking at the stop band rejection the "resample" and the "polyphase" algorithm deliver a very low noise floor above 4 kHz, while linear interpolation produces a lot of noise above 4 kHz. Due to the conservative default settings the cut off starts at 3 kHz using "resample". The "polyphase" algorithm obviously was improved in the newer versions of sox and leaves more energy below 4 kHz. The "linear" algorithm is the worst, as it has decreased by 10 dB at 4 kHz and continues down to 20 dB at 12 kHz.
Each of these signals appears in more detail in the following figures.
This shape is very characteristic and can be mathematically derived, but we won't do so. The important things to note are that signal degradation starts almost immediately (the spectrum should be flat) and that a large "hump" of energy appears around 12 kHz, which will sound like a quiet high-pitched noise. As it is only 25 dB down from the maximum signal energy, this is significant.
Band-limited interpolation is implemented by the "resample" effect, which is also the default mechanism of Sox. It used to have some bugs, which seem to be removed: The result shows extremly low noise in the stop band (4 kHz - 22 kHz) and an acceptable low pass cut off starting at 3 kHz.
Polyphase filtering is implemented by the "polyphase" special effect. The original spectrum is flat up to 3.7 kHz, and then is more than 80 dB down by 4 kHz. There is essentially no aliased energy, it is more than 80 dB down above 4 kHz.
Results for all three tests appear in the figure below.
The data here is similar to that obtained from the random noise, but the presence of aliased signals is more apparant. The following subsections look at each mechanism in turn.
The signal is down 3dB at 2.5 kHz, and down 25 dB by 12 kHz, but strong signals every 500 Hz still appear in the band between 4 and 8 kHz.
Essentially no signal energy occurred in the stop band and the low pass behaviour is as expected from the white noise test.
The signal energy at 3.5 kHz is unchanged, only at 3.9 kHz a little energy is removed, and the noise floor above 4 kHz is very low.
The signal source is originally at 44.1 kHz, and written to a 16-bit, single channel .WAV file (PCM encoding). Sox is used to perform sample rate conversion to 8 kHz using each of the sample-rate conversion algorithms.
Each of the resulting up-sampled files is loaded into Matlab using a function that reads the binary format into memory, and then a 64k-point FFT is performed. The resulting spectrum is plotted in dB against the new sampling rate.
There is about 80 dB of rejection at 4 kHz which starts at 3 kHz.
Results for all three tests appear in the figure below.
Some aliasing is detectable, which will be addressed with each method below.
Peaks are observed at intervals of 125 Hz at varying amplitudes, which are aliased from the original signal. If the linear interpolator does a good job, these are much lower in energy; since it's not doing so well, these are high in energy. Result: a noisy output.
Almost no aliasing is evident. Residual peaks observed are more than 70 dB lower than the main signal energy.
For less critical quality demands, e.g. resampling between high sample rates (both actual and target sample rates are above say 32 kHz) or on a slow machine the time do the resampling might be interesting. On my machine (Athlon 800 MHz), downsampling 270 seconds of music at 44100 Hz sample rate to 32000 Hz took as little as 2 seconds with the linear interpolation, 26 seconds with bandlimited interpolation and 64 seconds with polyphase. So the impatient using slow machines (poor you ;-)) might consider bandlimited interpolation, as the difference in the results will be hardly audible.
If you don't care about sound quality or you have to clock your cpu by hand, use linear interpolation.
Written by K. Bradley on Septebmer 9, 1998.
This page relies mostly on the original page by Kevin Bradley, which was discontinued. I modified the parts concerning the improved resample and polyphase effects.
Andreas Wilde, 19. Dec. 2003