ResampAudio


Routine:

ResampAudio [options] AFileI AFileO

Purpose:

Resample data from an audio file

Description:

This program resamples data from an audio file. This process involves interpolating between the samples in the original file to create a new sequence of samples with a new spacing (sampling rate). This program allows for an arbitrary ratio of output sampling rate to input rate. The default settings give a high quality sample rate conversion.

Theory of Operation:

The process used for interpolation depends on the ratio of the output sampling rate to the input sampling rate.

1: The output/input sampling rate is a ratio of small integers.
The sample rate change process is done using a conventional interpolation filter designed for the interpolation factor (numerator of the sampling rate ratio) followed by subsampling by the subsampling factor (denominator of the sampling rate ratio).
2: General case.
An interpolating filter is designed using an interpolation factor of 24. For each output sample, the interpolating filter is used to create two samples that bracket the desired sampling point. Linear interpolation is used between these values to generate the output value.

The default interpolation filter is a linear phase FIR filter designed by applying a Kaiser window to an ideal lowpass filter response. The filter is characterized by a cutoff frequency, a window shape parameter, and the number of coefficients. The window shape parameter (alpha) controls the passband ripple and the stopband attenuation. For a fixed number of coefficients, decreasing ripple and increasing attenuation (larger alpha) come at the expense of a wider transition width.

The cutoff of the default interpolation filter depends on the input and output sampling rates. Let fsi be the sampling rate of the input signal and fso be the sampling rate of the output signal.

1: fso > fsi. The cutoff of the interpolation filter is set to fsi/2.
2: fso < fsi. The cutoff of the interpolation filter is set to fso/2.

The default design aims for an 80 dB stopband attenuation and a transition width which is 15% of the cutoff frequency. The attenuation directly determines alpha. The value of alpha together with the transition width determines the number of filter coefficients.

The parameters of the interpolating filter can also be set by the user. The design parameters are the interpolation factor, the filter cutoff frequency, the Kaiser window parameter, and the number of filter coefficients. The following table shows the effect of changing the Kaiser window parameter alpha.

   stopband   alpha  transition   passband
  attenuation         width D      ripple
     30 dB    2.210     1.536    +/- 0.270 dB
     40 dB    3.384     2.228    +/- 0.0864 dB
     50 dB    4.538     2.926    +/- 0.0274 dB
     60 dB    5.658     3.621    +/- 0.00868 dB
     70 dB    6.764     4.317    +/- 0.00275 dB
     80 dB    7.865     5.015    +/- 0.00089 dB  (default)
     90 dB    8.960     5.712    +/- 0.00027 dB
    100 dB   10.056     6.408    +/- 0.00009 dB

The filter transition width parameter is D = (N-1) dF, where N is the number of filter coefficients and dF is the normalized transition width of the filter.

Consider interpolating from 8 kHz to 44.1 kHz. The interpolation ratio is 441/80. For this example we will design the filter for an oversampling ratio of 10. This means that the filter will will be operating at a sampling rate of 80 kHz. (The default filter for this program would have used an oversampling ratio of 24.) The cutoff of the filter will be 4 kHz. The stopband attenuation is to be 80 dB. The attenuation requirement gives alpha=7.865. The parameter D corresponding to this value of alpha is 5.015. A transition width which is 15% of the cutoff corresponds to a width of 600 Hz. The normalized filter transition width of dF = 600/80000 = 0.0075. Solving for D = (N-1) dF for the number of coefficients N, gives N = 670. It is common to choose N to be of the form 2*Ir*M+1, where Ir is the filter interpolation factor (here 10). Such a time response has M sidelobes on either side of the reference point. In this example, we can choose M = 34, giving N = 681 coefficients.

If we designate the interpolation factor for the interpolation filter as Ir, about 1/Ir of the coefficients are used to calculate each output sample. The number of coefficients needed for a given value of alpha and given transition width is proportional to Ir. Increasing Ir improves the accuracy of the linear interpolation step and increases the total number of filter coefficients, but does not increase the computation effort time for the filtering operation.

For the transition width expressed as a percentage of the cutoff frequency, the number of coefficients needed to calculate each output sample is approximately 2D/P where P is the fractional bandwidth (e.g. 0.15 for a 15% transition width). The number of coefficients (rounded up) used to calculate each interpolated point is shown in the following table.

   stopband   alpha  transition  no. coeffs per output
  attenuation         width D    15% trans. 25% trans.
     30 dB    2.210     1.536       22         14
     40 dB    3.384     2.228       31         19
     50 dB    4.538     2.926       41         25
     60 dB    5.658     3.621       50         30
     70 dB    6.764     4.317       59         36
     80 dB    7.865     5.015       68         42 (default)
     90 dB    8.960     5.712       78         47
    100 dB   10.056     6.408       87         53

On a Windows PC (1 GHz processor), with the default filter (15% transition width), this program generates about 900,000 output samples per second for general interpolation and about twice that number for ordinary interpolation.

The accuracy of the sample rate operation depends on the frequency content of the input signal. Consider increasing the sampling rate for a speech file with a 8000 Hz sampling rate. The spectrum of the signal repeats every 8000 Hz. The default filter uses a cutoff frequency of 4000 Hz with a transition width of 600 Hz. The filter passband extends to 3700 Hz and the stopband starts at 4300 Hz. The interpolation will be imperfect in that (1) frequencies falling in the lower part of the transition band will be attenuated and (2) frequencies falling in the upper part of the transition band (the image frequencies due to the repetition of the frequency response) will be only be partially attenuated. If the input signal has little energy above 3700 Hz, then the error due to both effects will be small. Tests with speech files indicate that the signal-to-distortion ratios after interpolation (say from 8000 Hz to 8001 Hz) range from 46 to 77 dB. The poorest SDR occurs for signals that have significant energy above 3700 Hz. For a fixed stopband attenuation, the SDR can be improved by increasing the number of filter coefficients to affect a decrease in the transition band width. However, the number of coefficients should not be too large, since filters with a large time span can introduce pre-echo effects.

The interpolation filter can also be read in as a filter file. For such a filter, the filter interpolation factor must be specified.

The output sample positions are determined by the output sampling rate and a sample offset parameter. The sample offset determines the position of the first output sample relative to the input samples. The default is that the first output sample coincides with the first input sample. The number of samples in the output file can also be specified. The default is to make the time corresponding to the end of the output (rounded to the nearest sample) be the same as the time corresponding to the end of the input.

Options:

Input file name, AFileI:
The environment variable AUDIOPATH specifies a list of directories to be searched for the input audio file. Specifying "-" as the input file indicates that input is from standard input.
Output file name, AFileO:
The second file name is the output file. Specifying "-" as the output file name indicates that output is to be written to standard output. If the output file type is not explicitly given (-F option), the extension of the output file name is used to determine the file type.
  ".au"   - AU audio file
  ".wav"  - WAVE file
  ".aif"  - AIFF sound file
  ".afc"  - AIFF-C sound file
  ".raw"  - Headerless file (native byte order)
  ".txt"  - Text audio file (with header)
-s SFREQ, --srate=SFREQ
Sampling frequency for the output file. The sampling rate can be expressed as a single value or as a ratio of the form N/D, where each of N and D can be a floating point value.
-i SRATIO, --interpolate=SRATIO
Ratio of the output sampling rate to the input sampling rate. This argument is specified as a single number or as a ratio of the form N/D, where each of N and D can be a floating point value. This option is an alternate means to specify the output sampling rate.
-a OFFS, --alignment=OFFS
Time offset of the first output sample relative to the input data. The units are samples of the input data. This value can be specified as a single number or a ratio.
-f FPARMS, --filter_spec=FPARMS
Filter parameters. The filter parameters are given as keyword values. There are two cases: the filter coefficients are supplied in a file or the filter is calculated as a Kaiser windowed lowpass filter.
  Filter file:
    file="file_name"  Input filter file name.  If specified, the filter
                      coefficients are read from the named file.
    ratio=Ir          Filter interpolation factor
    delay=Del         Filter delay in units of filter samples (default
                      for symmetrical filters is (N-1)/2, where N is the
                      number of coefficients).  The delay can be
                      specified as a single number or as a ratio.  The
                      filter delay must be supplied for non-symmetrical
                      filters.
  Windowed lowpass:
   ratio=Ir           Filter interpolation factor.  The default depends
                      on the ratio of output sampling frequency to
                      input sampling frequency.  This parameter can be
                      specified as a single number or as a ratio.
   cutoff=Fc          Filter cutoff in normalized frequency relative to
                      the filter interpolation factor (0 to Ir/2).  This
                      value can be specified as a single number or as a
                      ratio.  The default cutoff frequency is determined
                      from the input and output sampling rates.  For an
                      increase in sampling rate, it is set to 0.5.  For
                      a decrease in sampling rate it is set to
                      0.5*fso/fsi.
   atten=A            Filter stopband attenuation in dB.  The attenuation
                      must be at least 21 dB.  The default is 80.  The
                      attenuation is an alternate way to specify the
                      Kaiser window parameter alpha.
   alpha=a            Kaiser window parameter.  Zero corresponds to a
                      rectangular window (stopband attenuation 21 dB).
                      The default is 7.865 corresponding to a stopband
                      attenuation of 80 dB.
   N=Ncof             Number of filter coefficients.  The default is
                      to choose the number of coefficients to give a
                      transition band which is 15% of the cutoff
                      frequency.
   span=Wspan         Window span.  This is the span of the non-zero part
                      of the window.  The default window span is equal
                      to the number of filter coefficients minus one.
   offset=Woffs       Window offset in units of filter samples.  This
                      is the offset of the first filter sample from
                      the beginning of the window.  The default is a
                      fractional value determined from the fractional
                      part of the input sample offset value.
   gain=g             Passband gain.  The default gain is equal to
                      the filter interpolation factor.  This choice
                      reproduces signals within the passband with the
                      correct amplitude.
   write="file_name"  Output filter file name.  If specified, the filter
                      coefficients are written to the named file.
-n NSAMPLE, --number_samples=NSAMPLE
Number of samples (per channel) for the output file.
-g GAIN, --gain=GAIN
A gain factor applied to the data from the input files. This gain applies to all channels in a file. The gain value can be given as a real number (e.g., "0.003") or as a ratio (e.g., "1/256"). This option may be given more than once. Each invocation applies to the input files that follow the option.
-F FTYPE, --file-type=FTYPE
output file type. If this option is not specified, the file type is determined by the output file name extension.
  "AU" or "au"             - AU audio file
  "WAVE" or "wave"         - WAVE file. Whether or not to use the WAVE
                             file extensible format is automatically
                             determined.
  "WAVE-EX" or "wave-ex"   - WAVE file. Use the WAVE file extensible
                             format.
  "WAVE-NOEX" or "wave-noex" - WAVE file; do not use the WAVE file
                             extensible format
  "AIFF-C" or "aiff-c"     - AIFF-C sound file
  "AIFF-C/sowt" or "aiff-c/sowt" - AIFF-C (byte-swapped data)
  "AIFF" or "aiff"         - AIFF sound file
  "noheader" or "noheader-native" - Headerless file (native byte order)
  "noheader-swap"          - Headerless file (byte swapped)
  "noheader-big-endian"    - Headerless file (big-endian byte order)
  "noheader-little-endian" - Headerless file (little-endian byte order)
  "text-audio"             - Text audio file (with header)
-h, --help
Print a list of options and exit.
-v, --version
Print the version number and exit.

See routine CopyAudio for a description of other parameters.

-t FTYPE, --type=FTYPE
Input file type and environment variable AF_FILETYPE
-P PARMS, --parameters=PARMS
Input file parameters and environment variable AF_INPUTPAR
-D DFORMAT, --data-format=DFORMAT
Details on allowed data formats for the output file
-I INFO, --info-INFO
Details on usage and default information records
-S SPEAKERS, --speakers=SPEAKERS
Loudspeaker configuration

Examples:

1: File copy. Copy audio file abc.au to new.au.
  ResampAudio -i 1 abc.au new.au
2: Delay the input signal. The output samples are delayed by 1/8 sample.
  ResampAudio -i 1 -a -1/8 abc.au new.au
3: Change the sampling rate to 8001 Hz.
  ResampAudio -s 8001 abc.au new.au
4: Change the sampling rate by an integral value (e.g. 8000 to 48000 Hz).
  ResampAudio -i 6 abc.au new.au

Environment variables:

AUDIOPATH:

This environment variable specifies a list of directories to be searched when opening the input audio files. Directories in the list are separated by colons (semicolons for Windows).

Author / version:

P. Kabal / v10r2 2018-11-16

See Also

CopyAudio, FiltAudio


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