Routine

Purpose

Description

Theory of Operation

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

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

  ".au"   - AU audio file
  ".wav"  - WAVE file
  ".aif"  - AIFF sound file
  ".afc"  - AIFF-C sound file
  ".raw"  - Headerless file (native byte order)
  ".txt"  - Headerless file (text data)

  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.

  "AU" or "au"             - AU audio file
  "WAVE" or "wave"         - WAVE file
  "WAVE-NOEX" or "wave-noex" - WAVE file (no extensible data)
  "AIFF-C" "aiff-c"        - AIFF-C sound file
  "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)

  "mu-law8"   - 8-bit mu-law data
  "A-law8"    - 8-bit A-law data
  "unsigned8" - offset-binary 8-bit integer data
  "integer8"  - two's-complement 8-bit integer data
  "integer16" - two's-complement 16-bit integer data
  "integer24" - two's-complement 24-bit integer data
  "integer32" - two's-complement 32-bit integer data
  "float32"   - 32-bit floating-point data
  "float64"   - 64-bit floating-point data
  "text"      - text data

  mu-law, A-law, 8/16/24/32-bit integer, 32/64-bit float

  mu-law, A-law, offset-binary 8-bit integer, 16/24/32-bit integer,
  32/64-bit float

  mu-law, A-law, 8/16/24/32-bit integer, 32/64-bit float

  8/16/24/32-bit integer

  all data formats

  "FL"  - Front Left
  "FR"  - Front Right
  "FC"  - Front Center
  "LF"  - Low Frequency
  "BL"  - Back Left
  "BR"  - Back Right
  "FLC" - Front Left of Center
  "FRC" - Front Right of Center
  "BC"  - Back Center
  "SL"  - Side Left
  "SR"  - Side Right
  "TC"  - Top Center
  "TFL" - Top Front Left
  "TFC" - Top Front Center
  "TFR" - Top Front Right
  "TBL" - Top Back Lefty
  "TBC" - Top Back Center
  "TBR" - Top Back Right
  "-"   - none

By default, the output file contains a standard audio file information string.

  Standard Audio File Information:
     date: 2001-01-25 19:19:39 UTC    date
     program: ResampAudio             program name

  Record delimiter: Newline character or the two character escape
      sequence "\" + "n".
  Line delimiter: Within records, lines are delimiteded by a carriage
      control character, the two character escape sequence "\" + "r",
      or the two character sequence "\" + newline.

Examples

  ResampAudio -i 1 abc.au new.au

  ResampAudio -i 1 -a -1/8 abc.au new.au

  ResampAudio -s 8001 abc.au new.au

  ResampAudio -i 6 abc.au new.au

Environment variables

  "auto"       - determine the input file type from the file header
  "AU" or "au" - AU audio file
  "WAVE" or "wave" - WAVE file
  "AIFF" or "aiff" - AIFF or AIFF-C sound file
  "noheader"   - headerless (non-standard or no header) audio file
  "SPHERE"     - NIST SPHERE audio file
  "ESPS"       - ESPS sampled data feature file
  "IRCAM"      - IRCAM soundfile
  "SPPACK"     - SPPACK file
  "INRS"       - INRS-Telecom audio file
  "SPW"        - Comdisco SPW Signal file
  "CSL" or "NSP" - CSL NSP file
  "text"       - Text audio file

AF_NOHEADER:
This environment variable defines the data format for headerless or non-standard input audio files. The string consists of a list of parameters separated by commas. The form of the list is

  "Format, Start, Sfreq, Swapb, Nchan, ScaleF"

 "undefined" - Headerless files will be rejected
 "mu-law8"   - 8-bit mu-law data
 "A-law8"    - 8-bit A-law data
 "unsigned8" - offset-binary 8-bit integer data
 "integer8"  - two's-complement 8-bit integer data
 "integer16" - two's-complement 16-bit integer data
 "integer24" - two's-complement 24-bit integer data
 "integer32" - two's-complement 32-bit integer data
 "float32"   - 32-bit floating-point data
 "float64"   - 64-bit floating-point data
 "text"      - text data

 "native"        - no byte swapping
 "little-endian" - file data is in little-endian byte order
 "big-endian"    - file data is in big-endian byte order
 "swap"          - swap the data bytes as the data is read

 "default" - Scale factor chosen appropriate to the type of data. The
    scaling factors shown below are applied to the data in the file.
    8-bit mu-law:    1/32768
    8-bit A-law:     1/32768
    8-bit integer:   128/32768
    16-bit integer:  1/32768
    24-bit integer:  1/(256*32768)
    32-bit integer:  1/(65536*32768)
    float data:      1
 "<number or ratio>" - Specify the scale factor to be applied to
    the data from the file.

  "undefined, 0, 8000., native, 1, default"

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

See Also