Marc Lehmann > PDL-Audio > PDL::Audio

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NAME ^

PDL::Audio - Some PDL functions intended for audio processing.

SYNOPSIS ^

  use PDL;
  use PDL::Audio;

DESCRIPTION ^

Oh well ;) Not much "introductory documentation" has been written yet :(

Installing this distribution also installs pdlaudio-demo, which showcases some of the oeprators, and pdlaudio-birds, which imites some bird calls with PDL::Audio. You should study them to get the hang of it.

NOTATION

Brackets around parameters indicate that the respective parameter is optional and will be replaced with some default value when absent (or undef, which might be different in other packages).

The sampling frequency and duration are by default (see individual descriptions) given in cycles/sample (or samples in case of a duration). That means if you want to specify a duration of two seconds, you have to multiply by the sampling frequency in HZ, and if you want to specify a frequency of 440 Hz, you have to divide by the sampling frequency:

 # Syntax: gen_oscil duration*, frequency/
 $signal = gen_oscil 2*HZ, 440/HZ;
 # with a sampling frequency of 44100 Hertz:
 $signal = gen_oscil 2*44100, 440/44100;

 print describe_audio $signal, "\n";
 playaudio $signal->scale2short;

To help you, the required unit is given as a type suffix in the parameter name. A "/" means that you have to divide by the sampling frequency (to convert from Hertz) and a suffix of "*" indicates that a multiplication is required.

Most parameters named "size", "duration" (or marked with "*") can be replaced by a piddle, which is then used to give length and from (mono/stereo).

HEADER ATTRIBUTES

The following header attributes are stored and evaluated by most functions. PDL::Audio provides mutator methods for all them (e.g.

 print "samplerate is ", $pdl->rate;
 $pdl->comment("set the comment to this string");
rate

The sampling rate in hz.

filetype

The filetype (wav, au etc..). Must be one of:

  FILE_NEXT FILE_AIFC FILE_RIFF FILE_BICSF FILE_NIST FILE_INRS FILE_ESPS
  FILE_SVX FILE_VOC FILE_SNDT FILE_RAW FILE_SMP FILE_SD2 FILE_AVR
  FILE_IRCAM FILE_SD1 FILE_SPPACK FILE_MUS10 FILE_HCOM FILE_PSION
  FILE_MAUD FILE_IEEE FILE_DESKMATE FILE_DESKMATE_2500 FILE_MATLAB
  FILE_ADC FILE_SOUNDEDIT FILE_SOUNDEDIT_16 FILE_DVSM FILE_MIDI
  FILE_ESIGNAL FILE_SOUNDFONT FILE_GRAVIS FILE_COMDISCO FILE_GOLDWAVE
  FILE_SRFS FILE_MIDI_SAMPLE_DUMP FILE_DIAMONDWARE FILE_REALAUDIO
  FILE_ADF FILE_SBSTUDIOII FILE_DELUSION FILE_FARANDOLE FILE_SAMPLE_DUMP
  FILE_ULTRATRACKER FILE_YAMAHA_SY85 FILE_YAMAHA_TX16 FILE_DIGIPLAYER
  FILE_COVOX FILE_SPL FILE_AVI FILE_OMF FILE_QUICKTIME FILE_ASF
  FILE_YAMAHA_SY99 FILE_KURZWEIL_2000 FILE_AIFF FILE_AU
path

The filename (or file specification) used to load or save a file.

format

Specifies the type the underlying file format uses. The samples will always be in short or long signed format.

Must be one of

   FORMAT_NO_SND FORMAT_16_LINEAR FORMAT_8_MULAW FORMAT_8_LINEAR
   FORMAT_32_FLOAT FORMAT_32_LINEAR FORMAT_8_ALAW FORMAT_8_UNSIGNED
   FORMAT_24_LINEAR FORMAT_64_DOUBLE FORMAT_16_LINEAR_LITTLE_ENDIAN
   FORMAT_32_LINEAR_LITTLE_ENDIAN FORMAT_32_FLOAT_LITTLE_ENDIAN
   FORMAT_64_DOUBLE_LITTLE_ENDIAN FORMAT_16_UNSIGNED
   FORMAT_16_UNSIGNED_LITTLE_ENDIAN FORMAT_24_LINEAR_LITTLE_ENDIAN
   FORMAT_32_VAX_FLOAT FORMAT_12_LINEAR FORMAT_12_LINEAR_LITTLE_ENDIAN
   FORMAT_12_UNSIGNED FORMAT_12_UNSIGNED_LITTLE_ENDIAN COMPATIBLE_FORMAT

PDL::Audio conviniently defines the following aliases for the following constants, that are already correct for the host byteorder:

   FORMAT_ULAW_BYTE FORMAT_ALAW_BYTE FORMAT_LINEAR_BYTE
   FORMAT_LINEAR_SHORT FORMAT_LINEAR_USHORT FORMAT_LINEAR_LONG
   FORMAT_LINEAR_FLOAT FORMAT_LINEAR_DOUBLE
comment

The file comment (if any).

device

The device to output audio. One of:

   DEV_DEFAULT DEV_READ_WRITE DEV_ADAT_IN DEV_AES_IN DEV_LINE_OUT
   DEV_LINE_IN DEV_MICROPHONE DEV_SPEAKERS DEV_DIGITAL_IN DEV_DIGITAL_OUT
   DEV_DAC_OUT DEV_ADAT_OUT DEV_AES_OUT DEV_DAC_FILTER DEV_MIXER
   DEV_LINE1 DEV_LINE2 DEV_LINE3 DEV_AUX_INPUT DEV_CD_IN DEV_AUX_OUTPUT
   DEV_SPDIF_IN DEV_SPDIF_OUT

EXPORTED CONSTANTS

In addition to the exported constants described above (and later in the function descriptions), this module also exports the mathematical constants M_PI and M_2PI, so watch out for clashes!

sound_format_name format_code

Return the human-readable name of the file format with code format_code.

sound_type_name type_code

Return the human-readable name of the sample type with code type_code.

describe_audio piddle

Describe the audio stream contained in piddle and return it as a string. A fresh piddle might return:

 mono sound with 27411 samples

Whereas a freshly loaded soundfile might yield:

 stereo sound with 27411 samples, original name "kongas.wav", type 2 (RIFF),
 rate 11025/s (duration 2.49s), format 7 (8-bit unsigned)

raudio path, [option-hash], option => value, ...

Reads audio data into the piddle. Options can be anything, most useful values are filetype, rate, channels and format. The returned piddle is represents "time" in the outer dimension, and samples in the inner (i.e. scalars for mono files, 2-vectors for stereo files):

 [ [left0, right0], [left1, right1], [left2, right2], ...]

 # read any file
 $pdl = raudio "file.wav";
 # read a file. if it is a raw file preset values
 $pdl = raudio "file.raw", filetype => FILE_RAW, rate => 44100, channels => 2;

waudio pdl, [option-hash], option => value, ...

Writes a pdl as a file. See raudio for options and format. The path and other metadata is taken from the header, whcih cna be overwritten using options, e.g.:

 # write a file, using the header of another piddle
 $pdl->waudio ($orig_file->gethdr);
 # write pdl as .au file, take rate from the header
 $pdl->waudio (path => "piddle.au", filetype => FILE_AU, format => FORMAT_16_LINEAR;

cut_leading_silence pdl, level

Cuts the leading silence (i.e. all samples with absolute value < level) and returns the resulting part.

cut_trailing_silence pdl, level

Cuts the trailing silence.

cut_silence pdl, level

Calls cut_leading_silence and cut_trailing_silence and returns the result.

playaudio pdl, [option-hash], option => value ...

Play the piddle as an audio file. Options can be supplied either through the option hash (a hash-reference), through the pdl header or the options:

 # play a piddle that has a valid header (e.g. from raudio)
 $pdl->playaudio;
 # play it with a different samplerate
 $pdl->playaudio(rate => 22050);

gen_oscil duration*, freq/, phase-mod, [fm-mod/]

gen_sawtooth duration*, freq/, phase-mod, [fm-mod/]

gen_square duration*, freq/, phase-mod, duty, [fm-mod/]

gen_triangle duration*, freq/, phase-mod, [fm-mod/]

gen_pulse_train duration*, freq/, phase-mod, [fm-mod/]

gen_rand duration*, freq/

gen_rand_1f duration*

All of these functions generate appropriate waveforms with frequency freq (cycles/sample) and phase phase (0..1).

The duration might be either a piddle (which gives the form of the output) or the number of samples to generate.

The output samples are between -1 and +1 (i.e. "-1 <= s <= +1").

The duty parameter of the square generator influences the duty cycle of the signal. Zero means 50%-50%, 0.5 means 75% on, 25% off, -0.8 means 10% on, 90% off etc... Of course, the duty parameter might also be a vector of size duration.

gen_env duration*, xvals, yvals, [base]

Generates an interpolated envelope between the points given by xvals and yvals. When base == 1 (the default) then the values will be linearly interpolated, otherwise they follow an exponential curve that is bend inwards (base < 1) or outwards (base > 1).

 # generate a linear envelope with attack in the first 10%
 gen_env 5000, [0 1 2 9 10], [0 1 0.6 0.6 0];

gen_adsr duration*, sustain-level, attack-time, decay-time, sustain-time, release-time

Simple ADSR envelope generator. The sustain-level is the amplitude (0 to 1) of the sustain level. The other for parameters give the relative interval times, in any unit you like, only their relative ratios are important. Any of these times might be zero, in which case the corresponding part is omitted from the envelope.

gen_asymmetric_fm duration*, freq/, phase, [r , [ratio]]

gen_asymmetric_fm provides a way around the symmetric spectra normally produced by FM. See Palamin and Palamin, "A Method of Generating and Controlling Asymmetrical Spectra" JAES vol 36, no 9, Sept 88, p671-685.

gen_sum_of_cosines duration*, freq/, phase, ncosines, [fm_mod/]

Generates a sum of n cosines (1 + 2(cos(x) + cos(2x) + ... cos(nx)) = sin((n+.5)x) / sin(x/2)). Other arguments are similar to to gen_oscil.

gen_sine_summation duration*, freq/, phase, [nsines, [a, [b_ratio, [fm_mod/]]]]

gen_sine_summation provides a kind of additive synthesis. See J.A.Moorer, "Signal Processing Aspects of Computer Music" and "The Synthesis of Complex Audio Spectra by means of Discrete Summation Formulae" (Stan-M-5). The basic idea is very similar to that used in gen_sum_of_cosines generator.

The default value for nsines is 1 (but zero is a valid value), for a is 0.5 and for b_ratio is 1.

(btw, either my formula is broken or the output indeed does not lie between -1 and +1, but rather -5 .. +5).

gen_from_table duration*, frequency/, table, [phase], [fm_mod/]

gen_from_table generates a waveform by repeating a waveform given in table, linearly interpolating between successive points of the waveform.

partials2waveshape size*, partials, amplitudes, [phase], [fm_mod/]

Take a (perl or pdl) list of (integer) partials and a list of amplitudes and generate a single wave shape that results by adding these partial sines.

This could (and should) be used by the gen_from_table generator.

gen_from_partials duration*, frequency/, partials, amplitudes, [phase], [fm_mod/]

Take a (perl list or pdl) list of (possibly noninteger) partials and a list of amplitudes and generate the waveform resulting by summing up all these partial sines.

filter_ppolar pdl, radius/, frequency/

apply a two pole filter (given in polar form). The filter has two poles, one at (radius,frequency), the other at (radius,-frequency). Radius is between 0 and 1 (but less than 1), and frequency is between 0 and 0.5. This is the standard resonator form with poles specified by the polar coordinates of one pole.

filter_zpolar pdl, radius/, frequency/

apply a two zero filter (given in polar form). See filter_ppolar.

partials2polynomial partials, [kind]

partials2polynomial takes a list of harmonic amplitudes and returns a list of Chebychev polynomial coefficients. The argument kind determines which kind of Chebychev polynomial we are interested in, 1st kind or 2nd kind. (default is 1).

ring_modulate in1, in2

ring modulates in1 with in2 (this is just a multiply).

amplitude_modulate am_carrier, in1, in2

amplitude modulates am_carrier and in2 with in1 (this calculates in1 * (am_carrier + in2)).

filter_fir input, xcoeffs

Apply a fir (finite impulse response) filter to input. This is the same as calling:

 filter_sir input, xcoeffs, pdl()

filter_iir input, ycoeffs

Apply a iir (infinite impulse response) filter to input. This is just another way of saying:

 filter_sir input, pdl(1), ycoeffs

That is, the first member of ycoeffs is being ignored AND SHOULD BE SPECIFIED AS ONE FOR FUTURE COMPATIBILITY!

filter_comb input, delay*, scaler

Apply a comb filter to the piddle input. This is implemented using a delay line of length delay (which must be 1 or larger and can be non-integer) and a feedback scaler.

 y(n) = x(n-size-1) + scaler * y(n-size)

cf. filter_notch and http://www.harmony-central.com/Effects/Articles/Reverb/comb.html

filter_notch input, delay*, scaler

Apply a comb filter to the piddle input. This is implemented using a delay line of length delay (which must be 1 or larger and can be non-integer) and a feedforward scaler.

 y(n) = x(n-size-1) * scaler + y(n-size)

As a rule of thumb, the decay time of the feedback part is 7*delay/(1-scaler) samples, so to get a decay of Dur seconds, scaler <= 1-7*delay/(Dur*Srate). The peak gain is 1/(1-(abs scaler)). The peaks (or valleys in notch's case) are evenly spaced at srate/delay. The height (or depth) thereof is determined by scaler -- the closer to 1.0, the more pronounced. See Julius Smith's "An Introduction to Digital Filter Theory" in Strawn "Digital Audio Signal Processing", or Smith's "Music Applications of Digital Waveguides"

filter_allpass input, delay*, scaler-feedback, scaler-feedforward

filter_allpass or "moving average comb" is just like filter_comb but with an added feedforward term. If scaler-feedback == 0, we get a moving average comb filter. If both scaler terms == 0, we get a pure delay line.

 y(n) = feedforward*x(n-1) + x(n-size-1) + feedback*y(n-size)

cf. http://www.harmony-central.com/Effects/Articles/Reverb/allpass.html

design_remez_fir filter_size, bands(2,b), desired_gain(b), type, [weight(b)]

Calculates the optimal (in the Chebyshev/minimax sense) FIR filter impulse response given a set of band edges, the desired reponse on those bands, and the weight given to the error in those bands, using the Parks-McClellan exchange algorithm.

The first argument sets the filter size: design_remez_fir returns as many coefficients as specified by this parameter.

bands is a vector of band edge pairs (start - end), which specify the start and end of the bands in the filter specification. These must be non-overlapping and sorted in increasing order. Only values between 0 (0 Hz) and 0.5 (the Nyquist frequency) are allowed.

des specifies the desired gain in these bands.

weight can be used to give each band a different weight. If absent, a vector of ones is used.

type is any of the exported constants BANDPASS, DIFFERENTIATOR or HILBERT and can be used to select various design types (use BANDPASS until this is documented ;)

filter_src input, srate, [width], [sr-mod]

Generic sampling rate conversion, implemented by convoluting input with a sinc function of size width (default when unspecified or zero: 5).

srate determines the input rate / output rate ratio, i.e. values > 1 speed up, values < 1 slow down. Values < 0 are allowed and reverse the signal.

If sr_mod is omitted, the size of the output piddle is calculcated as length(input)/abs(srate), e.g. it provides the full stretched or shrinked input signal.

If sr_mod is specified it must be as large as the desired output, i.e. it's size determines the output size. Each value in sr_mod is added to srate at the given point in "time", so it can be used to "modulate" the sampling rate change.

 # create a sound effect in the style of "Forbidden Planet"
 $osc = 0.3 * gen_oscil $osc, 30 / $pdl->rate;
 $output = filter_src($input, 1, 0, $osc);

filter_contrast_enhance input, enhancement

Contrast-enhancement phase-modulates a sound file. It's like audio MSG. The actual algorithm is (applied to the normalised sound) sin(input*pi/2 + (enhancement*sin(input*2*pi))). The result is to brighten the sound, helping it cut through a huge mix.

filter_granulate input, expansion, [option-hash], option => value...

filter_granulate "granulates" the sound file file. It is the poor man's way to change the speed at which things happen in a recorded sound without changing the pitches. It works by slicing the input file into short pieces, then overlapping these slices to lengthen (or shorten) the result; this process is sometimes known as granular synthesis, and is similar to the "freeze" function. The duration of each slice is length -- the longer, the more like reverb the effect. The portion of the length (on a scale from 0 to 1.0) spent on each ramp (up or down) is ramp. This can control the smoothness of the result of the overlaps. The more-or-less average time between successive segments is hop. The accuracy at which we handle this hopping is set by the float jitter -- if jitter is very small, you may get an annoying tremolo. The overall amplitude scaler on each segment is scaler -- this is used to try to to avoid overflows as we add all these zillions of segments together. expansion determines the input hop in relation to the output hop; an expansion-amount of 2.0 should more or less double the length of the original, whereas an expansion-amount of 1.0 should return something close to the original speed.

The defaults for the arguments/options are:

 expansion      1.0
 length(*)      0.15
 scaler         0.6
 hop(*)         0.05
 ramp           0.4
 jitter(*)      0.5
 maxsize        infinity

The parameters/options marked with (*) actually depend on the sampling rate, and are always multiplied by the rate attribute of the piddle internally. If the piddle lacks that attribute, 44100 is assumed. NOTE: This is different to most other filters, but should be ok since filter_granulate only makes sense for audiofiles.

audiomix pos1, data1, pos2, data2, ...

Generate a mix of all given piddles. The resulting piddle will contain the sum of all data-piddles at their respective positions, so some scaling will be necessary before or after the mixing operation (e.g. scale2short).

 # mix the sound gong1 at position 0, the sound bass5 at position 22100
 # and gong2 at position 44100. The resulting piddle will be large enough
 # to accomodate all the sounds:
 $mix = audiomix 0, $gong1, 44100, $gong2, 22100,  $gong2

filter_center piddle

Normalize the piddle so that it is centered around y = 0 and has maximal amplitude of 1.

scale2short piddle

This method takes a sound in any format (preferably float or double) and scales it to fit into a signed short value, suitable for playback using playudio or similar functions.

gen_fft_window size*, type, [$beta]

Creates and returns a specific fft window. The type is any of the following. These are (case-insensitive) strings, so you might need to quote them.

 RECTANGULAR    just ones (the identity window)
 HANNING        0.50 - 0.50 * cos (0 .. 2pi)
 HAMMING        0.54 - 0.46 * cos (0 .. 2pi)
 WELCH          1 - (-1 .. 1) ** 2
 PARZEN         the triangle window
 BARTLETT       the symmetric triangle window
 BLACKMAN2      blackman-harris window of order 2
 BLACKMAN3      blackman-harris window of order 3
 BLACKMAN4      blackman-harris window of order 4
 EXPONENTIAL    the exponential window
 KAISER         the kaiser/bessel window (using the parameter C<beta>)
 CAUCHY         the cauchy window (using the parameter <beta>)
 POISSON        the poisson window (exponential using parameter C<beta>)
 RIEMANN        the riemann window (sinc)
 GAUSSIAN       the gaussian window of order C<beta>)
 TUKEY          the tukey window (C<beta> specifies how much of the window
                consists of ones).
 COSCOS         the cosine-squared window (a partition of unity)
 SINC           same as RIEMANN
 HANN           same as HANNING (his name was Hann, not Hanning)

 LIST           this "type" is special in that it returns a list of all types

cplx(2,n) = rfft real(n)

Do a (complex fft) of real (extended to complex so that the imaginary part is zero), and return the complex fft result. This function tries to use PDL::FFTW (which is faster for large vectors) when available, and falls back to PDL::FFT, which is likely to return different phase signs (due to different kernel functions), so beware! In fact, since rfft has to shuffle the data when using PDL::FFT, the fallback is always slower.

When using PDL::FFTW, a wisdom file ~/.pdl_wisdom is used and updated, if possible.

real(n) = irfft cplx(2,n)

The inverse transformation (see rfft). irfft rfft $pdl == $pdl always holds.

spectrum data, [norm], [window], [beta]

Returns the spectrum of a given pdl. If norm is absent (or undef), it returns the magnitude of the fft of data. When norm == 1 (or eq 'NORM', case-insensitive), it returns the magnitude, normalized to be between zero and one. If norm == 0 (or eq 'dB', case-insensitive), then it returns the magnitude in dB.

data is multiplied with window (if not undef) before calculating the fft, and usually contains a window created with gen_fft_window (using beta). If window is a string, it is handed over to gen_fft_window (together with the beta parameter) to create a window of suitable size.

This function could be slightly faster.

concat pdl, pdl...

This is not really an audio-related function. It simply takes all piddles and concats them into a larger one. At the moment it only supports single-dimensional piddles and is implemented quite slowly using perl and data-copying, but that might change...

Shift vector elements without wrap and fill the free space with a constant. Flows data back & forth, for values that overlap.

Positive values shift right, negative values shift left.

EOD Pars => 'x(n); int shift(); c(); [oca]y(n)', DefaultFlow => 1, Reversible => 1, PMCode => ' sub PDL::rshift { my @a = @_; if($#a == 3) { &PDL::_rshift_int(@a);@a=(); } elsif($#a == 1 || $#a == 2) { $a[3] = PDL->nullcreate($a[0]); &PDL::_rshift_int(@a); $a[3]; } else { barf "Invalid number of arguments for shiftin"; } } ', Code=>' int i,j; int n_size = $SIZE(n); for(i = -$shift(), j=0; j < n_size; i++, j++) $y(n=>j) = i >= 0 && i < n_size ? $x(n=>i) : $c(); ', BackCode=>' int i,j; int n_size = $SIZE(n); for(i = -$shift(), j=0; j < n_size; i++, j++) if (i >= 0 && i < n_size) $x(n=>i) = $y(n=>j); ' ;

pp_def 'polynomial', Pars => 'coeffs(n); x(m); [o]out(m)', Doc => 'evaluate the polynomial with coefficients coeffs at the position(s) x. coeffs[0] is the constant term.', Code => q! loop(m) %{ $GENERIC() x = 1; $GENERIC() o = 0;

             loop(n) %{
                o += $coeffs() * x;
                x *= $x();
             %}

             $out() = o;
          %}
       !
;

pp_def 'linear_interpolate', Pars => 'x(); fx(n); fy(n); [o]y()', GenericTypes => [L,F,D], Doc => ' Look up the ordinate x in the function given by fx and fy and return a linearly interpolated value (somewhat optimized for many lookups).

fx specifies the ordinates (x-coordinates) of the function and most be sorted in increasing order. fy are the y-coordinates of the function in these points. ', Code => q! int d = 0; int D = $SIZE(n) - 1; /* a tribute to PP's stupidity */ $GENERIC() xmin =$fx(n=>0); $GENERIC() xmax =$fx(n=>D);

          threadloop %{
             $GENERIC() x = $x();
             $GENERIC() x1, x2, y1, y2;

             if (x <= xmin)
               $y() = $fy(n=>0);
             else if (x >= xmax)
               $y() = $fy(n=>D);
             else
               {
                 while ($fx(n=>d) >  x) d--;
                 while ($fx(n=>d) <= x) d++;
                 /* 0       < d <= D     */
                 /* fx(d-1) < x <= fx(d) */
                 x2 = $fx(n=>d);
                 y2 = $fy(n=>d);
                 d--;
                 x1 = $fx(n=>d);
                 y1 = $fy(n=>d);
                 $y() = y1 + (x-x1)*(y2-y1)/(x2-x1);
               }
          %}
       !
;

pp_def 'bessi0', Pars => 'a(); [o]b()', Doc => 'calculate the (approximate) modified bessel function of the first kind', GenericTypes => [F,D], Code => q! $GENERIC() x = $a(); if (x > -3.75 && x < 3.75) { $GENERIC() y = (x / 3.75); y *= y; $b() = 1 + (y * (3.5156229 + (y * (3.0899424 + (y * (1.2067492 + (y * (0.2659732 + (y * (0.360768e-1 + (y * 0.45813e-2))))))))))); } else { $GENERIC() ax = x < 0 ? -x : x; $GENERIC() y = ax / 3.75; $b() = ((exp(ax) / sqrt(ax)) * (0.39894228 + (y * (0.1328592e-1 + (y * (0.225319e-2 + (y * (-0.157565e-2 + (y * (0.916281e-2 + (y * (-0.2057706e-1 + (y * (0.2635537e-1 + (y * (-0.1647633e-1 + (y * 0.392377e-2))))))))))))))))); } !, ;

pp_def 'fast_sin', Pars => 'r(n); [o]s(n)', GenericTypes => [F,D], Doc => 'fast sine function (inaccurate table lookup with ~12 bits precision)', Code => q^ # define SINE_SIZE 16384 static float *sine_table = 0;

         if (!sine_table)
           {
             int i;
             Float phase, incr;
             sine_table = (float *) calloc (SINE_SIZE + 1, sizeof (float));
             incr = M_2PI / (Float) SINE_SIZE;
             for (i = 0, phase = 0.0; i < SINE_SIZE + 1; i++, phase += incr)
               sine_table[i] = (float) sin (phase);
           }

         threadloop %{
           loop(n) %{
             $s() = sine_table[((int)($r() * (SINE_SIZE / M_2PI)) % SINE_SIZE + SINE_SIZE) % SINE_SIZE];
           %}
         %}^
;

pp_addpm {At => Bot}, <<'EOD';

AUTHOR ^

Marc Lehmann <schmorp@schmorp.de>. The ideas were mostly taken from common lisp music (CLM), by Bill Schottstaedt bil@ccrma.stanford.edu. I also borrowed many explanations (and references) from the clm docs and some code from clm.c. Highly inspiring!

SEE ALSO ^

perl(1), PDL.

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