1
SRT Matlab Audio Toolkit Manual
Spring Term 2009
2
User Notes....................................................................................................................... 4
Simple Oscillators ........................................................................................................... 4
cosine .......................................................................................................................... 4
sawtooth ...................................................................................................................... 4
sine .............................................................................................................................. 5
spike ............................................................................................................................ 5
square .......................................................................................................................... 5
synthesize .................................................................................................................... 6
unit .............................................................................................................................. 6
Other Sound Generators.................................................................................................. 6
fm_instr ....................................................................................................................... 6
lpnoise ......................................................................................................................... 7
mygrain ....................................................................................................................... 7
mygrainu ..................................................................................................................... 7
noisefilter .................................................................................................................... 7
pluck............................................................................................................................ 8
plucklp ........................................................................................................................ 8
vowel ........................................................................................................................... 8
Synthesizer Units ............................................................................................................ 8
vca ............................................................................................................................... 8
vcf ............................................................................................................................... 9
vco ............................................................................................................................... 9
Filters .............................................................................................................................. 9
flt ................................................................................................................................. 9
lpflt ............................................................................................................................ 10
shelving ..................................................................................................................... 10
Vibrato and Tremolo ..................................................................................................... 10
tremolo ...................................................................................................................... 10
vibrato ....................................................................................................................... 11
vibrato2 ..................................................................................................................... 11
vibratox ..................................................................................................................... 11
Envelope Shapers .......................................................................................................... 12
a_r (Matlab Student Edition) .................................................................................... 12
ar ............................................................................................................................... 12
env ............................................................................................................................. 12
FadeIn ....................................................................................................................... 12
FadeOut ..................................................................................................................... 13
Delay Lines ................................................................................................................... 13
allpdelay .................................................................................................................... 13
delay .......................................................................................................................... 13
firdelay ...................................................................................................................... 14
iirdelay ...................................................................................................................... 14
lpiirdelay ................................................................................................................... 14
unidelay ..................................................................................................................... 15
3
Pitch- and Time-Shifting Functions .............................................................................. 15
deci ............................................................................................................................ 15
lint ............................................................................................................................. 15
pitch_shift ................................................................................................................. 16
resample .................................................................................................................... 16
time_stretch ............................................................................................................... 16
Miscellaneous Digital FX ............................................................................................. 17
auto_wah ................................................................................................................... 17
denoise ...................................................................................................................... 17
flanger ....................................................................................................................... 17
fuzzexp ...................................................................................................................... 18
inflimit ...................................................................................................................... 18
leslie .......................................................................................................................... 18
limiter ........................................................................................................................ 19
mutate........................................................................................................................ 19
noisegt ....................................................................................................................... 19
phaser ........................................................................................................................ 20
robotize ..................................................................................................................... 20
spreader ..................................................................................................................... 20
symclip ...................................................................................................................... 21
wah ............................................................................................................................ 21
wah_wah ................................................................................................................... 21
whisperize ................................................................................................................. 22
Stereo ............................................................................................................................ 22
destereo ..................................................................................................................... 22
stereo ......................................................................................................................... 22
General Vector Operations ........................................................................................... 23
fastconv ..................................................................................................................... 23
grand ......................................................................................................................... 23
mask .......................................................................................................................... 23
midi2freq ................................................................................................................... 23
mix ............................................................................................................................ 24
mvgrms ..................................................................................................................... 24
mul ............................................................................................................................ 24
reverse ....................................................................................................................... 25
trim ............................................................................................................................ 25
Data Analysis ................................................................................................................ 25
analyze ...................................................................................................................... 25
rifft ............................................................................................................................ 26
4
User Notes
1. Except as noted, Toolkit functions accept either row- or column-vector
arguments.
2. Except as noted, Toolkit functions return row-vector results.
3. Toolkit functions have been successfully tested with audio-friendly input
arguments, but they do little or no checking of argument values.
4. A few Toolkit functions are available under more than one name in order to avoid
conflicts with functions already defined in the Matlab Student Edition. The
correct function name to use in each of these special cases is noted in the
documentation below.
Simple Oscillators
cosine
y = cosine( freq , dur , sr )
Generates samples of a sine tone of specified frequency and duration.
Inputs:
freq = frequency in Hz.
dur = duration in seconds
sr
= sample rate in samples per second
Output
y
= vector of sine tone samples
sawtooth
y = sawtooth( freq , dur , sr )
Generates samples of a sawtooth tone of specified frequency and
duration.
Inputs:
freq = frequency in Hz.
dur = duration in seconds
sr
= sample rate in samples per second
Output:
y
= vector of sawtooth tone samples
5
sine
y = sine( freq , dur , sr )
Generates samples of a sine tone of specified frequency and duration.
Inputs:
freq = frequency in Hz.
dur = duration in seconds
sr
= sample rate in samples per second
Output:
y
= vector of sine tone samples
spike
y = spike( freq , dur , sr )
Generates a stream of unit impulses.
Inputs:
freq = frequency in Hz.
dur = duration in seconds
sr
= sampling frequency in Hz.
Output:
y = impulse stream
square
y = square( freq , dur , sr )
Generates samples of a square wave tone of specified frequency and
duration.
Inputs:
freq = frequency in Hz.
dur = duration in seconds
sr
= sample rate in samples per second
Output:
y
= vector of square wave tone samples
6
synthesize
y = synthesize( freq , dur , amp , sr )
Performs additive synthesis of a tone with an arbitrary number of
harmonics.
Inputs:
freq =
dur =
amp =
sr
=
fundamental frequency in Hz.
duration of the tone in seconds
vector of amplitudes of the harmonics
sample rate in samples per second
Output:
y
= vector of samples of the synthesized tone
unit
y = unit( dur , sr )
Creates a unit impulse.
Inputs:
dur = duration of the time interval in which the impulse occurs
sr = sample rate in samples per second
Output:
y
= unit impulse
Other Sound Generators
fm_instr
y = fm_instr( cf , cm , mi , amp , dur , sr )
Implements an FM instrument. The amp argument specifies the amplitudes
of a single multi-segment linear envelope, which is applied both to
output amplitude and modulation index. The modulating frequency is
obtained by c:m ratio. See FMDemo for a demonstration of the use of
fm_instr.
Inputs:
cf =
cm =
mi =
amp =
carrier frequency in Hz.
c:m ratio
modulation index
vector of ending amplitudes of envelope segments (start is
always 0)
dur = vector of envelope segment durations in seconds
sr = sample rate in samples per second
Output
y
= vector of samples of the instrument sound
7
lpnoise
y = lpnoise( cutoff , dur , sr )
Generates low-pass noise with specified cut-off frequency. Gaussian
white noise is filtered by a 128-point Hanning-windowed ideal low-pass
filter.
Inputs:
cutoff = lowpass cutoff frequency in Hz
dur
= duration in seconds
sr
= sample rate in samples per second
Output:
y
= vector of samples of filtered noise
mygrain
mygrainu
y = mygrain( cf , dur , dev , gs , sr )
y = mygrainu( cf , dur , dev , gs , sr )
Generates a segment of granular sound.
Inputs:
cf = center frequency of the segment
dur = duration of the segment in seconds
dev = average deviation above and below the center frequency,
in Hz.
gs = grain separation in seconds
sr = sample rate in samples per second
Output:
y
= vector of samples of granular sound
noisefilter
y = noisefilter( type , lf , hf , dur , sr )
Generates filtered white noise.
Inputs:
type =
lf
=
hf
=
dur =
sr
=
filter type (1=lowpass, 2=highpass, 3=bandpass, 4=notch)
lowpass cutoff frequency in Hz.
highpass cutoff frequency in Hz.
duration of the example in seconds
sample rate in samples per second
Output:
y
= vector of samples of filtered noise
8
pluck
plucklp
y = pluck( freq , dur , pw , sr )
y = plucklp( freq , dur , pw , sr )
Simulates the sound of a plucked string using an IIR comb filter. A
low-pass filter in the feedback loop of plucklp gives greater realism
than can be achieved with pluck.
Inputs:
freq =
dur =
pw
=
sr
=
approximate frequency of output in Hz.
duration of output in seconds
width of driving pulse in samples
sample rate in samples per second
Output:
y
= vector of samples of plucked string sound
vowel
y = vowel( f0 , f1 , f2 , f3 , dur , sr )
Creates vowel sounds using formant filtering. See VowelDemo for a
demonstration of the use of this function.
Inputs:
f0
= fundamental frequency of driving signal in Hz.
f1, f2, f3 = formant frequencies in Hz.
dur
= duration in seconds
sr
= sample rate in samples per second
Output:
y
= vector of samples of the vowel sound
Synthesizer Units
vca
y = vca( x , ctrl )
Uses a control signal to regulate the gain of the input signal. The
input signal should be in the range [-1,+1]. If the control signal goes
negative, the corresponding output samples will be set to zero. If the
input signal and the control signal are not of the same length, the
longer will be trimmed to the length of the shorter.
Inputs:
x
= input signal
ctrl = control signal in the range [ 0 , 1 ]
Output:
y
= vector of samples of the input signal with gain controlled by
ctrl
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vcf
y = vcf( x , ctrl , fl , fh , d , sr )
Applies a control signal to a resonant filter to continuously update
the filter’s center frequency.
Inputs:
x
=
ctrl =
fl
=
fh
=
d
=
sr
=
input signal
control signal in the range [ 0 , 1 ]
lowest center frequency of the filter in Hz
highest center frequency of the filter in Hz
half-bandwidth of the filter in Hz. (100 Hz typical)
sample rate in samples per second
Output:
y
= vector of samples of the input signal filtered as specified
vco
y = vco( rf , vc , dev , wave , sr )
Simulates a voltage-controlled oscillator that generates an arbitrary
waveform whose frequency is determined by a control input. The control
signal, vc, is normalized and then multiplied by the frequency
deviation, dev, to obtain the actual instantaneous frequency of the
oscillator output. Because the sampling of the input waveform, wave, is
fairly crude, the output waveform is denoised before it is returned to
the calling program.
Inputs:
rf
=
vc
=
dev =
wave =
sr
=
reference frequency in Hz
"voltage control" signal
maximum deviation from reference frequency, in Hz.
desired output waveform (vector, 512 samples typical)
sample rate in samples per second
Output:
y
= vector of samples of the oscillator tone
Filters
flt
y = flt( x , F , D , R )
Implements a resonant bandpass filter.
Inputs:
x = signal to be filtered
F = the center frequency of the filter in Hz.
D = the half-bandwidth of the filter in Hz.
R = the sample rate in samples per second
Output:
y = vector of samples of the filtered signal
10
lpflt
y = lpflt( x , cutoff , sr )
Implements a 128-point Hanning-windowed ideal low-pass filter.
Inputs:
x
= input signal
cutoff = lowpass cutoff frequency in Hz.
sr
= sample rate in samples per second
Output:
y
= vector of samples of the filtered signal
shelving
[ b , a ]
= shelving( type , g , fc , Q , sr )
Derives coefficients for a shelving filter with a given amplitude and
cutoff frequency. Use Matlab filter to apply filter to signal. See
Toolkit ShelvingDemo for examples of the use of shelving.
Inputs:
type = a character string defining filter type.
Choices are: 'Bass_Shelf' or 'Treble_Shelf'
g
= the logarithmic gain in dB; positive for boost, negative for
cut
fc
= the center frequency
Q
= adjusts the slope
sr
= the sample rate in samples per second
Outputs:
[ b , a ] = filter coefficients to be used with Matlab filter
Vibrato and Tremolo
tremolo
y = tremolo( x , lfo , mi , sr )
Applies tremolo to the input signal.
Inputs:
x
=
lfo =
mi =
sr =
input signal
tremolo frequency in Hz.
tremolo depth (normally in the range [0,1])
sample rate in samples per second
Output:
y
= vector of samples of the input signal with tremolo applied
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vibrato
y = vibrato( x , lfo , mi , sr )
Applies frequency modulation to the input signal. Because this function
uses a fairly crude algorithm, it should be used only where a quickand-dirty process is acceptable. For the cleanest sound, use either
vibrato2 or vibratox (which are two orders of magnitude slower than this
function).
Inputs:
x
=
lfo =
mi =
sr =
input signal
vibrato frequency in Hz. (3-8 Hz typical)
modulation index (0.001-0.005 typical)
sample rate in samples per second
Output:
y
= input signal with vibrato applied
vibrato2
vibratox
y = vibrato2( x , lfo , mi , sr )
y = vibratox( x , lfo , mi , sr )
Applies vibrato (low-frequency frequency modulation) to the input
signal. These functions produce much cleaner results than the Toolkit
function vibrato but they compute much more slowly. vibratox is slightly
faster than vibrato2.
Inputs:
x
=
lfo =
mi =
sr =
input signal
vibrato frequency (5-8 Hz. typical)
the depth of vibrato (0.05 typical)
sample rate in samples per second
Output:
y = vector of samples of the input signal with vibrato applied
12
Envelope Shapers
a_r (Matlab Student Edition)
ar
y = a_r( x , at , rt , sr )
y = ar( x , at , rt , sr )
A simple attack/release envelope shaper. Users of Matlab Student
Edition must use a_r.
Inputs:
x = input signal
at = attack time in seconds
rt = release time in seconds
sr = sample rate in samples per second
Output:
y = vector of samples of the input signal with the specified attack
and release applied
env
y = env( amp , dur , sr )
Generates a multi-segment linear envelope. The envelope can be applied
to a signal with mul or vca.
Inputs:
amp = vector containing the amplitude at the end of each
segment(starting amplitude is always 0)
dur = vector containing the durations of the segments
sr = sample rate in samples per second
Output:
y
= vector of samples of the specified envelope
FadeIn
y = FadeIn( x , sr , fa )
Attenuates the first fa*sr elements of the vector x linearly from 0 to
1.
Inputs:
x = input signal
sr = sample rate in samples per second
fa = fade-in time, in seconds
Output:
y = vector of samples of the input signal with specified fade-in
13
FadeOut
y = FadeOut( x , sr , fa )
Attenuates the last fa*sr elements of the vector x linearly from 1 to
0.
Inputs:
x = input signal
sr = sample rate in samples per second
fa = fade-out time, in seconds
Output:
y = vector of samples of the input signal with specified fade-out
Delay Lines
allpdelay
y = allpdelay(
x , dur , g , sr )
The classic Manfred Schroeder allpass filter, which is typically used
as an inexpensive reverb unit.
Inputs:
x
=
dur =
g
=
sr =
input signal
length of delay in seconds
gain in the range [ 0 , 1 ]
sample rate in seconds
Output:
y
= vector of samples of the filtered input signal
delay
[ a b ] = delay( x , dur , sr )
A simple delay-line. Vector x is delayed dur seconds and stored in
output vector b. The original un-delayed vector is stored in output
vector a. Both a and b are lengthened by padding with dur*sr zero
samples.
Inputs:
x
= input signal
dur = delay time in seconds
sr = sample rate in samples per second
Outputs:
a = original input vector (zero-padded at the end)
b = delayed version of input vector (zero-padded at the beginning)
14
firdelay
y = firdelay( x , dur , g , sr )
A single-delay fir comb filter.
Inputs:
x
= input signal
dur = delay time in seconds. Standard effects based on the length of
the delay are:
0 - .020 sec
= resonator
.025 - .050 sec = slapback
.050 sec
= echo
g
= gain in the range [ 0 , 1 ]
sr = sample rate in samples per second
Output:
y
= vector of samples of the filtered input signal
iirdelay
function y = iirdelay( x , dur , g , sr )
A single-delay iir comb filter. This can be used for simple echo and
reverb effects.
Inputs:
x
=
dur =
g
=
sr =
input signal
delay time in seconds
gain in the range [ 0 , 1 ]
sample rate in samples per second
Output:
y
= vector of samples of the filtered input signal
lpiirdelay
An iir comb filter with lowpass filter in the feedback loop. This
configuration is often used in room simulators.
Inputs:
x
=
dur =
g
=
sr =
input signal
length of delay in seconds
gain in the range [ 0 , 1 ]
sample rate in samples per second
Output:
y
= vector of samples of the filtered input signal
15
unidelay
y = unidelay( x , BL , FB , FF , dur , sr )
Universal (fir and iir) comb filter with a single delay.
Inputs:
x
=
BL =
FB =
FF =
dur =
sr =
input signal
blend control for feedforward of input sample
gain for feedback (iir) in the range [ 0 , 1 ]
gain for feedforward (fir) in the range [ 0 , 1 ]
delay duration in seconds
sample rate in samples per second
Output:
y
= vector of samples of the filtered input signal
Pitch- and Time-Shifting Functions
deci
y = deci( x , ratio )
Decimates the input signal, raising its pitch by up to one octave
(e.g., a ratio of 2 gives the "chipmunk" or "munchkin" effect). NB:
deci also reduces the length of the input signal by a factor of
1/ratio.
Inputs:
x
ratio
= input signal
= pitch increase factor: >=1 and <= 2
Output:
y
= vector of samples of the decimated input signal
lint
y = lint( x , ratio )
Shifts the pitch of the input signal down by linearly interpolating
between samples. NB: this function will lengthen the duration of the
sound by a factor of 1/ratio. With speech input, this typically
produces the effect of slurred, drunken speech.
Inputs:
x
ratio
= input signal
= pitch reduction factor: >0 and <= 1
Output:
y
= vector of samples of the interpolated input signal
16
pitch_shift
pitch_shift( x , r )
Performs pitch shifting. If r>1, pitch will be shifted up; if r<1,
pitch will be shifted down. Duration is unaffected.
Inputs:
x = input vector
r = ratio of output pitch to input pitch
Output:
y
= vector of samples of the pitch-shifted input signal
resample
y = resample( x , oldsr , newsr )
Resamples an array of samples so it is usable at a higher or lower
sample rate without change of pitch or duration.
Inputs:
x
= input signal
oldsr = original sample rate of x
newsr = desired new sample rate
Output:
y
= resampled signal
time_stretch
y = time_stretch( x , r )
This function performs time stretching. If r>0, duration will be
increased; if r<1, duration will be reduced. Pitch is unaffected.
Inputs:
x = input signal
r = ratio of output duration to input duration
Output:
y = vector of samples of the time-stretched input signal
17
Miscellaneous Digital FX
auto_wah
y = auto_wah( x , damp , minf , maxf , fw , sr )
State variable BP filter with narrow pass band. The center frequency
oscillates up and down the spectrum to produce a continuous wah-wah
effect.
Inputs:
x
= input signal
damp = damping factor (typically 0.05); the lower the damping factor
the smaller the pass band.
minf = minimum center cutoff frequency (typically 500 Hz)
maxf = maximum center cutoff frequency (typically 3000 Hz)
fw
= center cutoff frequency change rate (typically 2000 Hz/sec)
sr
= sample rate in samples per second
Output
y
= vector of samples of the input signal with wah-wah applied
denoise
y = denoise( x )
"Denoises" a signal
Input:
x = input signal
Output:
y = vector of samples of the denoised input signal
flanger
y = flanger( x , max_time_delay , rate , sr )
Creates a single delay, with the delay time oscillating from zero to
max_time_delay seconds at the frequency specified by rate.
Inputs:
x
max_time_delay
rate
sr
Output:
y
=
=
=
=
input signal
maximum flange delay in seconds (.003-.015 typical)
flange delay oscillation rate in Hz. (3-10 typical)
sample rate in samples per second
= vector of samples of the flanged input signal
18
fuzzexp
y = fuzzexp( x , gain , mix )
Creates distortion based on an exponential function.
Inputs:
x
= input signal
gain = amount of distortion, > 0
mix = mix of original and distorted sound: 1=only distorted
Output:
y
= vector of samples of the distorted input signal.
inflimit
y = inflimit( x , a )
An infinite limiter. Restricts the level of the input signal so that
the output level can never exceed the range [-1,+1] regardless of the
input level.
Inputs:
x = input signal
a = the limiter parameter. Typical values range from 0.5 to 2. As
the value of a increases, the onset of limiting becomes
increasingly abrupt at high signal levels.
Outputs:
y = vector of samples of the input signal limited as specified
leslie
y = leslie( x , lfo , td , vd , sr )
Simulates the effect of a rotary loudspeaker. See Toolkit LeslieDemo for
a demonstration of the use of this function.
Inputs:
x
=
lfo =
td =
vd =
sr =
mono input signal
speaker rotation rate in revolutions per second
tremolo depth (~0.3)
vibrato depth (~0.003)
sample rate in samples per second
Output
y
= stereo matrix, ready to used as input to sound or wavwrite
19
limiter
y = limiter( x , thresh , rt , at )
Limits peak signal amplitude, with user-specified attack and
release times.
Inputs:
x
thresh
rt
at
=
=
=
=
Output:
y
= vector of samples of the input signal with limiting applied
input signal
signal level at which gain is reduced
release time (0.01 typical)
attack time (0.4 typical)
mutate
y = mutate( x1 , x2 )
This function performs a mutation between two sounds, taking the phase
of the first one and the modulus of the second one. The longer input
vector is trimmed to the length of the shorter prior to processing to
assure conformability.
Inputs:
x1 = input vector to provide phase information
x2 = input vector to provide amplitude information
Output:
y = vector of samples of the mutated input signals
noisegt
y = noisegt( x , holdtime , ltrhold , utrhold , release , attack , a , sr )
Simulates a noise gate with hysteresis.
Inputs:
x
= input vector
holdtime = time in seconds the sound level has to be below the
threshold value before the gate is activated
ltrhold = threshold value for activating the gate
utrhold = threshold value for deactivating the gate: > ltrhold
release = time in seconds before the sound level reaches zero
attack
= time in seconds before the output sound level is the
same as the input level after deactivating the gate
a
= pole placement of the envelope detecting filter: <1
sr
= sample rate in samples per second
Output:
y
= vector of samples of the gated input signal
20
phaser
y = phaser( x , damp , minf , maxf , fw , sr )
State variable notch filter with narrow reject band. The center
frequency oscillates up and down the spectrum, producing a continuous
phasing effect.
Inputs:
x
= input signal
damp = damping factor (typically 0.1-0.3); the smaller the damping
factor the greater the phasing effect.
minf = minimum center cutoff frequency (typically 200 Hz)
maxf = maximum center cutoff frequency (typically 1000 Hz)
fw
= phasing center frequency change rate (typically 1000-3000
Hz/sec)
sr
= sample rate in samples per second
Output:
y
= vector of samples of the phased input signal
robotize
y = robotize( x )
Performs a "robotization" of sound, especially voice.
Input:
x = input signal
Output:
y = vector of samples of the robotized input signal
spreader
y = spreader( mono , delayL , delayR , pitchL , pitchR , mixer , sr )
Spreads mono input across the stereo image by applying slightly
different time delays and pitch shifts to the left and right channels.
The output is a stereo matrix ready to be sent to sound or wavwrite.
Inputs:
mono
= mono input vector to be "spread"
delayL = delay time in miliseconds for the left side (5 to 15
typical)
delayR = delay time in miliseconds for the right side (5 to 15
typical)
pitchL = pitch shift in cents for left side (+/-9 to +/-15 typical)
pitchR = pitch shift in cents for right side (+/-9 to +/-15 typical)
mixer = fraction of dry sound in final mix, in the range [ 0 , 1 ]
sr
= sample rate in samples per second
Output:
y
= Nx2 stereo matrix of the spread signal
21
symclip
y = symclip( x )
"Overdrive" simulation with symmetrical clipping.
Input:
x = input signal
Output:
y = vector of samples of the clipped input signal
wah
y = wah( x , FS , FF , D , R )
Simulates a "wah" effect.
Inputs:
x = input signal
FS = center frequency of the filter in Hz. at start and end of wah
(100 Hz typical)
FF = center frequency of the filter in Hz. at middle of wah (1500 Hz.
typical)
D = half-bandwidth of the filter in Hz. (100 Hz. typical)
R = sample rate in samples per second
Output:
y = vector of samples of the input signal with wah effect applied
wah_wah
y = wah_wah( x , wr , fs , ff , d , sr )
Applies a continuous "wah-wah" effect to the input signal. This
function is similar to auto_wah but computes much faster.
Inputs:
x = input signal
wr = wah-wah frequency in Hz (1-3 Hz typical)
fs = center frequency of the filter in Hz at start and end of wah
(100 Hz typical)
ff = center frequency of the filter in Hz at middle of wah (1500 Hz
typical)
d = half-bandwidth of the filter in Hz. (100 Hz typical)
sr = sample rate in samples per second
Output:
y = vector of samples of the input signal with wah-wah applied
22
whisperize
y = whisperize( x , sr )
"Whisperizes" the input sound.
Input:
x = input signal
sr = sample rate in samples per second
Output:
y = vector of samples of the input signal whisperized
Stereo
destereo
[ a b ] = destereo( y )
The inverse of the stereo function: it separates a single Nx2 matrix
into two 1xN row vectors. These vectors may then be manipulated by
other Toolkit functions.
Input:
y = Nx2 matrix)
Outputs:
a , b = 1xN row vectors
stereo
y = stereo( a , b )
Combines two row vectors into a single Nx2 matrix that can be used as
input to sound or wavwrite. If the input vectors do not have the same
length, the longer will be trimmed to match the length of the shorter.
Inputs:
a , b = input signals
Output:
y
= stereo matrix
23
General Vector Operations
fastconv
cxy = fastconv( x , y )
Fast convolution of vectors x and y.
Inputs:
x = input vector (typically an impulse response)
y = input vector (typically sound samples)
Output:
cxy = x convolved with y
grand
y = grand( n )
Generates n normally distributed variates with mean = 0 and standard
deviation = 1.
Input:
n = the desired number of variates
Output:
y = vector of n normally distributed variates
mask
y = mask( x , itype )
Applies a data window or “mask” to a vector.
Inputs:
x
= input vector
itype = window type (1-6):
1(Rectangular) 2(Tapered rectangular)
4(Hanning)
5(Hamming)
3(Triangular)
6(Blackman)
Output:
y
= vector of samples of the input with mask applied
midi2freq
f = midi2freq( m )
Converts MIDI note numbers to frequencies in Hz.
Input:
m = vector or matrix of MIDI note numbers (0-127)
Output:
f = vector or matrix of the corresponding frequencies
24
mix
y = mix( a , b )
Adds two input vectors and returns the sum. Prior to the addition, the
longer vector will be trimmed to the length of the shorter to assure
conformability.
Inputs:
a , b = vectors to be trimmed
Output:
y = elementwise sum of a and b
mvgrms
y = mvgrms( x , n )
A moving-window rms averager that can be used to extract the envelope
of an audio signal. The envelope can be applied with mul or vca.
Inputs:
x = the signal to be processed
n = the number of samples to be averaged in the rms calculation
(1000-2000 typical at 44.1 kHz sample rate)
Output:
y = vector of samples of the averaged input signal
mul
y = mul( a , b )
Multiplies two input vectors and returns the product. Prior to the
multiplication, the longer vector will be trimmed to the length of the
shorter to assure conformability.
Inputs:
a , b = vectors to be multiplied
Output:
y
= elementwise product of a and b
25
reverse
y = reverse( x )
Reverses a vector. Octave users must use rev.
Input:
x = vector to be reversed
Output:
y = reversed vector
trim
[ a , b ] = trim( x , y )
Trims the length of the longer input vector to the length of the
shorter vector
Inputs:
x , y = any vectors
Outputs:
a , b = row vectors trimmed to common length
Data Analysis
analyze
[ f p ] = analyze( y , sr )
Computes the power spectrum of a vector of sound samples and plots it
side-by-side with the original input signal
Inputs:
y = the array to be analyzed
sr = sample rate in samples per second
Outputs:
f = vector of frequencies corresponding to the values in p
p = the power spectrum amplitudes
26
rifft
[ r i ] = rifft( y , sr )
Returns and plots the real and imaginary parts of the fft of a vector
of sound samples
Inputs:
y = the signal to be analyzed
sr = sample rate in samples per second
Outputs:
r = real part of fft
i = imaginary part of fft