LIST_ITEM (L" where %wc, %wle & %wr are user-supplied weights and")
LIST_ITEM (L" %d1 = \\su (%k=1..%nCoefficients; (%c__%ik_ - %c__%jk_)^2)")
LIST_ITEM (L" %d2 = (c__%i0_ - c__%j0_)^2")
LIST_ITEM (L" %d3 = \\su (%k=1..%nCoefficients; (%r__%ik_ - %r__%jk_)^2), with ")
LIST_ITEM (L" %r__%ik_ the regression coefficient of the cepstral coefficients "
"from the frames within a time span of %dtr seconds. "
"c__%ij_ is %j-th cepstral coefficient in frame %i. ")
NORMAL (L"Next we find the optimum path through the distance matrix with a "
"Viterbi-algorithm.")
MAN_END
MAN_BEGIN (L"CC: To Matrix", L"djmw", 20011123)
INTRO (L"Copies the cepstral coefficients of the selected @CC "
"object to a newly created @Matrix object.")
ENTRY (L"Behaviour")
FORMULA (L"%z__%ji_ = %c__%ij_, with 1 \\<_ %i \\<_ %nx and "
"1 \\<_ j \\<_ %numberOfCoefficients__%i_,")
NORMAL (L"where %z__%ji_ is the matrix element in row %j and column %i and "
"%c__%ij_ is the %j-th cepstral coefficient in frame %i.")
MAN_END
MAN_BEGIN (L"Cepstrum", L"djmw", 20010219)
INTRO (L"One of the @@types of objects@ in P\\s{RAAT}.")
ENTRY (L"Description")
NORMAL (L"An object of type Cepstrum represents the complex cepstrum.")
MAN_END
MAN_BEGIN (L"LFCC", L"djmw", 20040421)
INTRO (L"One of the @@types of objects@ in P\\s{RAAT}.")
NORMAL (L"An object of type LFCC represents cepstral "
"coefficients on a linear frequency scale as a function of time. "
"The coefficients are represented in frames with constant sampling "
CODE (L"select Sound hello") CODE (L"samplingFrequency = Get sampling frequency") ENTRY (L"Algorithm") NORMAL (L"The sampling frequency is defined as 1 / (\\De%t), where \\De%t is the @@sampling period@. " "See @@Get sampling period@.") MAN_END MAN_BEGIN (L"Get time from sample number...", L"ppgb", 20040420) INTRO (L"A command that becomes available in the #Query menu if you select a @Sound or @LongSound object.") NORMAL (L"The Info window will tell you the time (in seconds) associated with the sample number that you specify.") ENTRY (L"Setting") TAG (L"##Sample number") DEFINITION (L"the sample number whose time is sought.") ENTRY (L"Algorithm") NORMAL (L"the result is") FORMULA (L"%t__1_ + (%sample_number - 1) \\.c \\De%t") NORMAL (L"where %t__1_ is the time associated with the first sample, and \\De%t is the sampling period.") ENTRY (L"Details for hackers") NORMAL (L"If you select a Sound or LongSound and click @Inspect, " "you can see how the relation between sample numbers and times is stored in the object: " "%t__1_ is the #x1 attribute, and \\De%t is the #dx attribute.") MAN_END MAN_BEGIN (L"Get sample number from time...", L"ppgb", 20040505) INTRO (L"A command that becomes available in the #Query menu if you select a @Sound or @LongSound object.") NORMAL (L"The Info window will tell you the sample number belonging to the time that you specify. " "The result is presented as a real number.") ENTRY (L"Setting") TAG (L"##Time (s)") DEFINITION (L"the time (in seconds) for which you want to know the sample number.") ENTRY (L"Example")
"Text left... yes F1 (Hz)\n" "mdur_ae = 135\n" "mdur_ep = 95\n" "sdur = 25\n" "mf1_ae = 780\n" "mf1_ep = 620\n" "sf1 = 60\n" "Draw ellipse... mdur_ae-sdur mdur_ae+sdur mf1_ae-sf1 mf1_ae+sf1\n" "Text... mdur_ae Centre mf1_ae Half /æ/\n" "Draw ellipse... mdur_ep-sdur mdur_ep+sdur mf1_ep-sf1 mf1_ep+sf1\n" "Text... mdur_ep Centre mf1_ep Half /ɛ/\n" "Draw inner box\n" )*/ NORMAL (L"The logistic regression method will find values %α, %%β__F1_% and %%β__dur_% " "that optimize") FORMULA (L"%α + %%β__F1_% %F1__%k_ + %%β__dur_% %Dur__%k_ = ln (%p__%k_(/ɛ/)/%p__%k_(/æ/))") NORMAL (L"where %k runs from 1 to 10, and %p__%k_(/æ/) + %p__%k_(/ɛ/) = 1.") NORMAL (L"The optimization criterion is %%maximum likelihood%, i.e. those %α, %%β__F1_% and %%β__dur_% " "will be chosen that lead to values for %p__%k_(/æ/) and %p__%k_(/ɛ/) that make the observations in the table " "most likely.") NORMAL (L"Praat will create an object of type #LogisticRegression in the list. " "When you then click the #Info button, Praat will write the values of %α (the %intercept), " "%%β__F1_% and %%β__dur_% into the Info window (as well as much other information).") NORMAL (L"The number of factors does not have to be 2; it can be 1 or more. " "The number of dependent categories is always 2.") MAN_END } /* End of file manual_statistics.cpp */
"the target point, using a bell-shaped window whose left-hand half-length is the minimum " "of the left-hand periods adjacent to the source and target points " "(and analogously for the right-hand half-length).") MAN_END MAN_BEGIN (L"pitch floor", L"ppgb", 20060914) INTRO (L"The pitch floor is the bottom of the pitch range in the Sound window (see the @Intro). " "The standard setting is 75 hertz; pitch values below this pitch floor will not be computed or shown by Praat.") NORMAL (L"To change the pitch floor, choose @@Pitch settings...@.") MAN_END MAN_BEGIN (L"power spectral density", L"ppgb", 20101026) INTRO (L"The average power in a sound during a certain time range and in a certain frequency range, expressed in Pa^2/Hz.") ENTRY (L"Mathematical definition") NORMAL (L"The %%complex spectrum% of a sound %x(%t) in the time range (%t__1_, %t__2_) is") FORMULA (L"%X(%f) ≡ ∫__%%t%1_^^%%t%2^ %x(%t) e^^-2%π%ift^ %dt") NORMAL (L"for any frequency %f in the two-sided frequency domain (-%F, +%F). " "If %x(%t) is expressed in units of Pascal, %X(%f) is expressed in units of Pa/Hz. " "In Praat, this complex spectrum is the quantity stored in a @Spectrum.") NORMAL (L"From the complex spectrum we can compute the %%one-sided power spectral density% in Pa^2/Hz as") FORMULA (L"PSD(%f) ≡ 2|%X(%f)|^2 / (%t__2_ - %t__1_)") NORMAL (L"where the factor 2 is due to adding the contributions from positive and negative frequencies. " "In Praat, this power spectral density is the quantity stored in a @Spectrogram.") NORMAL (L"The PSD divides up the total power of the sound. " "To see this, we integrate it over its entire one-sided frequency domain (0, %F):") FORMULA (L"∫__0_^^%F^ PSD(%f) %df = ∫__0_^^%F^ 2|%X(%f)|^2/(%t__2_-%t__1_) %df =") FORMULA (L"= 1/(%t__2_-%t__1_) ∫__-%F_^^+%F^ |%X(%f)|^2 %df = 1/(%t__2_-%t__1_) ∫__%%t%1_^^%%t%2^ |%x(%t)|^2 %dt") NORMAL (L"where the last step uses %%Parceval's theorem%. " "The result is precisely the average power of the sound in the time range (%t__1_, %t__2_).") ENTRY (L"The logarithmic power spectral density") NORMAL (L"It is often useful to express the power spectral density in dB relative to %%P__ref_% = 2·10^^-5^ Pa:")
MAN_BEGIN (L"Sound: To CrossCorrelationTable...", L"djmw", 20110212)
INTRO (L"A command that creates a @@CrossCorrelationTable@ form every selected @@Sound@ object.")
ENTRY (L"Settings")
SCRIPT (5.4, Manual_SETTINGS_WINDOW_HEIGHT (2), L""
Manual_DRAW_SETTINGS_WINDOW ("Sound: To CrossCorrelationTable", 2)
Manual_DRAW_SETTINGS_WINDOW_RANGE("Time range", "0.0", "10.0")
Manual_DRAW_SETTINGS_WINDOW_FIELD ("Lag time", "0.0")
)
TAG (L"##Time range (s)#,")
DEFINITION (L"determines the time range over which the table is calculated.")
TAG (L"##Lag time (s)#,")
DEFINITION (L"determines the lag time.")
ENTRY (L"Algorithm")
NORMAL (L"The cross-correlation between channel %i and channel %j for lag time \\ta is defined as the "
"discretized #integral")
FORMULA (L"cross-corr (%c__%i_, %c__%j_) [%\\ta] \\=3 \\su__%t_ %c__%i_[%t] %c__%j_[%t+%\\ta] %%\\Det%,")
NORMAL (L"where %t and %t+%\\ta are discrete times and %%\\Det% is the @@sampling period@. ")
MAN_END
MAN_BEGIN (L"Sound: To Covariance (channels)...", L"djmw", 20120303)
INTRO (L"Detemines the @@Covariance|covariances@ between the channels of a selected @Sound.")
NORMAL (L"The covariance of a sound is determined by calculating the @@CrossCorrelationTable@ of a multichannel sound for a lag time equal to zero.")
MAN_END
MAN_BEGIN (L"Sound: To Sound (blind source separation)...", L"djmw", 20130502)
INTRO (L"Analyze the selected multi-channel sound into its independent components by an iterative method.")
NORMAL (L"The @@blind source separation@ method to find the independent components tries to simultaneously diagonalize a number of "
"@@CrossCorrelationTable@s that are calculated from the multi-channel sound at different lag times.")
ENTRY (L"Settings")
SCRIPT (5.4, Manual_SETTINGS_WINDOW_HEIGHT (6), L""
Manual_DRAW_SETTINGS_WINDOW ("Sound: To Sound (blind source separation)", 6)
"a bandwidth of 80 Hz, and ##Bandwidth cost# is 1.0, " "the cost of having this formant in any track is (80/400) \\.c 1.0 = 0.200. " "So we see that the procedure locally favours the inclusion of candidates " "with low relative bandwidths.") TAG (L"##Transition cost (per octave)") DEFINITION (L"the cost of having two different consecutive formant values in a track. " "For instance, if a proposed track through the candidates has two consecutive formant " "values of 300 Hz and 424 Hz, and ##Transition cost# is 1.0/octave, " "the cost of having this large frequency jump is (0.5 octave) \\.c (1.0/octave) = 0.500.") ENTRY (L"Algorithm") NORMAL (L"This command uses a Viterbi algorithm with multiple planes. For instance, if the selected Formant object " "contains up to five formants per frame, and you request three tracks, the Viterbi algorithm will have to choose " "between ten candidates (the number of combinations of three out of five) for each frame.") NORMAL (L"The formula for the cost of e.g. track 3, with proposed values %F__2%i_ (%i = 1...%N, " "where %N is the number of frames) is:") FORMULA (L"\\su__%i=1..%N_ %frequencyCost\\.c\\|f%F__3%i_ \\-- %referenceF3\\|f/1000 +") FORMULA (L"+ \\su__%i=1..%N_ %bandWidthCost\\.c%B__3%i_/%F__3%i_ +") FORMULA (L"+ \\su__%i=1..%N-1_ %transitionCost\\.c\\|flog__2_(%F__3%i_/%F__3,%i+1_)\\|f") NORMAL (L"Analogous formulas compute the cost of track 1 and track 2. " "The procedure will assign those candidates to the three tracks that minimize " "the sum of three track costs.") MAN_END MAN_BEGIN (L"FormantGrid", L"ppgb", 20080427) INTRO (L"One of the @@types of objects@ in Praat.") NORMAL (L"A FormantGrid object represents spectral structure as a function of time: a %%formant contour%. " "Unlike the evenly sampled @Formant object, it consists of a number of formant tiers and bandwidth tiers, " "each of which contains a number of formant or bandwidth %points (or %targets), sorted by time.") NORMAL (L"For examples, see @@Source-filter synthesis@.") ENTRY (L"FormantGrid commands") NORMAL (L"Creation:")
LIST_ITEM (U"1.1. @@Sound files 1.1. Sampling|Sampling@ (sampling frequency)") LIST_ITEM (U"1.2. @@Sound files 1.2. Quantization|Quantization@ (linear, μ-law, A-law)") LIST_ITEM (U"1.3. @@Sound files 1.3. Channels|Channels@ (mono, stereo)") LIST_ITEM (U"1.4. @@Sound files 1.4. The header|The header@") LIST_ITEM (U"1.5. @@Sound files 1.5. Size|Size@") LIST_ITEM (U"1.6. @@Sound files 1.6. Compression|Compression@") MAN_END MAN_BEGIN (U"Sound files 1.1. Sampling", U"ppgb", 20040330) NORMAL (U"When a sound signal from a microphone or on a tape needs to be read into a computer, " "it is %digitized, which means that it is %sampled and %quantized.") NORMAL (U"Sampling is the discretization of the time domain of the signal: " "each second of the signal is divided up into 11025, 22050, or 44100 " "slices (or any other suitable number), and a %%sample value% is associated with " "each slice. For instance, a continuous 377-Hz sine wave is expressed by") FORMULA (U"%x(%t) = sin (2%π 377 %t)") NORMAL (U"If the %%sampling frequency% (or %%sample rate%) is 44100 Hz, this sine wave will be sampled at " "points spaced Δ%t = 1/44100 second apart, and the sample values will be") FORMULA (U"%x__%i_ = sin (2%π 377 (%t__0_ + %i Δ%t))") NORMAL (U"where %t__0_ is the time after which sampling begins. " "Δ%t is called the %%sample period%.") NORMAL (U"Quantization is handled in the next section (@@Sound files 1.2. Quantization|§1.2@).") MAN_END MAN_BEGIN (U"Sound files 1.2. Quantization", U"ppgb", 20000126) NORMAL (U"Apart from sampling (@@Sound files 1.1. Sampling|§1.1@), " "digitization also involves quantization, which is the conversion of a sample value " "into a number that fits into 8 or 16 bits.") MAN_END MAN_BEGIN (U"Sound files 1.3. Channels", U"ppgb", 20000126)
