# Synthesis of time wave (additive model) This functions synthesizes pure or harmonic tone sound with amplitude modulation (am) and/or frequency modulation (fm). ```r synth(f, d, cf, a = 1, signal = "sine", shape = NULL, p = 0, am = c(0, 0, 0), fm = c(0, 0, 0, 0, 0), harmonics = 1, plot = FALSE, listen = FALSE, output = "matrix",...) ``` ## Arguments - `f`: sampling frequency (in Hz). - `d`: duration (in s). - `cf`: carrier frequency (in Hz). - `a`: amplitude (linear scale, relative when adding different waves). - `signal`: a character vector specifying the shape of the signal, see `details`. - `shape`: modification of the whole amplitude shape of the wave, see `details`. - `p`: initial phase (in radians). - `am`: a numeric vector of length 3 describing amplitude modulation parameters, see `details`. - `fm`: a numeric vector of length 5 describing frequency modulation parameters, see `details`. - `harmonics`: a numeric specifying the number and the relative amplitude of harmonics, see `details`. - `plot`: if `TRUE` returns the spectrogram of the synthezised sound (by default `FALSE`). - `listen`: if `TRUE` the new sound is played back. - `output`: character string, the class of the object to return, either `"matrix"`, `"Wave"`, `"Sample"`, `"audioSample"` or `"ts"`. - ``...``: other `spectro` graphical parameters. ## Details * `signal` is a character vector of length 1 that specifies the function used to synthesize the signal. There are three options: 1. "sine": for a sinus function, 2. "tria": for a triangle function, 3. "square": for a square function, 4. "saw": for a square function. * `shape` is a character vector of length 1 that allows to modify the whole amplitude shape of the wave. There are four options: 1. "incr": linear increase 2. "decr": linear decrease 3. "sine": sinusoid-like shape 4. "tria": triangular shape * `am` is a numeric vector of length 3 including: 1. the amplitude modulation depth (in %) 2. the frequency of the amplitude modulation (in Hz), 3. the phase of the amplitude modulation (in radian). * `fm` is a numeric vector of length 5 including: 1. the maximum excursion of a sinusoidal frequency modulation (in Hz), 2. the frequency of a sinusoidal frequency modulation (in Hz), 3. the maximum excursion of a linear frequency modulation (in Hz). 4. the phase of the frequency modulation (in radian). 5. the maximum excursion of an exponential frequency modulation (in Hz). * `harmonics` is a numeric vector that controls the number and the relative amplitude of harmonics synthesized. By default `harmonics = 1` meaning that a pure tone made of a single harmonic (fundamental) will be produced. To produce harmonics, the length of `harmonics` has to be greater than 1. The length of `harmonics` will set the number of harmonics, including the first one (fundamental). The value of each element of `harmonics` specify the relative ampltiude of each harmonic. The first value must equal to `1`. Here are some examples: * `harmonics = c(1, 0.5, 0.25)` will produce a sound with three harmonics (fundamental + 2 harmonics), the second harmonic having an amplitude half the fundamental ampltiude and the second harmonic an amplitude a quarter of the fundamental amplitude. * `harmonics = c(1, 0, 0.25)` will produce a sound with two harmonics (fundamental + 1 harmonic) the second harmonic having a null relative amplitude. * `harmonics = rep(1,4)` will produce a sound with four harmonics (fundamental + 3 harmonics) of equal amplitude. ## Returns If `plot` is `FALSE`, a new wave is returned. The class of the returned object is set with the argument `output`. ## References Hartmann, W. M. 1998 **Signals, sound and sensation**. New York: Springer. ## Author(s) Jerome Sueur and Laurent Lellouch. ## See Also `synth2`, `noisew`, `pulse`, `echo` ## Examples ```r ## You can use plot=TRUE and spectro() options ## to directly 'see' the new-built sounds f <- 8000 # sampling frequency d <- 1 # duration (1 s) cf <- 440 # carrier frequecy (440 Hz, i.e. flat A tone) # pure sinusoidal tone s <- synth(f=f,d=d,cf=cf) # pure triangular tone s <- synth(f=f,d=d,cf=cf, signal="tria") # pure tone with triangle overall shape s <- synth(f=f,d=d,cf=cf,shape="tria") # pure tones with am s <- synth(f=f,d=d,cf=cf,am=c(50,10)) # pure tones with am # and phase shift of pi radian (180 degrees) s <- synth(f=f,d=d,cf=cf,am=c(50,10,pi)) # pure tone with +1000 Hz linear fm s <- synth(f=f,d=d,cf=cf,fm=c(0,0,1000,0,0)) # pure tone with sinusoidal fm # (maximum excursion of 250 Hz, frequency of 10 Hz) s <- synth(f=f,d=d,cf=cf,fm=c(250,10,0,0,0)) # pure tone with sinusoidal fm # (maximum excursion of 250 Hz, frequency of 10 Hz, # phase shift of pi radian (180 degrees)) s <- synth(f=f,d=d,cf=cf,fm=c(250,10,0, pi,0)) # pure tone with sinusoidal am # (maximum excursion of 250 Hz, frequency of 10 Hz) # and linear fm (maximum excursion of 500 Hz) s <- synth(f=f,d=d,cf=cf,fm=c(250,10,500,0,0)) # the same with am s <- synth(f=f,d=d,cf=cf,am=c(50,10), fm=c(250,10,250,0,0)) # the same with am and a triangular overall shape s <- synth(f=f,d=d,cf=cf,shape="tria",am=c(50,10), fm=c(250,10,250,0,0)) # an harmonic sound s <- synth(f=f,d=d,cf=cf, harmonics=c(1, 0.5, 0.25)) # a clarinet-like sound clarinet <- c(1, 0, 0.5, 0, 0.14, 0, 0.5, 0, 0.12, 0, 0.17) s <- synth(f=f, d=d, cf = 235.5, harmonics=clarinet) # inharmonic FM sound built 'manually' fm <- c(250,5,0,0,0) F1<-synth(f=f,d=d,cf=cf,fm=fm) F2<-synth(f=f,d=d,a=0.8,cf=cf*2,fm=fm) F3<-synth(f=f,d=d,a=0.6,cf=cf*3.5,fm=fm) F4<-synth(f=f,d=d,a=0.4,cf=cf*6,fm=fm) final1<-F1+F2+F3+F4 spectro(final1,f=f,wl=512,ovlp=75,scale=FALSE) ```

synth function