# Set up Matrix of fft for Welch method Prepares a matrix for estimation of power spectrum via Welch's method. Also, is can be used for spectrogram. ```r setwelch(X, win = min(80, floor(length(X)/10)), inc = min(24, floor(length(X)/30)), coef = 64, wintaper=0.05) ``` ## Arguments - `X`: Time series vector - `win`: window length - `inc`: increment - `coef`: coefficient for fft - `wintaper`: percent taper window taper ## Returns List: - **values**: Matrix of fft's staggered along the trace - **windowsize**: window length used - **increment**: increment used - **wintaper**: percent taper window taper ## References Welch, P.D. (1967) The use of Fast Fourier Transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms IEEE Trans. Audio Electroacoustics 15, 70-73. ## Author(s) originally written by Andreas Weingessel, modified Jonathan M. Lees ## See Also stft ## Examples ```r dt <- 0.001 t <- seq(0, 6, by=dt) x <- 6*sin(2*pi*50*t) + 10* sin(2*pi*120*t) y <- x + rnorm(length(x), mean=0, sd=10) plot(t,y, type='l') title('sin(2*pi*50*t) + sin(2*pi*120*t)+ rnorm') Y <- fft(y) Pyy <- Y * Conj(Y) N <- length(y) n <- length(Pyy)/2 Syy <- (Mod(Pyy[1:n])^2)/N fn <- 1/(2*dt) f <- (0:(length(Syy)-1))*fn/length(Syy) plot(f, Syy, type='l', log='y' , xlim=c(0, 150)); abline(v=c(50, 120),col='blue', lty=2) plot(f, Syy, type='l', log='y' , xlim=c(0, 150)); abline(v=c(50, 120),col='blue', lty=2) win <- 1024 inc <- min(24, floor(length(y)/30)) coef <- 2048 w <- setwelch(y, win=win, inc=inc, coef=coef, wintaper=0.2) KK <- apply(w$values, 2, FUN="mean") fw <- seq(from=0, to=0.5, length=coef)/(dt) plot(fw, KK^2, log='', type='l' , xlim=c(0, 150)) ; abline(v=c(50, 120), col='blue', lty=2) Wyy <- (KK^2)/w$windowsize plot(f, Syy, type='l', log='y' , xlim=c(0, 150)) lines(fw,Wyy , col='red') DBSYY <- 20*log10(Syy/max(Syy)) DBKK <- 20*log10(Wyy/max(Wyy)) plot(f, DBSYY, type='l' , xlim=c(0, 150), ylab="Db", xlab="Hz") lines(fw, DBKK, col='red') title("Compare simple periodogam with Welch's Method") ```

setwelch function