How to extract a specific frequency range from a .wav file?

Question

I'm really new on sound processing, so maybe my question will be trivial. What I want to do is to extract a specific frequency range (let's say 150-400 Hz) from a wav file, using R. In other words, I want to create another wave file (wave2) that contains only the frequency component that I specify (150 to 400 Hz, or what else).

I read something on the net, and I discovered out that this can be done with a FFT analysis, and here's come the problems.

Suppose I've this code:

library(sound)
s1 <- Sine(440, 1)
s2 <- Sine(880, 1)
s3 <- s1 + s2

s3.s <- as.vector(s3$sound)
  # s3.s is now a vector, with length 44100; 
  # bitrate is 44100 (by default)
  # so total time of s3 is 1sec.

  # now I calculate frequencies
N <- length(s3.s)   # 44100
k <- c(0:(N-1))
Fs <- 44100         # sampling rate
T <- N / Fs
freq <- k / T
x <- fft(s3.s) / N

plot(freq[1:22050], x[1:22050], type="l") # we need just the first half of FFT computation

The plot we obtain is:

Well, there are two peaks. If we want to know to what frequency they correspond, just find:

order(Mod(x)[1:22050], decreasing=T)[1:10]
[1] 441 881 882 880 883 442 440 879 884 878

First two values are really near to the frequency I've used to create my sound:

        real     computed
 Freq1: 440   |  441 
 Freq2: 880   |  881 

So, now comes the problem: how to proceed, if I want to delete from my sound the frequencies in the range, say, (1, 500) ? And how to select (and save) only the range (1, 500) ? What I attend, is that my new sound (with deleted frequencies) will be something near to simple Sine(freq=880, duration=1) (I know, it cannot be exactly like so!). Is that possible?

I'm pretty sure that fft(DATA, inverse = TRUE) is what I need. But I'm not sure, and however I don't know how to proceed.

Answer 1

If you don't want to programm it, you can use Praat.

Praat is a free scientific software program for the analysis of speech in phonetics. But you can also use it to edit the spectrum of any sound (remove frequencies, ...) and then export the result as a new sound file.

Answer 2

Maybe I missed the point, but don't you already have your answer? From your post:

order(Mod(x)[1:22050], decreasing=T)[1:10]
[1] 441 881 882 880 883 442 440 879 884 878 

Simply collect all values above 500:

junk <- order(Mod(x)[1:22050], decreasing=T)[1:10]
(junk1 <- junk[junk > 500])
[1] 881 882 880 883 879 884 878

To generate the new signal simply repeat what you did to build the original signal:

junk2 <- Sine(0, 1)    
for (i in 1:length(junk1)) {     
    junk2 <- junk2 + Sine(junk1[i], 1)    
}    
junk2.s <- as.vector(junk2$sound)    

To keep the values below 500:

(junk3 <- junk[junk <= 500])
[1] 441 442 440