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I am using the following code to convert a Bitmap to Complex and vice versa.
Even though those were directly copied from Accord.NET framework, while testing these static methods, I have discovered that, repeated use of these static methods cause 'data-loss'. As a result, the end output/result becomes distorted.
public partial class ImageDataConverter
{
#region private static Complex[,] FromBitmapData(BitmapData bmpData)
private static Complex[,] ToComplex(BitmapData bmpData)
{
Complex[,] comp = null;
if (bmpData.PixelFormat == PixelFormat.Format8bppIndexed)
{
int width = bmpData.Width;
int height = bmpData.Height;
int offset = bmpData.Stride - (width * 1);//1 === 1 byte per pixel.
if ((!Tools.IsPowerOf2(width)) || (!Tools.IsPowerOf2(height)))
{
throw new Exception("Imager width and height should be n of 2.");
}
comp = new Complex[width, height];
unsafe
{
byte* src = (byte*)bmpData.Scan0.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, src++)
{
comp[y, x] = new Complex((float)*src / 255,
comp[y, x].Imaginary);
}
src += offset;
}
}
}
else
{
throw new Exception("EightBppIndexedImageRequired");
}
return comp;
}
#endregion
public static Complex[,] ToComplex(Bitmap bmp)
{
Complex[,] comp = null;
if (bmp.PixelFormat == PixelFormat.Format8bppIndexed)
{
BitmapData bmpData = bmp.LockBits( new Rectangle(0, 0, bmp.Width, bmp.Height),
ImageLockMode.ReadOnly,
PixelFormat.Format8bppIndexed);
try
{
comp = ToComplex(bmpData);
}
finally
{
bmp.UnlockBits(bmpData);
}
}
else
{
throw new Exception("EightBppIndexedImageRequired");
}
return comp;
}
public static Bitmap ToBitmap(Complex[,] image, bool fourierTransformed)
{
int width = image.GetLength(0);
int height = image.GetLength(1);
Bitmap bmp = Imager.CreateGrayscaleImage(width, height);
BitmapData bmpData = bmp.LockBits(
new Rectangle(0, 0, width, height),
ImageLockMode.ReadWrite,
PixelFormat.Format8bppIndexed);
int offset = bmpData.Stride - width;
double scale = (fourierTransformed) ? Math.Sqrt(width * height) : 1;
unsafe
{
byte* address = (byte*)bmpData.Scan0.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, address++)
{
double min = System.Math.Min(255, image[y, x].Magnitude * scale * 255);
*address = (byte)System.Math.Max(0, min);
}
address += offset;
}
}
bmp.UnlockBits(bmpData);
return bmp;
}
}
(The DotNetFiddle link of the complete source code)
(ImageDataConverter)
Output:
As you can see, FFT is working correctly, but, I-FFT isn't.
That is because bitmap to complex and vice versa isn't working as expected.
What could be done to correct the ToComplex() and ToBitmap() functions so that they don't loss data?
I do not code in C# so handle this answer with extreme prejudice!
Just from a quick look I spotted few problems:
ToComplex()
Is converting BMP into 2D complex matrix. When you are converting you are leaving imaginary part unchanged, but at the start of the same function you have:
Complex[,] complex2D = null;
complex2D = new Complex[width, height];
So the imaginary parts are either undefined or zero depends on your complex class constructor. This means you are missing half of the data needed for reconstruction !!! You should restore the original complex matrix from 2 images one for real and second for imaginary part of the result.
ToBitmap()
You are saving magnitude which is I think sqrt( Re*Re + Im*Im ) so it is power spectrum not the original complex values and so you can not reconstruct back... You should store Re,Im in 2 separate images.
8bit per pixel
That is not much and can cause significant round off errors after FFT/IFFT so reconstruction can be really distorted.
[Edit1] Remedy
There are more options to repair this for example:
use floating complex matrix for computations and bitmap only for visualization.
This is the safest way because you avoid additional conversion round offs. This approach has the best precision. But you need to rewrite your DIP/CV algorithms to support complex domain matrices instead of bitmaps which require not small amount of work.
rewrite your conversions to support real and imaginary part images
Your conversion is really bad as it does not store/restore Real and Imaginary parts as it should and also it does not account for negative values (at least I do not see it instead they are cut down to zero which is WRONG). I would rewrite the conversion to this:
// conversion scales
float Re_ofset=256.0,Re_scale=512.0/255.0;
float Im_ofset=256.0,Im_scale=512.0/255.0;
private static Complex[,] ToComplex(BitmapData bmpRe,BitmapData bmpIm)
{
//...
byte* srcRe = (byte*)bmpRe.Scan0.ToPointer();
byte* srcIm = (byte*)bmpIm.Scan0.ToPointer();
complex c = new Complex(0.0,0.0);
// for each line
for (int y = 0; y < height; y++)
{
// for each pixel
for (int x = 0; x < width; x++, src++)
{
complex2D[y, x] = c;
c.Real = (float)*(srcRe*Re_scale)-Re_ofset;
c.Imaginary = (float)*(srcIm*Im_scale)-Im_ofset;
}
src += offset;
}
//...
}
public static Bitmap ToBitmapRe(Complex[,] complex2D)
{
//...
float Re = (complex2D[y, x].Real+Re_ofset)/Re_scale;
Re = min(Re,255.0);
Re = max(Re, 0.0);
*address = (byte)Re;
//...
}
public static Bitmap ToBitmapIm(Complex[,] complex2D)
{
//...
float Im = (complex2D[y, x].Imaginary+Im_ofset)/Im_scale;
Re = min(Im,255.0);
Re = max(Im, 0.0);
*address = (byte)Im;
//...
}
Where:
Re_ofset = min(complex2D[,].Real);
Im_ofset = min(complex2D[,].Imaginary);
Re_scale = (max(complex2D[,].Real )-min(complex2D[,].Real ))/255.0;
Im_scale = (max(complex2D[,].Imaginary)-min(complex2D[,].Imaginary))/255.0;
or cover bigger interval then the complex matrix values.
You can also encode both Real and Imaginary parts to single image for example first half of image could be Real and next the Imaginary part. In that case you do not need to change the function headers nor names at all .. but you would need to handle the images as 2 joined squares each with different meaning ...
You can also use RGB images where R = Real, B = Imaginary or any other encoding that suites you.
[Edit2] some examples to make my points more clear
example of approach #1
The image is in form of floating point 2D complex matrix and the images are created only for visualization. There is little rounding error this way. The values are not normalized so the range is <0.0,255.0> per pixel/cell at first but after transforms and scaling it could change greatly.
As you can see I added scaling so all pixels are multiplied by 315 to actually see anything because the FFT output values are small except of few cells. But only for visualization the complex matrix is unchanged.
example of approach #2
Well as I mentioned before you do not handle negative values, normalize values to range <0,1> and back by scaling and rounding off and using only 8 bits per pixel to store the sub results. I tried to simulate that with my code and here is what I got (using complex domain instead of wrongly used power spectrum like you did). Here C++ source only as an template example as you do not have the functions and classes behind it:
transform t;
cplx_2D c;
rgb2i(bmp0);
c.ld(bmp0,bmp0);
null_im(c);
c.mul(1.0/255.0);
c.mul(255.0); c.st(bmp0,bmp1); c.ld(bmp0,bmp1); i2iii(bmp0); i2iii(bmp1); c.mul(1.0/255.0);
bmp0->SaveToFile("_out0_Re.bmp");
bmp1->SaveToFile("_out0_Im.bmp");
t. DFFT(c,c);
c.wrap();
c.mul(255.0); c.st(bmp0,bmp1); c.ld(bmp0,bmp1); i2iii(bmp0); i2iii(bmp1); c.mul(1.0/255.0);
bmp0->SaveToFile("_out1_Re.bmp");
bmp1->SaveToFile("_out1_Im.bmp");
c.wrap();
t.iDFFT(c,c);
c.mul(255.0); c.st(bmp0,bmp1); c.ld(bmp0,bmp1); i2iii(bmp0); i2iii(bmp1); c.mul(1.0/255.0);
bmp0->SaveToFile("_out2_Re.bmp");
bmp1->SaveToFile("_out2_Im.bmp");
And here the sub results:
As you can see after the DFFT and wrap the image is really dark and most of the values are rounded off. So the result after unwrap and IDFFT is really pure.
Here some explanations to code:
c.st(bmpre,bmpim) is the same as your ToBitmap
c.ld(bmpre,bmpim) is the same as your ToComplex
c.mul(scale) multiplies complex matrix c by scale
rgb2i converts RGB to grayscale intensity <0,255>
i2iii converts grayscale intensity ro grayscale RGB image
I'm not really good in this puzzles but double check this dividing.
comp[y, x] = new Complex((float)*src / 255, comp[y, x].Imaginary);
You can loose precision as it is described here
Complex class definition in Remarks section.
May be this happens in your case.
Hope this helps.
I'm completely new to the world of SVM. I'm using LibSvmWrapper for c# from this link
but I can't figure out how to use it and how to specify the right parameters specially the documentation seems to be corrupted when I tried to run it using Doxygen
here is my attempt:
libSVM_Problem prob = new libSVM_Problem();
libSVM classifier = new libSVM();
libSVM_Parameter parameters = new libSVM_Parameter();
parameters.svm_type = libSVMWrapper.SVM_TYPE.C_SVC;
parameters.kernel_type = KERNEL_TYPE.LINEAR;
parameters.C = 1;
double[] labels = new double[trainClasses.Rows];
//prepare classes labels
for (int i = 0; i < trainClasses.Rows; i++)
{
labels[i] = trainClasses[i, 0];//trainClasses is an array of floats
}
//prepare samples
double[][] samples = new double[trainData.Rows][];
for (int i = 0; i < samples.Length; i++)
{
samples[i] = new double[trainData.Cols];
for (int j = 0; j < samples[i].Length; j++)
{
//trainData is 980 training sample * 400 features
samples[i][j] = trainData[i, j];
}
}
//prepare data and attach it to prob object
prob.labels = labels;
prob.samples = samples;
parameters.nu = 0;
classifier.Train(prob, parameters);
This code throws an exception on calling Train method which states that the weight parameter within libSVM_Parameter is null referenced. I have no idea how to specify these weights and generally the parameters of libSVM_Parameter.
So, if anyone has an example of how to specify the right parameters it would be very helpful.
I would suggest you to use https://github.com/ccerhan/LibSVMsharp
API for libsvm with c#.NET. It has some examples also which will help you to understand SVM too.
I've searched for an hour for the methods doing numerical integration. I'm new to Rcpp and rewriting my old programs now. What I have done in R was:
x=smpl.x(n,theta.true)
joint=function(theta){# the joint dist for
#all random variable
d=c()
for(i in 1:n){
d[i]=den(x[i],theta)
}
return(prod(d)*dbeta(theta,a,b)) }
joint.vec=Vectorize(joint)##vectorize the function, as required when
##using integrate()
margin=integrate(joint.vec,0,1)$value # the
##normalizeing constant at the donominator
area=integrate(joint.vec,0,theta.true)$value # the values at the
## numeritor
The integrate() function in R will be slow, and since I am doing the integration for a posterior distribution of a sample of size n, the value of the integration will be huge with large error.
I am trying to rewrite my code with the help of Rcpp, but I　don't know how to deal with the integrate. Should I include a c++ h file? Or any suggestions?
You can code your function in C and call it, for instance, via the sourceCpp function and then integrate it in R. In alternative, you can call the integrate function of R within your C code by using the Function macro of Rcpp. See Dirk's book (Seamless R and C++ Integration with Rcpp) on page 56 for an example of how to call R functions from C. Another alternative (which I believe is the best for most cases) is to integrate your function written in C , directly in C, using the RcppGSL package.
As about the huge normalizing constant, sometimes it is better to scale the function at the mode before integrating it (you can find modes with, e.g., nlminb, optim, etc.). Then, you integrate the rescaled function and to recover the original nroming constant multiply the resulting normalizing constant by the rescaling factor. Hope this may help!
after reading your #utobi advice, I felt programming by my own maybe easier. I simply use Simpson formula to approximate the integral:
// [[Rcpp::export]]
double den_cpp (double x, double theta){
return(2*x/theta*(x<=theta)+2*(1-x)/(1-theta)*(theta<x));
}
// [[Rcpp::export]]
double joint_cpp ( double theta,int n,NumericVector x, double a, double b){
double val = 1.0;
NumericVector d(n);
for (int i = 0; i < n; i++){
double tmp = den_cpp(x[i],theta);
val = val*tmp;
}
val=val*R::dbeta(theta,a,b,0);
return(val);
}
// [[Rcpp::export]]
List Cov_rate_raw ( double theta_true, int n, double a, double b,NumericVector x){
//This function is used to test, not used in the fanal one
int steps = 1000;
double s = 0;
double start = 1.0e-4;
std::cout<<start<<" ";
double end = 1-start;
std::cout<<end<<" ";
double h = (end-start)/steps;
std::cout<<"1st h ="<<h<<" ";
double area = 0;
double margin = 0;
for (int i = 0; i < steps ; i++){
double at_x = start+h*i;
double f_val = (joint_cpp(at_x,n,x,a,b)+4*joint_cpp(at_x+h/2,n,x,a,b)+joint_cpp(at_x+h,n,x,a,b))/6;
s = s + f_val;
}
margin = h*s;
s=0;
h=(theta_true-start)/steps;
std::cout<<"2nd h ="<<h<<" ";
for (int i = 0; i < steps ; i++){
double at_x = start+h*i;
double f_val = (joint_cpp(at_x,n,x,a,b)+4*joint_cpp(at_x+h/2,n,x,a,b)+joint_cpp(at_x+h,n,x,a,b))/6;
s = s + f_val;
}
area = h * s;
double r = area/margin;
int cover = (r>=0.025)&&(r<=0.975);
List ret;
ret["s"] = s;
ret["margin"] = margin;
ret["area"] = area;
ret["ratio"] = r;
ret["if_cover"] = cover;
return(ret);
}
I'm not that good at c++, so the two for loops like kind of silly.
It generally works, but there are still several potential problems:
I don't really know how to choose the steps, or how many sub intervals do I need to approximate the integrals. I've taken numerical analysis when I was an undergraduate, I think maybe I need to check my book about the expression of the error term, to decide the step length.
I compared my results with those from R. the integrate() function in R can take care of the integral over the interval [0,1]. That helps me because my function is undefined at 0 or 1, which takes infinite value. In my C++ code, I can only make my interval from [1e-4, 1-1e-4]. I tried different values like 1e-7, 1e-10, however, 1e-4 was the one most close to R's results....What should I do with it?
this is what i have of the function so far. This is only the beginning of the problem, it is asking to generate the random numbers in a 10 by 5 group of numbers for the output, then after this it is to be sorted by number size, but i am just trying to get this first part down.
/* Populate the array with 50 randomly generated integer values
* in the range 1-50. */
void populateArray(int ar[], const int n) {
int n;
for (int i = 1; i <= length - 1; i++){
for (int i = 1; i <= ARRAY_SIZE; i++) {
i = rand() % 10 + 1;
ar[n]++;
}
}
}
First of all we want to use std::array; It has some nice property, one of which is that it doesn't decay as a pointer. Another is that it knows its size. In this case we are going to use templates to make populateArray a generic enough algorithm.
template<std::size_t N>
void populateArray(std::array<int, N>& array) { ... }
Then, we would like to remove all "raw" for loops. std::generate_n in combination with some random generator seems a good option.
For the number generator we can use <random>. Specifically std::uniform_int_distribution. For that we need to get some generator up and running:
std::random_device device;
std::mt19937 generator(device());
std::uniform_int_distribution<> dist(1, N);
and use it in our std::generate_n algorithm:
std::generate_n(array.begin(), N, [&dist, &generator](){
return dist(generator);
});
Live demo
I am trying to build a system that will be able to process a record of someone whistling and output notes.
Can anyone recommend an open-source platform which I can use as the base for the note/pitch recognition and analysis of wave files ?
Thanks in advance
As many others have already said, FFT is the way to go here. I've written a little example in Java using FFT code from http://www.cs.princeton.edu/introcs/97data/. In order to run it, you will need the Complex class from that page also (see the source for the exact URL).
The code reads in a file, goes window-wise over it and does an FFT on each window. For each FFT it looks for the maximum coefficient and outputs the corresponding frequency. This does work very well for clean signals like a sine wave, but for an actual whistle sound you probably have to add more. I've tested with a few files with whistling I created myself (using the integrated mic of my laptop computer), the code does get the idea of what's going on, but in order to get actual notes more needs to be done.
1) You might need some more intelligent window technique. What my code uses now is a simple rectangular window. Since the FFT assumes that the input singal can be periodically continued, additional frequencies are detected when the first and the last sample in the window don't match. This is known as spectral leakage ( http://en.wikipedia.org/wiki/Spectral_leakage ), usually one uses a window that down-weights samples at the beginning and the end of the window ( http://en.wikipedia.org/wiki/Window_function ). Although the leakage shouldn't cause the wrong frequency to be detected as the maximum, using a window will increase the detection quality.
2) To match the frequencies to actual notes, you could use an array containing the frequencies (like 440 Hz for a') and then look for the frequency that's closest to the one that has been identified. However, if the whistling is off standard tuning, this won't work any more. Given that the whistling is still correct but only tuned differently (like a guitar or other musical instrument can be tuned differently and still sound "good", as long as the tuning is done consistently for all strings), you could still find notes by looking at the ratios of the identified frequencies. You can read http://en.wikipedia.org/wiki/Pitch_%28music%29 as a starting point on that. This is also interesting: http://en.wikipedia.org/wiki/Piano_key_frequencies
3) Moreover it might be interesting to detect the points in time when each individual tone starts and stops. This could be added as a pre-processing step. You could do an FFT for each individual note then. However, if the whistler doesn't stop but just bends between notes, this would not be that easy.
Definitely have a look at the libraries the others suggested. I don't know any of them, but maybe they contain already functionality for doing what I've described above.
And now to the code. Please let me know what worked for you, I find this topic pretty interesting.
Edit: I updated the code to include overlapping and a simple mapper from frequencies to notes. It works only for "tuned" whistlers though, as mentioned above.
package de.ahans.playground;
import java.io.File;
import java.io.IOException;
import java.util.Arrays;
import javax.sound.sampled.AudioFormat;
import javax.sound.sampled.AudioInputStream;
import javax.sound.sampled.AudioSystem;
import javax.sound.sampled.UnsupportedAudioFileException;
public class FftMaxFrequency {
// taken from http://www.cs.princeton.edu/introcs/97data/FFT.java.html
// (first hit in Google for "java fft"
// needs Complex class from http://www.cs.princeton.edu/introcs/97data/Complex.java
public static Complex[] fft(Complex[] x) {
int N = x.length;
// base case
if (N == 1) return new Complex[] { x[0] };
// radix 2 Cooley-Tukey FFT
if (N % 2 != 0) { throw new RuntimeException("N is not a power of 2"); }
// fft of even terms
Complex[] even = new Complex[N/2];
for (int k = 0; k < N/2; k++) {
even[k] = x[2*k];
}
Complex[] q = fft(even);
// fft of odd terms
Complex[] odd = even; // reuse the array
for (int k = 0; k < N/2; k++) {
odd[k] = x[2*k + 1];
}
Complex[] r = fft(odd);
// combine
Complex[] y = new Complex[N];
for (int k = 0; k < N/2; k++) {
double kth = -2 * k * Math.PI / N;
Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
y[k] = q[k].plus(wk.times(r[k]));
y[k + N/2] = q[k].minus(wk.times(r[k]));
}
return y;
}
static class AudioReader {
private AudioFormat audioFormat;
public AudioReader() {}
public double[] readAudioData(File file) throws UnsupportedAudioFileException, IOException {
AudioInputStream in = AudioSystem.getAudioInputStream(file);
audioFormat = in.getFormat();
int depth = audioFormat.getSampleSizeInBits();
long length = in.getFrameLength();
if (audioFormat.isBigEndian()) {
throw new UnsupportedAudioFileException("big endian not supported");
}
if (audioFormat.getChannels() != 1) {
throw new UnsupportedAudioFileException("only 1 channel supported");
}
byte[] tmp = new byte[(int) length];
byte[] samples = null;
int bytesPerSample = depth/8;
int bytesRead;
while (-1 != (bytesRead = in.read(tmp))) {
if (samples == null) {
samples = Arrays.copyOf(tmp, bytesRead);
} else {
int oldLen = samples.length;
samples = Arrays.copyOf(samples, oldLen + bytesRead);
for (int i = 0; i < bytesRead; i++) samples[oldLen+i] = tmp[i];
}
}
double[] data = new double[samples.length/bytesPerSample];
for (int i = 0; i < samples.length-bytesPerSample; i += bytesPerSample) {
int sample = 0;
for (int j = 0; j < bytesPerSample; j++) sample += samples[i+j] << j*8;
data[i/bytesPerSample] = (double) sample / Math.pow(2, depth);
}
return data;
}
public AudioFormat getAudioFormat() {
return audioFormat;
}
}
public class FrequencyNoteMapper {
private final String[] NOTE_NAMES = new String[] {
"A", "Bb", "B", "C", "C#", "D", "D#", "E", "F", "F#", "G", "G#"
};
private final double[] FREQUENCIES;
private final double a = 440;
private final int TOTAL_OCTAVES = 6;
private final int START_OCTAVE = -1; // relative to A
public FrequencyNoteMapper() {
FREQUENCIES = new double[TOTAL_OCTAVES*12];
int j = 0;
for (int octave = START_OCTAVE; octave < START_OCTAVE+TOTAL_OCTAVES; octave++) {
for (int note = 0; note < 12; note++) {
int i = octave*12+note;
FREQUENCIES[j++] = a * Math.pow(2, (double)i / 12.0);
}
}
}
public String findMatch(double frequency) {
if (frequency == 0)
return "none";
double minDistance = Double.MAX_VALUE;
int bestIdx = -1;
for (int i = 0; i < FREQUENCIES.length; i++) {
if (Math.abs(FREQUENCIES[i] - frequency) < minDistance) {
minDistance = Math.abs(FREQUENCIES[i] - frequency);
bestIdx = i;
}
}
int octave = bestIdx / 12;
int note = bestIdx % 12;
return NOTE_NAMES[note] + octave;
}
}
public void run (File file) throws UnsupportedAudioFileException, IOException {
FrequencyNoteMapper mapper = new FrequencyNoteMapper();
// size of window for FFT
int N = 4096;
int overlap = 1024;
AudioReader reader = new AudioReader();
double[] data = reader.readAudioData(file);
// sample rate is needed to calculate actual frequencies
float rate = reader.getAudioFormat().getSampleRate();
// go over the samples window-wise
for (int offset = 0; offset < data.length-N; offset += (N-overlap)) {
// for each window calculate the FFT
Complex[] x = new Complex[N];
for (int i = 0; i < N; i++) x[i] = new Complex(data[offset+i], 0);
Complex[] result = fft(x);
// find index of maximum coefficient
double max = -1;
int maxIdx = 0;
for (int i = result.length/2; i >= 0; i--) {
if (result[i].abs() > max) {
max = result[i].abs();
maxIdx = i;
}
}
// calculate the frequency of that coefficient
double peakFrequency = (double)maxIdx*rate/(double)N;
// and get the time of the start and end position of the current window
double windowBegin = offset/rate;
double windowEnd = (offset+(N-overlap))/rate;
System.out.printf("%f s to %f s:\t%f Hz -- %s\n", windowBegin, windowEnd, peakFrequency, mapper.findMatch(peakFrequency));
}
}
public static void main(String[] args) throws UnsupportedAudioFileException, IOException {
new FftMaxFrequency().run(new File("/home/axr/tmp/entchen.wav"));
}
}
i think this open-source platform suits you
http://code.google.com/p/musicg-sound-api/
Well, you could always use fftw to perform the Fast Fourier Transform. It's a very well respected framework. Once you've got an FFT of your signal you can analyze the resultant array for peaks. A simple histogram style analysis should give you the frequencies with the greatest volume. Then you just have to compare those frequencies to the frequencies that correspond with different pitches.
in addition to the other great options:
csound pitch detection: http://www.csounds.com/manual/html/pvspitch.html
fmod: http://www.fmod.org/ (has a free version)
aubio: http://aubio.org/doc/pitchdetection_8h.html
You might want to consider Python(x,y). It's a scientific programming framework for python in the spirit of Matlab, and it has easy functions for working in the FFT domain.
If you use Java, have a look at TarsosDSP library. It has a pretty good ready-to-go pitch detector.
Here is an example for android, but I think it doesn't require too much modifications to use it elsewhere.
I'm a fan of the FFT but for the monophonic and fairly pure sinusoidal tones of whistling, a zero-cross detector would do a far better job at determining the actual frequency at a much lower processing cost. Zero-cross detection is used in electronic frequency counters that measure the clock rate of whatever is being tested.
If you going to analyze anything other than pure sine wave tones, then FFT is definitely the way to go.
A very simple implementation of zero cross detection in Java on GitHub