I'm trying to use C++ to recreate the spectrogram function used by Matlab. The function uses a Short Time Fourier Transform (STFT). I found some C++ code here that performs a STFT. The code seems to work perfectly for all frequencies but I only want a few. I found this post for a similar question with the following answer:
Just take the inner product of your data with a complex exponential at the frequency of interest. If g is your data, then just substitute for f the value of the frequency you want (e.g., 1, 3, 10, ...)
Having no background in mathematics, I can't figure out how to do this. The inner product part seems simple enough from the Wikipedia page but I have absolutely no idea what he means by (with regard to the formula for a DFT)
a complex exponential at frequency of interest
Could someone explain how I might be able to do this? My data structure after the STFT is a matrix filled with complex numbers. I just don't know how to extract my desired frequencies.
Relevant function, where window is Hamming, and vector of desired frequencies isn't yet an input because I don't know what to do with them:
Matrix<complex<double>> ShortTimeFourierTransform::Calculate(const vector<double> &signal,
const vector<double> &window, int windowSize, int hopSize)
{
int signalLength = signal.size();
int nOverlap = hopSize;
int cols = (signal.size() - nOverlap) / (windowSize - nOverlap);
Matrix<complex<double>> results(window.size(), cols);
int chunkPosition = 0;
int readIndex;
// Should we stop reading in chunks?
bool shouldStop = false;
int numChunksCompleted = 0;
int i;
// Process each chunk of the signal
while (chunkPosition < signalLength && !shouldStop)
{
// Copy the chunk into our buffer
for (i = 0; i < windowSize; i++)
{
readIndex = chunkPosition + i;
if (readIndex < signalLength)
{
// Note the windowing!
data[i][0] = signal[readIndex] * window[i];
data[i][1] = 0.0;
}
else
{
// we have read beyond the signal, so zero-pad it!
data[i][0] = 0.0;
data[i][1] = 0.0;
shouldStop = true;
}
}
// Perform the FFT on our chunk
fftw_execute(plan_forward);
// Copy the first (windowSize/2 + 1) data points into your spectrogram.
// We do this because the FFT output is mirrored about the nyquist
// frequency, so the second half of the data is redundant. This is how
// Matlab's spectrogram routine works.
for (i = 0; i < windowSize / 2 + 1; i++)
{
double real = fft_result[i][0];
double imaginary = fft_result[i][1];
results(i, numChunksCompleted) = complex<double>(real, imaginary);
}
chunkPosition += hopSize;
numChunksCompleted++;
} // Excuse the formatting, the while ends here.
return results;
}
