STFT - Plotting is not a true representation

Question

I might be going crazy here. Following my question: here

I did some thinking and probably understood that my STFT algorithm was not performing correctly.

I followed this algorithm:

-> Get 256 of data

-> Apply windowing function

-> Get the FFT

-> get the first 128 points

Here is my result. I have used NFFT = 256 which should give me 128 points. I firstly calculated the FFT (after the windowing function was applied) and only counted the first 128 values of this. I.e. FFT_RESULT / 2

Whereas my last output was the following:

I don't quite understand why the values along the X axis are particular that high?

EDIT:

Ok, so following the advice, I did the following:

1) Created a 2D vector for each of the "256 resulting FFT values"

for(size_t i=0; (i < signal.size()); i++)
{
    std::vector<double> temp_vector;
    // store blocks of 256 inside temp_vector 

    // Compute Hanning Window 

    // Compute FFT

    std::vector<std::vector<complex> stft; 

    stft.push_back(temp_vector);
}

This gave me a total of 74 blocks within the 2D vector.

I then took the absolute value of the REAL values and stored these inside a double, read these in and with pylab library I used imshow() and got the following result:

However, If I plot normally, I get the following:

I think my calculations are correct, I just don't think I'm plotting them right using the spectrogram!!

Answer 1

Regarding your first 2 plots: for FFT results, the X axis is usually labeled with the FFT_bin_index * sample_rate / FFT_length, and the Y axis with either the magnitude (absolute value of the complex bin value), or the log magnitude of the FFT result bin.

Answer 2

Your calculations are correct, but that's not how you plot STFT. If you think about it, you're trying to plot three-dimensional data, namely value that is a function of both time and frequency. To represent three-dimensional data we use images rather than graphs. Vertical and horizontal coordinates represent frequency and time respectively, and pixel color or intensity represents FFT magnitude of a specific frequency at a specific time. We call these images spectrograms. MATLAB Signal Processing Toolbox comes with a spectrogram command which lets you plot spectrograms.