Is 0.001Hz resolution possible with a 2.5Ms/s file while preserving the time resolution?

I have an audio signal that was sampled at 2.5Ms/s, 24bit resolution, 10min. in duration, captured to a wave file. The signal bandwidth is 1MHz.

Is it possible to setup the fft function with a large enough fft size (bins) to have 0.001Hz resolution while preserving the time resolution? I suspect that this may require a fft size of 500M or larger to acheive. The output will be a spectragraph plot(s).

Is this possible with the Signal Processing Toolbox?

Computing power and speed is not an issue.

Thanks, Jonathan

Answer 1

[Wayne King]

It sounds like you have

    dt = 1/2.5e6;
    N = 600/dt;

N samples is that correct? To achieve a frequency resolution of 0.001 Hz with a sampling rate of 2.5 megahertz you need

   1/(0.001*dt)

samples, which you don't have. Padding the fft does not increase your frequency resolution. That is determined by your sampling rate and the number of samples you acquire. Padding the fft() only interpolates the frequency grid.

So in short, no, you don't have enough data for the DFT to have 0.001 Hz resolution, let alone the short-time Fourier transform for which you would have to segment your data.