This means that the frequencies of all sinusoids we measure will be a multiple of the inverse of the analysis window length - so if our “nails” are N samples away, our STFT bins will have a spacing of sampleRate/N Hertz. As a result, this concept imposes an artificial frequency grid on our analysis by requiring the reference frequencies to be an integer multiple of our signal window in period to make them seamlessly fit into our analysis frame.
I often see DFT bin in some DFT/stft literature,What does the term "bin" mean exactly?
Does it refer to a specific single frequency or a frequency range?
If we do N points DFT,then have N DFT bins, where do the 0-bin and N-1 bin refer to?
If N = 256,then where does 112.5 bin refer to?
Thank.
Hyee
I often see DFT bin in some DFT/stft literature,What does the term "bin" mean exactly?
Does it refer to a specific single frequency or a frequency range?
If we do N points DFT,then have N DFT bins, where do the 0-bin and N-1 bin refer to?
If N = 256,then where does 112.5 bin refer to?
In a sense, it's like a histogram, where the bin contains a range of frequencies between upper and lower bounds.
If the original time-domain chunk contained N=256 samples, that's 256 real values and 256 imaginary values (usually, the Imaginary part of each complex number is zero when we're considering Real data, such as audio waveforms).
The transform-domain chunk will also contain N=256 samples, meaning 256 real paired with 256 imaginary values, or combined, they could be considered 256 complex numbers. If you think about it, you'd be losing Information if you didn't have N=256 complex numbers, so you couldn't reconstruct the time-domain signal by performing the inverse DFT.
With certain kinds of symmetry in the original signal chunk it is possible to prove that the imaginary part must be zero, which can save some computation (e.g. even symmetry, IIRC, which you obtain when performing the autocorrelation function, whose transform is the power spectrum of the original signal - Wiener-Khinchin Theorem).
Anyhow, these N=256 complex numbers represent the full range of positive and negative frequencies. Negative frequencies do mean something in reconstructing the waveform, but in general analysis they tend to be ignored. So you have half the number of frequency bins.
The book Fourier Optics is quite an accessible academic text which I think covered much of this, and I have it in a box somewhere.
I often see DFT bin in some DFT/stft literature,What does the term "bin" mean exactly?
Does it refer to a specific single frequency or a frequency range?
If we do N points DFT,then have N DFT bins, where do the 0-bin and N-1 bin refer to?
If N = 256,then where does 112.5 bin refer to?
In a sense, it's like a histogram, where the bin contains a range of frequencies between upper and lower bounds.
If the original time-domain chunk contained N=256 samples, that's 256 real values and 256 imaginary values (usually, the Imaginary part of each complex number is zero when we're considering Real data, such as audio waveforms).
The transform-domain chunk will also contain N=256 samples, meaning 256 real paired with 256 imaginary values, or combined, they could be considered 256 complex numbers. If you think about it, you'd be losing Information if you didn't have N=256 complex numbers, so you couldn't reconstruct the time-domain signal by performing the inverse DFT.
With certain kinds of symmetry in the original signal chunk it is possible to prove that the imaginary part must be zero, which can save some computation (e.g. even symmetry, IIRC, which you obtain when performing the autocorrelation function, whose transform is the power spectrum of the original signal - Wiener-Khinchin Theorem).
Anyhow, these N=256 complex numbers represent the full range of positive and negative frequencies. Negative frequencies do mean something in reconstructing the waveform, but in general analysis they tend to be ignored. So you have half the number of frequency bins.
The book Fourier Optics is quite an accessible academic text which I think covered much of this, and I have it in a box somewhere.
Thank you .
You talk a lot. But only the first sentence is my interest.
If you conceptualize the Fourier Transform as a bank of bandpass filters, the "bin" would correspond to the Q (bandwidth) of each bandpass filter.
Take an FFT (or DFT or DCT or whatever) with bins located at DC, 8, 16, 24, 32Hz, etc. A signal with content at 10 Hz would would up in the 8Hz bin (and maybe to a lesser extent in the 16Hz bin).
Windowing and overlap-add will change the size and shape of the "bin".