Incorrect size of mel spectrogram

Hi,

I compute the mel spectrogram on a time-domain signal that has 13230080 samples, like so:

mel_spectrogram = librosa.feature.melspectrogram(audio_data, sr=44100, n_fft=2048, hop_length=512)

The resulting shape of the mel_spectrogram is (128, 25841), however as far as I understand it should be (128, 25840) (n_mel, length of time domain signal / hope size). For some reason it has one extra frame.

Can you please explain? Thanks!

[bmcfee]

why is it 1 + (n - n_fft) in the numerator?

It’s (n - n_fft) in the numerator.

Working backwards, say you have a maximum frame number T and that frames are left-aligned. For the last frame to be contained in the signal, you need T * hop_length + n_fft < n. Rearranging terms, you get T < (n - n_fft) / hop_length.

The 1+ is there to handle the zero-hop case (ie the first frame).

[nevosegal]

Right, I computed it incorrectly, got it now. Thanks again! 💯