mathematics//signal processing//Fourier analysis//spectrogram

A spectrogram is a time-frequency image built by computing the spectrum of short, overlapping windows of a signal and stacking them side by side, and it is how engineers read signals whose frequency content changes: a motor running up, a gearbox under varying load, a fault that appears halfway through a test. Time runs along the horizontal axis, frequency up the vertical one, and the brightness of each cell is the energy at that frequency in that window.

A spectrogram is a time-frequency image built by computing the spectrum of short, overlapping windows of a signal and stacking them side by side, and it is how engineers read signals whose frequency content changes: a motor running up, a gearbox under varying load, a fault that appears halfway through a test. Time runs along the horizontal axis, frequency up the vertical one, and the brightness of each cell is the energy at that frequency in that window.

Each column is a discrete Fourier transform of one window (the short-time Fourier transform), so the image inherits that transform's trade: a short window follows changes quickly and resolves frequency coarsely, a long one resolves frequency finely and blurs when things happen. A 0.25 s window cannot separate lines closer than 4 Hz; a 4 s window separates 0.25 Hz and smears a speed change of one second across the whole column. On the image, steady harmonics draw horizontal lines, an impact draws a vertical stripe across many frequencies, and a machine speeding up draws lines that climb together.

It turns a vibration into a picture, and pictures are what convolutional networks read.

A small CNN can classify spectrograms of a bearing or a pump, much as it classifies photographs, which is a common route from raw vibration to a learned fault detector (vibration analysis).

The analogy with photographs has a limit. In a photo a crack means the same thing wherever it sits, which is what convolution assumes; in a spectrogram a pattern shifted in frequency changes meaning (100 Hz is not 200 Hz), so the learned filters must be told where they are, or the axis normalised.

Normalising frequency by shaft speed fixes the drift. Expressed in orders (multiples of the running speed), each defect's signature stays at the same height when the rpm changes, which helps human readers and learned models alike (physics-based features).

Its boundary is the plain spectrum on one side and the raw trace on the other. When the signal keeps its character for the whole record, one longer spectrum resolves better; when an event lasts a few samples, the waveform itself shows it more sharply than any window (Fourier analysis).