Magnitudespekteret

Magnitudespekteret, or the magnitude spectrum, is a representation of the amplitudes of a signal’s frequency components. It is obtained by applying a Fourier transform to the signal and taking the magnitude of the resulting complex frequency components. For real-valued signals, the spectrum is symmetric and the zero-frequency component appears at the center of the low-frequency region.

In discrete form, if X[k] denotes the Fourier transform of a time-domain signal x[n], the magnitude spectrum is M[k] = |X[k]|. The magnitude is often displayed on a linear or logarithmic scale, with 20 log10(M[k]) used to convert amplitudes to decibels. The magnitude spectrum shows which frequencies contribute most to the signal and how energy is distributed across the spectrum. The phase spectrum, which is not shown in the magnitude spectrum, contains information about the timing and alignment of frequency components.

Practical considerations include the symmetry of M[k] for real signals and the fact that phase information is discarded in a pure magnitude plot. When analyzing non-stationary signals, the short-time Fourier transform (STFT) or other time–frequency methods are used to produce a time-varying magnitude spectrum, often visualized as a spectrogram.

Applications span audio processing, speech analysis, music information retrieval, vibration and fault detection, and communications. Limitations include spectral leakage and resolution depending on window length and sampling rate, and the loss of phase information which can be important for signal reconstruction. The magnitude spectrum is closely related to the power spectrum, since P[k] = M[k]^2.