Frekvenciatérbe

Frekvenciatérbe is a term used in signal processing to describe the representation of a signal in the frequency domain rather than in time. Moving a signal into the frequency space allows analysis of which frequencies are present and with what strength, independent of when those frequencies occur.

In mathematical terms, continuous-time signals are transformed by the Fourier transform: X(f) = ∫ x(t) e^{-i 2π f t} dt, with the inverse transform x(t) = ∫ X(f) e^{i 2π f t} df. For discrete signals, the discrete Fourier transform provides X[k] = ∑_{n=0}^{N-1} x[n] e^{-i 2π k n / N}, and x[n] = (1/N) ∑_{k=0}^{N-1} X[k] e^{i 2π k n / N}. The transformed data can be described by its magnitude spectrum |X(f)| and phase spectrum ∠X(f).

The frequency-domain representation is central to many tasks, including spectral analysis, filtering, convolution (via the convolution theorem), and modulation. In imaging, a two-dimensional Fourier transform analyzes spatial frequencies. When signals vary in time, time-localized spectra are required, leading to methods such as the short-time Fourier transform or wavelet analysis, which approximate frekvenciatérbe with a trade-off between time and frequency resolution. Practical implementations often rely on the fast Fourier transform (FFT) for efficiency, and attention must be paid to sampling rate and the Nyquist limit to avoid aliasing.

Overall, frekvenciatérbe provides a complementary view to the time domain, enabling efficient analysis and processing of signals based on their frequency content.