Sagedusruumi

Sagedusruum, or frequency space, is a way of describing signals by their frequency components rather than by time. In this domain, a time-domain signal x(t) is transformed into a spectrum X(f) by a Fourier transform, revealing the signal's spectral content. The magnitudes |X(f)| indicate how much of each frequency is present, while the phase of X(f) encodes the timing of the sinusoidal components. Continuous-time signals use the continuous Fourier transform, while discrete-time signals use the discrete-time Fourier transform or the discrete Fourier transform. The frequency axis is typically measured in hertz for continuous transforms or in radians per sample for digital transforms.

Key properties include linearity and invertibility (subject to normalization). The convolution theorem states that convolving a signal with a system impulse response in time corresponds to multiplication of their spectra in frequency, which underpins filtering and system analysis. Real-valued signals exhibit conjugate symmetry, yielding a symmetric magnitude spectrum.

Applications span spectrum analysis, filtering and equalization, communications, audio and image processing, and scientific data analysis. The frequency domain is essential for identifying dominant bands, noise characteristics, and resonance. Important related concepts include the Nyquist-Shannon sampling theorem, which relates sampling rate to bandwidth and aliasing, and spectral leakage, which arises from finite observation windows and is mitigated by windowing.

Limitations include the loss of time localization in a pure frequency-domain representation; time-frequency methods, such as the short-time Fourier transform, address this by providing partial localization in both time and frequency.

In science and engineering, frequency-space analysis helps describe wave behavior, energy spectra, and signal propagation.