Fourier Transforms Calculator-time-frequency domain calculator

Example

Given f(t) = cos(ω₀t), the calculator computes F(ω) = π [δ(ω - ω₀) + δ(ω + ω₀)].

Scenario

Useful in signal processing, where determining the frequency components of a signal is essential for filtering and communication applications.

Example

For F(ω) = \(\frac{1}{\sqrt{2π}(σ² + iω)}\), it provides the time-domain function f(t) = e^{-σ²|t|}.

Scenario

Important in physics and engineering, especially when reconstructing signals after frequency domain operations like filtering or equalization.

Example

Given a sequence x[n] = u[n] (unit step function), the calculator can provide X(e^{iω}) = \(\frac{1}{1 - e^{-iω}}\), appropriately adjusted for the discrete nature of the signal.

Scenario

Critical in digital signal processing for analyzing sequences that represent digital signals, aiding in the development of algorithms for digital audio, speech processing, and other applications.