Question

The Fourier transform of input signal x(t) is X(f),then fourier transform of d/dt[x(t)] is

Answer 1

The Fourier Transform is a mathematical technique that transforms a function of time, x(t), to a function of frequency, X(ω). It is closely related to the Fourier Series.

Answer 2

Answer:

Explanation:

Fourier Transform:

A mathematical operation known as the Fourier transform uses a time-based pattern as input to calculate the strength, rotation speed, and overall cycle offset for each potential cycle. Waveforms, which are fundamentally a function of time, space, or another variable, are subjected to the Fourier transform. The Fourier transform offers another another way to represent a waveform by breaking it down into a sinusoid. It offers a another approach to depict a waveform.

Fourier transform's characteristics:

It is a linear transform - The Fourier transform of the linear combination of g and t may be determined with ease if g(t) and h(t) are two Fourier transforms given by G(f) and H(f), respectively.

The Fourier transform of input signal$x(t)$ is $X(f)$,then fourier transform of $d/dt[x(t)]$ is

If x(t) ↔ X(jω) then d/dt[x(t)] ↔ (jω) X(jω)

or d/dt[x(t)] ↔ j2πf·X(f)

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