Forward and Inverse Fourier Transform
The forward Fourier transform can converts a signal from the time domain to the frequency domain. The inverse Fourier transform should converts a signal from the frequency domain to the time domain.
The inverse Fourier transform is defined as follows:
x(t) = \int_{-\infty}^{\infty} X(f) e^{j2\pi ft} df
Forward Sine Transform and Fourier Cosine Transform
The forward sine transform and the forward cosine transform are basically two variants of the Fourier transform. The forward sine transform is defined as follows:
S(f) = \int_{-\infty}^{\infty} x(t) sin(2\pi ft) dt
The forward cosine transform is defined as follows:
C(f) = \int_{-\infty}^{\infty} x(t) cos(2\pi ft) dt
The forward sine transform and forward cosine transform are very useful for analyzing signals with the even and odd symmetry, respectively.
Fourier Transform in Circuit Analysis
In this article, we will study about the Fourier transform analysis or Fourier Transform in Circuit Analysis. The Fourier transform is basically a mathematical operation that decomposes a signal into its constituent frequency components. In simple words, it converts a signal from the time domain to the frequency domain. The time domain will represent the signal as a function of time, while the frequency domain represents the signal as a function of frequency.