Signals and Systems

In this topic, you study the Fourier Transform Pairs of Basic Signals as Decaying Exponential, Impulse function, DC, Cosine function, Sine function, Unit step function, Signum function, Complex Exponential, and, Exponential Pulse.

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Sine Function

\[\sin {\omega _0}t \longleftrightarrow  j\pi \left[ {\delta (\omega + {\omega _0}) {}- \delta ({}\omega {}- {\omega _0})} \right]\]

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In this topic, you study the Fourier Transform Properties as Linearity, Time Scaling, Time Shifting, Frequency Shifting, Time differentiation, Time integration, Frequency differentiation, Time Reversal, Duality, Convolution in time and Convolution in frequency.

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Linearity
if

\[a{f_1}(t) \leftrightarrow a{F_1}(\omega )\]

\[b{f_2}(t) \leftrightarrow b{F_2}(\omega )\]

Then

\[a{f_1}(t){\text{ }}+{\text{ }}b{f_2}(t) \leftrightarrow a{F_1}(\omega ){\text{ }} + {\text{ }}b{F_2}(\omega )\]

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