Question 6.13: CTFT of a scaled and shifted rectangle Find the CTFT of x(t)......

Signals and Systems Analysis Using Transform Methods and MATLAB [1050783]

CTFT of a scaled and shifted rectangle

Find the CTFT of x(t) = 25rect((t − 4)/10).

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We can find the CTFT of the unit rectangle function in the table of Fourier transforms rect(t) $\overset{\mathcal{F}}{\longleftrightarrow }sinc(f)$ . First apply the linearity property 25rect(t) $\overset{\mathcal{F}}{\longleftrightarrow }25 sinc(f)$ . Then apply the time-scaling property 25rect(t /10) $\overset{\mathcal{F}}{\longleftrightarrow }$ 250 sinc(10 f). Then apply the time-shifting property

$25rect((t − 4)/10)\overset{\mathcal{F}}{\longleftrightarrow }250 sinc(10 f)e^{− j8πf}$ .

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