Let $y(t)=x(4t)$, where $x(t)$ is a continuous–time periodic signal with fundamental period $100~ ext{s}$. The fundamental period of $y(t)$ is _______ s (rounded off to the nearest integer).

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Let $y(t)=x(4t)$, where $x(t)$ is a continuous–time periodic signal with fundamental period $100~	ext{s}$. The fundamental period of $y(t)$ is _______ s (rounded off to the nearest integer).

cdquestions Admin · Accepted Answer

Time–scaling rule. If $x(t)$ has fundamental period $T_0$, then $x(at)$ has fundamental period $T_0/|a|$. Here $a=4$ and $T_0=100~\text{s}$, so $$ T_y=\frac{T_0}{|a|}=\frac{100}{4}=25~\text{s}. $$

Let $y(t)=x(4t)$, where $x(t)$ is a continuous–time periodic signal with fundamental period $100~\text{s}$. The fundamental period of $y(t)$ is _______ s (rounded off to the nearest integer).

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Correct Answer: 25

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