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Let $x(t) = \sin (10\pi t)$ be a signal to be sampled, processed as a discrete-time signal, and\nconverted back to continuous-time. Model the sampled signal as\n$x_s(t) = x(t)p(t)$,\nwhere the sampling function, with sampling interval $T_s = 0.125$, is an impulse train:\n$p(t) = \sum_{n=-\infty}^{\infty} \delta(t - nT_s)$.\nThen the sampled signal is converted back to continuous-time through a reconstruction filter:\n$x_R(t) = x_s(t) * h_R(t)$.\nThe reconstruction filter cuts off at half the sampling frequency and has frequency response\n$\tilde{H}_R(\omega) = T_s \text{rect}\left(\frac{\omega}{\omega_s}\right)$.\nSketch the magnitude spectra of the following signals:\na. The input signal: $x(t)$\nb. The sampled signal: $x_s(t)$\nc. The reconstructed signal: $x_R(t)$

          Let $x(t) = \sin (10\pi t)$ be a signal to be sampled, processed as a discrete-time signal, and\nconverted back to continuous-time. Model the sampled signal as\n$x_s(t) = x(t)p(t)$,\nwhere the sampling function, with sampling interval $T_s = 0.125$, is an impulse train:\n$p(t) = \sum_{n=-\infty}^{\infty} \delta(t - nT_s)$.\nThen the sampled signal is converted back to continuous-time through a reconstruction filter:\n$x_R(t) = x_s(t) * h_R(t)$.\nThe reconstruction filter cuts off at half the sampling frequency and has frequency response\n$\tilde{H}_R(\omega) = T_s \text{rect}\left(\frac{\omega}{\omega_s}\right)$.\nSketch the magnitude spectra of the following signals:\na. The input signal: $x(t)$\nb. The sampled signal: $x_s(t)$\nc. The reconstructed signal: $x_R(t)$

Let x(t) = sin (10π t) be a signal to be sampled, processed as a discrete-time signal, andback to continuous-time. Model the sampled signal asxs(t) = x(t)p(t),the sampling function, with sampling interval Ts = 0.125, is an impulse train:p(t) = ∑n=-∞^∞δ(t - nTs).the sampled signal is converted back to continuous-time through a reconstruction filter:xR(t) = xs(t) * hR(t).reconstruction filter cuts off at half the sampling frequency and has frequency responseH̃R(ω) = Ts rect((ω)/()).the magnitude spectra of the following signals:. The input signal: x(t). The sampled signal: xs(t). The reconstructed signal: xR(t)

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