EC > GATE 2025 > Sampling
Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [-ωc,ωc], where ωc is in rad/sec.
The signal f(t) is uniformly sampled to obtain y(t)=f(t)p(t). Here, p(t)=Σn=-∞∞δ(t-τ-nTs), with δ(t) being the Dirac impulse, Ts>0, and τ>0. The sampled signal y(t) is passed through an ideal lowpass filter h(t)=ωcTssin(ωct)/(πωct) with cutoff frequency ωc and passband gain Ts.
The output of the filter is given by
The signal f(t) is uniformly sampled to obtain y(t)=f(t)p(t). Here, p(t)=Σn=-∞∞δ(t-τ-nTs), with δ(t) being the Dirac impulse, Ts>0, and τ>0. The sampled signal y(t) is passed through an ideal lowpass filter h(t)=ωcTssin(ωct)/(πωct) with cutoff frequency ωc and passband gain Ts.
The output of the filter is given by
Correct : c
Similar Questions
Consider a continuous-time signal defined as x(t) = [sin(π t/2)/(π t/2)] * ∑n=-∞∞ δ(t-10n) where '*' denotes the convolution operati...
Consider two real valued signals, x(t) band-limited to [-500 Hz, 500 Hz] and y(t) band-limited to [-1 kHz, 1 kHz]. For z(t) = x(t) · y(t), the Nyquist sampling...
Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies...
Total Unique Visitors
Loading......