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The signal x(t) = sinc²(5t) is sampled at 15Hz to produce the signal x,(t). (a) Derive the Fourier transform of the sampled signal xs(t). (b) Sketch the spectrum of the sampled signal xs(t).

The signal x(t) = sinc²(5t) is sampled at 15Hz to produce the signal x,(t). (a) Derive the Fourier transform of the sampled signal xs(t). (b) Sketch the spectrum of the sampled signal xs(t).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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The signal x(t) = sinc²(5t) is sampled at 15Hz to produce the signal x,(t). (a) Derive the Fourier transform of the sampled signal x,(t). (b) Sketch the spectrum of the sampled signal xs(t).
Transcribed Image Text:The signal x(t) = sinc²(5t) is sampled at 15Hz to produce the signal x,(t). (a) Derive the Fourier transform of the sampled signal x,(t). (b) Sketch the spectrum of the sampled signal xs(t).
Expert Solution
Step 1: Sampling and Its Implications

Sampling is converting a continuous-time signal into a discrete-time signal by taking periodic "samples" of the continuous signal at regular intervals. This process is fundamental in digital signal processing and is the bridge between the analogue world and the digital world.

Key Concepts:

  1. Nyquist-Shannon Sampling Theorem

  2. Aliasing

  3. Quantization

Practical Implications:

  • Anti-Aliasing Filters

  • Digital Storage & Processing

  • Reconstruction

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