(A) Consider the bandlimited signal x(t) = sinc(4t)sinc(t). What is fs,min, the minimum sam- pling rate for ideal reconstruction? What is the energy of x? (use Parseval's identity) (B) Let x[n] denote samples of x(t) obtained by sampling at rate fs = = = 1.5fs,min (i.e., 50% faster than the minimum sampling rate). Compute analytically and sketch the DTFT Ŷ (ƒ) of the samples over 3 periods, centered around f = 0. Hint: Use the relationship between the DTFT and the Fourier transform of the impulse trained sampled waveform Σn x(nT)(t − nT). (C) For our numerical experiments, we consider a truncated version of x(t): x1(t) = x(t)I|_To/2,To/2](t). Set To 8. What percentage of the energy of x is captured in this truncation interval? You will need to compute the energy of x₁ numerically and compare it with the energy of x computed analytically in (A). (D) Do a stem plot of samples x[n] at rate fs (of the truncated waveform in (C)).
(A) Consider the bandlimited signal x(t) = sinc(4t)sinc(t). What is fs,min, the minimum sam- pling rate for ideal reconstruction? What is the energy of x? (use Parseval's identity) (B) Let x[n] denote samples of x(t) obtained by sampling at rate fs = = = 1.5fs,min (i.e., 50% faster than the minimum sampling rate). Compute analytically and sketch the DTFT Ŷ (ƒ) of the samples over 3 periods, centered around f = 0. Hint: Use the relationship between the DTFT and the Fourier transform of the impulse trained sampled waveform Σn x(nT)(t − nT). (C) For our numerical experiments, we consider a truncated version of x(t): x1(t) = x(t)I|_To/2,To/2](t). Set To 8. What percentage of the energy of x is captured in this truncation interval? You will need to compute the energy of x₁ numerically and compare it with the energy of x computed analytically in (A). (D) Do a stem plot of samples x[n] at rate fs (of the truncated waveform in (C)).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
use python and show code with the outputs, including graphs
![(A) Consider the bandlimited signal x(t) = sinc(4t)sinc(t). What is fs,min, the minimum sam-
pling rate for ideal reconstruction? What is the energy of x? (use Parseval's identity)
(B) Let x[n] denote samples of x(t) obtained by sampling at rate fs = = = 1.5fs,min (i.e., 50%
faster than the minimum sampling rate). Compute analytically and sketch the DTFT Ŷ (ƒ) of
the samples over 3 periods, centered around f = 0.
Hint: Use the relationship between the DTFT and the Fourier transform of the impulse trained
sampled waveform Σn x(nT)(t − nT).
(C) For our numerical experiments, we consider a truncated version of x(t): x1(t) = x(t)I|_To/2,To/2](t).
Set To 8. What percentage of the energy of x is captured in this truncation interval? You will
need to compute the energy of x₁ numerically and compare it with the energy of x computed
analytically in (A).
(D) Do a stem plot of samples x[n] at rate fs (of the truncated waveform in (C)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d86b7f3-5570-4ce2-ade5-b05f7393fda1%2F8c8418f5-1d4e-4c93-a0c1-5aae6de77b51%2Fhuelr0h_processed.png&w=3840&q=75)
Transcribed Image Text:(A) Consider the bandlimited signal x(t) = sinc(4t)sinc(t). What is fs,min, the minimum sam-
pling rate for ideal reconstruction? What is the energy of x? (use Parseval's identity)
(B) Let x[n] denote samples of x(t) obtained by sampling at rate fs = = = 1.5fs,min (i.e., 50%
faster than the minimum sampling rate). Compute analytically and sketch the DTFT Ŷ (ƒ) of
the samples over 3 periods, centered around f = 0.
Hint: Use the relationship between the DTFT and the Fourier transform of the impulse trained
sampled waveform Σn x(nT)(t − nT).
(C) For our numerical experiments, we consider a truncated version of x(t): x1(t) = x(t)I|_To/2,To/2](t).
Set To 8. What percentage of the energy of x is captured in this truncation interval? You will
need to compute the energy of x₁ numerically and compare it with the energy of x computed
analytically in (A).
(D) Do a stem plot of samples x[n] at rate fs (of the truncated waveform in (C)).
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