Impulse response of an LTI system is givenby h(n)=δ(n+2)-2δ(n+1)+3δ(n)-2δ(n-1)+δ(n-2) = {1,-2,3,-2,1}Calculate the 5 point DFT H(k) of h(n).Now, Calculate the 8 point DFT of h(n).Generate h’(n), periodic version of h(n) by 5. Assume x’(n)={1,1,0,-1,-1}5. Calculate the periodic convolution of h’(n) and x’(n). Also calculate the circular convolution of h(n) and x(n)={1,1,0,-1,-1}. Table 2-2 Properties of the DTFTPropertySequenceDiscrete-Time Fourier TransformLinearityax(n) + by(n)aX (ej") + bY (ejw)Shiftx(п — по)e-jnow X (ejw)Time-reversalx(-n)X(e-j@)Modulationejnun x(n)X(elw-)Convolutionx(п) * у(п)X (e j")Y (ejw)Conjugationx*(n)(ms_a).XdX(ej")Derivativenx(n)dwMultiplicationx(п)у(п)X(e®)Y (ejw-0))d®

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Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Impulse response of an LTI system is given

by h(n)=δ(n+2)-2δ(n+1)+3δ(n)-2δ(n-1)+δ(n-2) = {1,-2,3,-2,1}

Calculate the 5 point DFT H(k) of h(n).
Now, Calculate the 8 point DFT of h(n).
Generate h’(n), periodic version of h(n) by 5. Assume x’(n)={1,1,0,-1,-1}_5. Calculate the periodic convolution of h’(n) and x’(n). Also calculate the circular convolution of h(n) and x(n)={1,1,0,-1,-1}.

Table 2-2 Properties of the DTFT
Property
Sequence
Discrete-Time Fourier Transform
Linearity
ax(n) + by(n)
aX (ej") + bY (ejw)
Shift
x(п — по)
e-jnow X (ejw)
Time-reversal
x(-n)
X(e-j@)
Modulation
ejnun x(n)
X(elw-)
Convolution
x(п) * у(п)
X (e j")Y (ejw)
Conjugation
x*(n)
(ms_a).X
dX(ej")
Derivative
nx(n)
dw
Multiplication
x(п)у(п)
X(e®)Y (ejw-0))d®

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