Periodic Signals-DT: Fundamental Period and Frequency

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Match the following with their definitions:

Periodic signal in discrete-time = A signal which repeats itself at integer multiples of a fundamental period Periodic signal in continuous-time = A signal which repeats itself at regular intervals Unit step function = A function which is 0 for negative inputs and 1 for non-negative inputs Unit impulse function = A function which is infinite at t=0 and 0 elsewhere

Match the following examples with their fundamental periods:

x(t) = sin(2t) = $T = \pi$ x(t) = 3cos(4t) + sin($\pi$t) = $T = 2$ x1(t) = x1(t + kT1) = $T1 = \pi/2$ x2(t) = x2(t + lT2) = $T2 = 2$

Match the following terms with their meanings:

Least common multiple (LCM) = The smallest positive integer divisible by two given integers Fundamental period = The smallest positive value T for which x(t) is periodic

Match the following signal types with their characteristics:

Periodic signals in discrete-time = Have a fundamental period Periodic signals in continuous-time = Have a fundamental frequency Unit step function = Aperiodic signal Unit impulse function = Rational fundamental frequency Signup and view all the answers

Match the following functions with their periodicity:

$x[n] = cos(2n)$ = Aperiodic signal $x[n] = sin(2n)$ = Aperiodic signal $x[n] = cos(6n)$ = Periodic with fundamental period $N_0 = 31$ $x[n] = cos(8 ext{π}n/31)$ = Periodic with fundamental period $N_0 = 31$ Signup and view all the answers

Match the following signals with their fundamental frequency:

$x[n] = cos(8n ext{π}/31)$ = $f_0 = 1/31$ $x[n] = cos(n)$ = $f_0 = 1/2 ext{π}$ $x[n] = cos(6n)$ = $f_0 = 1/12 ext{π}$ $x[n] = sin(2n)$ = $f_0 = 1/(2 ext{π})$ Signup and view all the answers

Match the following signals with their type of periodicity:

$x[n] = cos(n)$ = Aperiodic signal $x[n] = sin(2n)$ = Aperiodic signal $x[n] = cos(6n)$ = Periodic with fundamental period $N_0 = 31$ $x[n] = cos(8n ext{π}/31)$ = Periodic with fundamental period $N_0 = 31$ Signup and view all the answers

Match the following functions with their fundamental period:

$x[n] = cos(8n)$ = $N_0 = 31$ $x[n] = sin(2n)$ = $N_0 =$ N/A (Aperiodic) $x[n] = cos(6n)$ = $N_0 =$ N/A (Aperiodic) $x[n] = cos(n)$ = $N_0 =$ N/A (Aperiodic) Signup and view all the answers

Match the following signals with their type in continuous-time signal processing:

x(t) = cos(3πt) + 2cos(4πt) = Periodic x(t) = cos(4t) + 2sin(8t) = Periodic x(t) = 3sin(2t) + 7cos(4t) = Periodic x(t) = u(t) = Unit step function Signup and view all the answers

Match the following signals with their type in discrete-time signal processing:

x[n] = cos(3πn) + 2cos(4πn) = Aperiodic x[n] = cos(4n) + 2sin(8n) = Periodic x[n] = 3sin(2n) + 7cos(6n) = Periodic x[n] = δ[n] = Unit impulse function Signup and view all the answers

Match the following signals with their fundamental period in continuous-time signal processing:

x(t) = cos(3πt) + 2cos(4πt) = $2\pi$ x(t) = cos(4t) + 2sin(8t) = $\pi$ x(t) = 3sin(2t) + 7cos(4t) = $\pi/2$ x(t) = u(t) = $\infty$ Signup and view all the answers

Match the following signals with their fundamental period in discrete-time signal processing:

x[n] = cos(3πn) + 2cos(4πn) = $2\pi/3$ x[n] = cos(4n) + 2sin(8n) = $\pi/2$ x[n] = 3sin(2n) + 7cos(6n) = $2\pi/3$ x[n] = δ[n] = $1$ Signup and view all the answers

Match the following signals with their type of periodicity in continuous-time signal processing:

x(t) = cos(3πt) + 2cos(4πt) = Rational value x(t) = cos(4t) + 2sin(8t) = Rational value x(t) = 3sin(2t) + 7cos(4t) = Rational value x(t) = u(t) = Non-periodic Signup and view all the answers

Match the following signals with their type of periodicity in discrete-time signal processing:

x[n] = cos(3πn) + 2cos(4πn) = Rational value x[n] = cos(4n) + 2sin(8n) = Rational value x[n] = 3sin(2n) + 7cos(6n) = Rational value x[n] = δ[n] = Non-periodic Signup and view all the answers