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How do you find the period of a discrete function?
H((f(x+N)g(x+N))=H(f(x)g(x)), if such N exists. Periods of the two functions are p=4 and q=8, and their common multiple is N=8, so that is the fundamental period of your discrete-time signal x[n].
Is the sum of discrete-time periodic signal periodic?
Is the sum of discrete time periodic signals periodic? Explanation: The sum of discrete time periodic signals always periodic because the period ratios N/N are always rational.
Can the sum of two non periodic signals be periodic?
Unlike the continuous case, given two discrete periodic signals, their sum is always periodic. We give a characterization for the period of the sum; as shown, the least common multiple of the periods of the signals being added is not necessarily the period of the sum.
What is the fundamental period of discrete signal?
Therefore, a discrete-time sinusoid is periodic if its radian frequency Ω is a rational multiple of π. Otherwise, the discrete-time sinusoid is non-periodic. The fundamental period is 12 which corresponds to k = 1 envelope cycles. The fundamental period is 31 which corresponds to k = 4 envelope cycles.
What is the fundamental period of discrete signal xn 1 N?
A discrete-time signal is periodic if there is a non-zero integer N ∈ discrete time such that for all n ∈ discrete time, x(n + N) = x(n). The smallest value of N is known as the fundamental period. The signal repeats after every N value. = 1, for n = 0, ±2, ±4, ±6, ±8, …
Is the periodicity of the sum of discrete signals rational?
“The sum z[n] = x[n] + y[n] of periodic signals x[n] with fundamental period N1, and y[n] with fundamental period N2 is periodic if the ratio of periods of the summands is rational, i.e., N2 N1 = p q and p and q are integers not divisible by each other. If so, the fundamental period of z[n] is qN2 = pN1 .”
When is a sinusoidal discrete time signal periodic?
Such signals are called discrete-time signals. A discrete-time signal is periodic if there is a non-zero integer p ∈ DiscreteTime such that for all n ∈ DiscreteTime, x ( n + p) = x ( n ). Note that, somewhat counterintuitively, not all sinusoidal discrete-time signals are periodic. Consider.
Is the signal x ( t ) periodic or non periodic?
Recall if a signal x(t) is periodic, thenthere existsa T >0such that x(t) = x(t + T) If no T >0can be found, then x(t) is non-periodic. Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids2 / 23 Discrete-Time Sinusoids
Which is the periodicity of the sequence X?
Thus, x[n] is the n -th element (remember that n is an integer) of the sequence x where x understood to be a mapping from Z to R or to C. Now, if x has period N, then it also can be said to have period kN where k is a positive integer.