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Do periodic signals have discrete spectrum?
As a result, spectrum of a periodic signal which is obtained via Fourier series is discrete in natüre. Notice that these components are separated in frequency by 1/T. In Fourier transform, the time domain signal is continuous and aperiodic and its Fourier spectrum is also continuous and and aperiodic.
What do you understand to be a periodic signal in discrete-time?
For a discrete-time signal to be periodic, the period must be a positive integer; otherwise, it is called nonperiodic. A continuous-time signal consisting of the sum of two time-varying functions is periodic, if and only if both functions are periodic and the ratio of these two periods is a rational number.
How do you know if a DT signal is periodic?
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). x(n) = cos(2π f n).
When is a discrete time signal a periodic signal?
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 discrete time sinusoid periodic or non periodic?
Otherwise, the discrete-time sinusoid is non-periodic. Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids6 / 23 Discrete-Time Sinusoids
Why are Fourier coefficients periodic in discrete time?
While for discrete-time signals, the model is based on the δ ( t) function, for which the changing is infinitely sharp and rapid, thus periodicity becomes possible in this case. The spectrum of any discrete signal has a period of 2*pi. Thus, the fourier coefficients occur periodically at interval of 2*pi.
How to calculate the power density of periodic signals?
Power Density Spectrum of Periodic Signals P x=1 N NP1 n=0 jx(n)j2 in terms of Fourier coe\cients fc kg P x=1 N NP1 n=0 x(n)x(n) =1 N N 1 n=0 x(n) \ NP1 k=0 c k e j2ˇkn=N P x= NP1 k=0 c k 1 N NP1 n=0 x(n)ej2ˇkn=N P x= NP1 k=0 jc kj 2 5/ 31 The Fourier Series for Discrete-Time Periodic Signals Real signals