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What are the aperiodic signals?
A signal that does not repeat itself after a specific interval of time is called an aperiodic signal. By applying a limiting process, the signal can be expressed as a continuous sum (or integral) of everlasting exponentials.
What is the necessary condition for discrete-time signal to be aperiodic?
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). For this to be periodic, we must be able to find a non-zero integer p such that for all integers n, x(n + p) = cos(2π f n + 2π f p) = cos(2π f n) = x(n).
How do you find the frequency of aperiodic signal?
Using that technique, an aperiodic signal can be represented using a continuous band of frequencies. Some signals can be represented using a finite band of frequencies (called its bandwidth). For example, some special aperiodic signal may be represented by a frequency band of 5-13Hz (whose bandwidth is 13-5 = 8Hz).
How is discrete-time signal generated?
Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals. Continuous signal may also be defined over an independent variable other than time.
How is a discrete time aperiodic signal defined?
A discrete periodic signal is completely defined by its values in one period, such as the interval [0,N]. Any aperiodic signal can be defined as an infinite sum of periodic functions, a useful definition that makes it possible to use Fourier Analysis on it by assuming all frequencies are present in the signal.
How is an aperiodic signal defined in Fourier analysis?
Any aperiodic signal can be defined as an infinite sum of periodic functions, a useful definition that makes it possible to use Fourier Analysis on it by assuming all frequencies are present in the signal.
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.
When does symmetry not hold in aperiodic signal?
1. Clearly if the signal is complex, the above symmetry will not hold. For instance, if x(t) = ejΩ0t = cos(Ω0t) + jsin(Ω0t), using the frequency shift property its Fourier transform is which occurs at Ω = Ω0 only, so the symmetry in the magnitude and phase does not exist.