What is the frequency of an aperiodic signal?

What is the frequency of an 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).

What is the frequency of a discrete signal?

The frequency is then simply f = 1/N or 2*pi/N (in angular frequency, radians). So far there are not much difference besides the fact that N can only be a positive integer smaller than the signal length in the discrete case.

What is the aperiodic signal?

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 know if a continuous signal is periodic?

A type of signal classification you need to be able to determine is periodic versus aperiodic. A signal is periodic if x(t) = x(t + T0), where T0, the period, is the largest value satisfying the equality. If a signal isn’t periodic, it’s aperiodic.

What is peak frequency?

The frequency (period/wavelength) of waves represented by a peak (maximum energy) in the wave spectrum; sometimes known as the dominant frequency.

How do you find the fundamental period of a discrete signal?

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].

What is the even component of a discrete-time signal?

A signal is referred to as an even if it is identical to its time-reversed counterparts; x(t) = x(-t).

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

When does the first period of an aperiodic signal appear?

Now, if y[n] is of finite length N, then when L ≥ N the periodic extension ˜ y[n] clearly displays a first period equal to the given signal y[n] (with some zeros attached at the end when L > N ).

Is it possible to calculate the DFT of an aperiodic signal?

If the signal y [ n] is a very long signal, in particular if N → ∞, it does not make sense to compute its DFT, even if we could. Such a DFT would give the frequency content of the whole signal and since an infinite-length signal could have all types of frequencies its DFT would just give no valuable information.

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.