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Can the convolution of an aperiodic signal with a periodic signal be periodic?
Yes it is possible. Any aperiodic signal can be represented as a periodic signal of period 0-2 pi, where the 2 pi is the time when the signal has stopped being observed.
Do aperiodic signals have Fourier series?
Finally, the Fourier series of a periodic signal approaches the Fourier transform of the aperiodic signal represented by a single period as the period goes to infinity. We now have a single framework, the Fourier transform, that incorpo- rates both periodic and aperiodic signals.
Can Fourier transform be used for periodic signals?
Thus, the Fourier transform of a periodic signal having the Fourier series coefficients is a train of impulses, occurring at multiples of the fundamental frequency, the strength of the impulse at being .
Why Fourier series is not used for aperiodic signals?
The Fourier series itself is a periodic function, so any function that equals its Fourier series must be periodic as well. A non-periodic function cannot equal its Fourier series, hence it is not that useful to use Fourier series to analyze non-periodic functions.
Which of the following is periodic signal?
A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. Examples of periodic signals include the sinusoidal signals and periodically repeated non-sinusoidal signals, such as the rectangular pulse sequences used in radar.
What is periodic and nonperiodic signals?
A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. A non-periodic or aperiodic signal is one for which no value of T satisfies Equation 10.11. In principle this includes all actual signals since they must start and stop at finite times.
Is Fourier series only for periodic functions?
Fourier originally defined the Fourier series for real-valued functions of real arguments, and using the sine and cosine functions as the basis set for the decomposition. A Fourier series, however, can be used only for periodic functions, or for functions on a bounded (compact) interval.
Are all power signals periodic?
All bounded periodic signals are power signals, because they do not converge to a finite value so their energy is infinite and their power is finite. So we say that a signal is a power signal if its power is finite and its energy is infinite. And the signal is an energy signal if its energy is finite and power is zero.
How does the Fourier transform of an aperiodic signal work?
Fourier Transform of aperiodic and periodic signals – C. LangtonPage2 keep doing this, such that the zeros go on forever on each side and effectively the period becomes infinitely long. The signal now has just the information part with zeros extending to infinity on each side.
How to find Fourier coefficients of periodic functions?
Given two periodic signals x(t), y(t) with fundamental period T with Fourier series coefficients cxm, cym respectively, find the Fourier coefficients of the signal z(t) = x(t) ∗ y(t) with relation to T, cxm, cym. Now, this can easily be solved when the aforementioned convolution is the circular convolution (integral over a period only).
Is the Fourier transform of an EKG periodic?
Fourier series discussions however always assume that the signal under our microscope is periodic. But a majority of signals we encounter in signal processing are not periodic. Even those that we think are periodic, such as an EKG which looks periodic, are not really so. Each period is slightly different.
How is a continuous time Fourier series expressed?
Signals and Systems 7-2 The continuous-time Fourier series expresses a periodic signal as a lin- ear combination of harmonically related complex exponentials. Alternatively, it can be expressed in the form of a linear combination of sines and cosines or sinusoids of different phase angles.