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How do you know if a system is stable or unstable?

Stable and Unstable Systems The system is said to be stable only when the output is bounded for bounded input. For a bounded input, if the output is unbounded in the system then it is said to be unstable. Note: For a bounded signal, amplitude is finite.

Which of the following system are stable?

Which of the following systems is stable? Explanation: Stability implies that a bounded input should give a bounded output. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.

Why do we use Fourier transformation?

The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The Fourier Transform is used in a wide range of applications, such as image analysis, image filtering, image reconstruction and image compression.

Where do we use Fourier series?

The Fourier series has many such applications in electrical engineering, vibration analysis, acoustics, optics, signal processing, image processing, quantum mechanics, econometrics, shell theory, etc.

Which statement is true Fourier series?

Fourier series is not true in case of discrete time signals. Explanation: Fourier series is also true in case of discrete time signals. They just need to follow the dirichlet’s conditions.

What is Fourier series in physics?

A Fourier (pronounced foor-YAY) series is a specific type of infinite mathematical series involving trigonometric functions. Fourier series are used in applied mathematics, and especially in physics and electronics, to express periodic functions such as those that comprise communications signal waveform s.

How many Dirichlet’s conditions are there?

three dirichlet’s conditions

What are the conditions for existence of Fourier Transform?

That is, the Fourier Transform exists if:

  • On any finite interval. (a) f(t) is bounded.
  • f(t) is absolutely integrable, that is. This can be seen because we know that |e-jωt| = 1:
  • Basically, if you can generate a signal in a laboratory, since it has finite energy, it will have a Fourier Transform.

What are periodic signals?

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 the condition for the existence of Fourier series for a signal?

The signal should have a finite number of maximas and minimas over any finite interval. 2. The signal should have a finite number of discontinuities over any finite interval. 3. The signal should be absolutely integrable..

What is a fundamental period?

Fundamental Period of a Function The fundamental period of a function is the period of the function which are of the form, f(x+k)=f(x) f(x+k)=f(x), then k is called the period of the function and the function f is called a periodic function.

What do you mean by Gibbs phenomenon?

From Wikipedia, the free encyclopedia. In mathematics, the Gibbs phenomenon, discovered by Henry Wilbraham (1848) and rediscovered by J. Willard Gibbs (1899), is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity.

What is the period of the signal when it is time shifted?

Explanation: The period of the periodic signal does not change even if it is time shifted. If x(t) and y(t) are two periodic signals with coefficients Xn and Yn, then if a signal is shifted to t0, then the property says, Xn = x(t-t0), Yn = Xne-njwt0.

What is a fundamental period Sanfoundry?

The smallest positive value of a periodic interval is called a fundamental period in case of both discrete and continuous time signal.

Is discrete time convolution possible?

Is discrete time convolution possible? Explanation: Yes, like continuous time convolution discrete time convolution is also possible with the same phenomena except that it is discrete and superimposition occurs only in those time interval in which signal is present.

What is a stable system Sanfoundry?

Control Systems Questions and Answers – Concept of Stability This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Concept of Stability”. 1. Stability of a system implies that : a) Small changes in the system input does not result in large change in system output.

What is discrete time convolution?

The sifting property of the discrete time impulse function tells us that the input signal to a system can be represented as a sum of scaled and shifted unit impulses. Hence, convolution can be used to determine a linear time invariant system’s output from knowledge of the input and the impulse response.

What does convolution mean?

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response.

What is a convolution sum?

The unit step function can be represented as sum of shifted unit impulses. The total response of the system is referred to as the CONVOLUTION SUM or superposition sum of the sequences x[n] and h[n]. The result is more concisely stated as y[n] = x[n] * h[n]. The convolution sum is realized as follows 1.