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Here, we’ll examine the “**Electrical and Electronics Engineering**” unit 02 **fourier transform analysis | basic signal and systems -AKTU**. I hope this article helps you with your AKTU exams.

Dudes 🤔.. You want more useful details regarding this subject. Please keep in mind this as well.Important Questions For Basic Signals and Systems :*Unit-01 *Unit-02 *Unit-03 *Unit-04 *Unit-05 *Short-Q/Ans *Question-Paper with solution 21-22

**Q1. Define Fourier series. Also state the conditions for the existence of Fourier series. **

**Ans. ****A. Fourier series: **The phrase “Fourier series” refers to the linear combination of orthogonal functions used to describe signals over a given period of time.

**B. Existence of Fourier series (Dirichlet’s condition):**

1. Dirichlet’s conditions are the circumstances in which a periodic signal can be represented by a Fourier series.

2. They are as follows:

- i. The function x(t) must only have one value.
- ii. There are only a finite number of maxima and minima for the function x(t)..
- iii. There are a finite number of discontinuities in the function x(t).
- iv. The function x(t) is absolutely integrable over one period, that is

**Q2. Briefly explain the three forms of Fourier series. **

**Ans. **Three forms of Fourier series are :

**1. Trigonometric Fourier series:** The trigonometric Fourier series representation of a periodic signal x(t) with fundamental period T, is given by:

**2. Harmonic Fourier series:** Another form of Fourier series representation of a real periodic signal x(t) with fundamental period T_{0} is.

**3. Exponential Fourier series:**

i. The Fourier series that is utilized the most is the exponential Fourier series.

ii. This uses a weighted sum of the complex exponential functions to represent the function x(t).

**Q3. Obtain the trigonometric Fourier series for the half wave rectified sine wave. **

**Ans. **

**Q4. Explain fourier transform of single sided exponential pulse. **

**Ans. **

Taking fourier transform

**Q5. Derive the Fourier transforms of the following functions: **

**i. rect (t)**

**ii. e**^{-|t|}

**iii. sin 2t**

**Ans. **

**Q6. Use fourier transform to find the output voltage V**_{0} in the Fig.

_{0}in the Fig.

**Ans. **

**Q7. Define DTFS. Also write the different properties of Discrete time Fourier series? **

**Ans. A. DTFS (Discrete time fourier series):** For a discrete-time signal x[n], DTFS of x[n] is defined as,

Eq. (2.18.1) and (2.18.2) are called discrete time fourier series pairs.

**B. Properties of discrete time fourier series: **

**1. Linearity property: **

Let x_{1}[n] and x_{2}[n] be two According periodic signals with fundamental period N_{0} to linearity property the linear combinations of these two signals is also periodic with the same fundamental frequency N_{0}.

**2. Time shifting property: **

If x[n] is time shifted by n_{0}, then the periodicity of x[n – n_{0}] is same as x[n].

**3. Time reversal property: **

If x[n] with fundamental period N_{o}, is the time reversal, the fundamental period is not changed but the Fourier coefficient changes its sign.

**4. Multiplication property: **

**5. Conjugation property:**

According to this property, the discrete time Fourier coefficient of x*[n] conjugate and time reversal of that of x[n],

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