## User: Krati Sharma

Krati Sharma •

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#### Academic profile

#### Posts by Krati Sharma

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... Given: x[n] = (1/3)^n u[n]
h[n] = (1/2)^n u[n]
Therefore, y[n] = x[n]*h[n] ------------ 1
y[n] = ∑_(k= -∞)^∞〖x[k] h[n-k]〗 -------------- 2
![enter image description here][1]
Using the formula, ∑_(k= 0)^N〖 a^k= (1-a^(N+1))/(1-a) 〗
y[n] = (1/2)^n (1-(2/3)^(n+1))/(1- 2/3)
∴y[n] =〖3(1/2)〗^n ...

written 7 weeks ago by
Krati Sharma •

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... ![enter image description here][1]
[1]: https://i.imgur.com/5fIVzcy.png
Subject : Signals & Systems
Topic :Fourier Series.
Difficulty: Medium ...

written 7 weeks ago by
Krati Sharma •

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... From the figure,
Period of the signal x(t) = T
x(t)=
\begin{cases}
A, & \text{0} x(t) \, dt$
$a(k) = 2T\int_{} x(t) cos(kω_O t) \, dt$
$b(k) = 2T\int_{} x(t) sin(kω_O t) \, dt$
Step 1: To calculate a(0)
$a(0) = 1T\int_{} x(t) \, dt$
$\ a(0) = 1T[\int_0^{T/2} A \, dt + \int_ ...

written 7 weeks ago by
Krati Sharma •

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... ![enter image description here][1]
Subject : Signals & Systems
Topic : Fourier Series.
Difficulty: Medium
[1]: https://i.imgur.com/w38yuOs.png ...

written 7 weeks ago by
Krati Sharma •

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... **Duality:**
![enter image description here][1]
**Proof:**
Inverse Fourier transform is given as
$x(t)=12π \int_{-∞}^∞ X(ω)e^{jωt} \, dω $
Interchanging t by ω we get,
$x(ω)=12π \int_{-∞}^∞ X(t)e^{jωt} \, dω $
Interchanging ω by –ω we get,
$x(-ω)=12π \int_{-∞}^∞ X(t)e^{-jωt} \, dt $
$i.e. 2π ...

written 7 weeks ago by
Krati Sharma •

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... ![enter image description here][1]
Subject : Signals & Systems
Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).
Difficulty: Medium
[1]: https://i.imgur.com/wnnJhKG.png ...

written 7 weeks ago by
Krati Sharma •

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... g[n] = {1 2 0 1}
h[n] = {2 2 1 1}
According to the definition of circular convolution,
$\sum_{n=0}^{N-1}[x_1 (n)].x_2 ((m-n))_N ----------- 1 $
Here given sequences are g(n) and h(n). The length of sequence is 4 that means N = 4. Thus equation 1 becomes
$\sum_{n=0}^{3} [g(n)]. h((m-n))_4 ----- ...

written 7 weeks ago by
Krati Sharma •

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... ![enter image description here][1]
Subject : Signals & Systems
Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).
Difficulty: Medium
[1]: https://i.imgur.com/5r5oDqm.png ...

written 7 weeks ago by
Krati Sharma •

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... Time scaling:
![enter image description here][1]
Compression of a signal in time domain is equivalent to expansion in frequency domain and vice versa.
Proof:
Proof:
$Y(ω)=\int_{-∞}^∞ y(t) e^{-jωt} \, dτ $
$Y(ω)=\int_{-∞}^∞ x(at) e^{-jωt} \, dτ $
Put at = τ then t = τa
∴dt = 1a dτ and limits w ...

written 7 weeks ago by
Krati Sharma •

**0**0

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54

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... Subject : Signals & Systems
Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).
Difficulty: Medium ...

written 7 weeks ago by
Krati Sharma •

**0**#### Latest awards to Krati Sharma

Centurion
10 weeks ago,
created 100 posts.

Rising Star
10 weeks ago,
created 50 posts within first three months of joining.