User: Krati Sharma

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Posts by Krati Sharma

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Answer: A: Solve the following fourier using
... 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 3 months ago by Krati Sharma0
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Solve the following fourier using
... ![enter image description here][1] [1]: https://i.imgur.com/5fIVzcy.png Subject : Signals & Systems Topic :Fourier Series. Difficulty: Medium ...
mumbai university ss(34) written 3 months ago by Krati Sharma0
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Answer: A: Determine the trigonometric form of Fourier series of the waveform shown below.
... 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 3 months ago by Krati Sharma0
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Determine the trigonometric form of Fourier series of the waveform shown below.
... ![enter image description here][1] Subject : Signals & Systems Topic : Fourier Series. Difficulty: Medium [1]: https://i.imgur.com/w38yuOs.png ...
mumbai university ss(34) written 3 months ago by Krati Sharma0
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Answer: A: State duality property of Fourier Transform.
... **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 3 months ago by Krati Sharma0
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State duality property of Fourier Transform.
... ![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 ...
mumbai university ss(34) written 3 months ago by Krati Sharma0
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Answer: A: Convolve the sequences shown in the following figure using circular convolution.
... 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 3 months ago by Krati Sharma0
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Convolve the sequences shown in the following figure using circular convolution.
... ![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 ...
mumbai university ss(34) written 3 months ago by Krati Sharma0
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Answer: A: Prove and explain time scaling and amplitude scaling property of continuous time
... 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 3 months ago by Krati Sharma0
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Prove and explain time scaling and amplitude scaling property of continuous time Fourier Transform.
... Subject : Signals & Systems Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT). Difficulty: Medium ...
mumbai university ss(34) written 3 months ago by Krati Sharma0

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