## User: Krati Sharma Reputation:
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#### 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] 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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... ![enter image description here] : https://i.imgur.com/5fIVzcy.png Subject : Signals & Systems Topic :Fourier Series. Difficulty: Medium ...
written 3 months ago by Krati Sharma0
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... From the figure, Period of the signal x(t) = T x(t)= \begin{cases} A, & \text{0} x(t) \, dta(k) = 2T\int_{} x(t) cos⁡(kω_O t) \, dtb(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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... ![enter image description here] Subject : Signals & Systems Topic : Fourier Series. Difficulty: Medium : https://i.imgur.com/w38yuOs.png ...
written 3 months ago by Krati Sharma0
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... **Duality:** ![enter image description here] **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, $x(-ω)=12π \int_{-∞}^∞ X(t)e^{-jωt} \, dt$ $i.e. 2π ... written 3 months ago by Krati Sharma0 1 answer 91 views 1 answer ... ![enter image description here] Subject : Signals & Systems Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT). Difficulty: Medium : https://i.imgur.com/wnnJhKG.png ... written 3 months ago by Krati Sharma0 1 answer 88 views 1 answers ... g[n] = {1 2 0 1} h[n] = {2 2 1 1} According to the definition of circular convolution,$\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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... ![enter image description here] Subject : Signals & Systems Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT). Difficulty: Medium : https://i.imgur.com/5r5oDqm.png ...
written 3 months ago by Krati Sharma0
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... Time scaling: ![enter image description here] 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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