5) [10 points] Answer the following questions. You can use tables in the textbook.\ a) What is the CTFT of the function $h(t) = \delta(t) - (2f_1\text{sinc}(2f_1t) - 2f_0\text{sinc}(2f_0t))$ where $f_1 > f_0$?\ b) If the impulse response function of one system is $h(t)$, what is the role of the system?\ c) [MATLAB] Plot $h(t)$ over $-5s < t < 5s$. $f_1 = 130Hz$ and $f_0 = 110Hz$. Use $600Hz$ for the sampling frequency $f_s$.\ d) [MATLAB] Plot $H(f)$ over $-300Hz < f < 300Hz$.
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Step 1: The CTFT of the function h(t) can be found by taking the Fourier transform of each term separately and then applying the properties of the Fourier transform. Show more…
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Madhur L.
Question 1 (a) From the given signal, x(t) below: Figure Q1a Describe the importance of autocorrelation in a communication system and determine the autocorrelation function of signal x(t) above. [5 marks] Find the Fourier Transform of the autocorrelation function of x(t). [5 marks] Determine the average power of the signal x(t). [2 marks] Find the spectral density of x(t) and plot it using Scilab. [8 marks] (b) An exponential truncated waveform f(t) is given in Figure Q2(b). Figure Q2(b) Determine the cross-correlation function between f(t) and x(t) in Q1. [8 marks] Find the Fourier transform of the cross-correlation function obtained in (b). [8 marks] (c) Plot the Fourier Transform of the following signal for -4 ≤ f ≤ 4: f(t) = 1/2 [4 Marks]
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QUESTION 4, NEED MATLAB CODING. SINE WAVE ONLY. OTHERS NOT NEEDED. TIME SHIFTING 17 LEFT AND RIGHT. COMPARE WITH QUESTION 3. CAN ANYONE WHO HAS MATLAB DO THIS? Question 1. Given a periodic function, x(t) as shown in Figure 1, PLOT the signal x(t). Only choose one signal for one group. Group 1: Sinusoidal wave Group 3: Half-wave Rectified Group 2: Sawtooth Group 4: Full-wave Rectified Figure 1 2. Perform EXPONENTIAL Fourier Series calculation for one period of x(t). PLOT both the AMPLITUDE and PHASE of the harmonics. 3. PLOT the reconstructed signal of x(t), using the following equation: x_N(t) = sum_{n=-N}^{+N} C_n e^{j n omega t} As more and more Fourier components are added, the sum gets closer and closer to the original waveform (Gibbs phenomenon). PLOT x_N(t) for N=1, 5, 15, 20, and 50 using subplot to show the effect of the Gibbs phenomenon. An example of how to write a Matlab code for the reconstructed signal is given in the APPENDIX. 4. Observe the difference in Q3 when a time shift is applied to the original signal.
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