X(t) = 5 sin(2pi f1 t / fs) + 2 sin(2pi f2 t / fs) +...

x(t) = 5 sin(2pi f_1 t / f_s) + 2 sin(2pi f_2 t / f_s) + Uniformly Distributed Random noise f_1 = 120 Hz, f_2 = 60 Hz and f_s = 1 kHz Show all the Matlab codes and the graphs for each case.

Transcript

00:01 Hello students this question is asked in such a way that we have a function so function is given x of t is given so x of t is equal to five times sine times 2 by f1 t by f s okay, plus we have the second function which is two times sign times 2 pi f2 times t by f s okay plus the random noise noise so this is a function that we are given now if you look at this data this is comprising of the first function let's call it b1 this is the second function which is calling b2 okay plus noise okay so this is the composition of this function so this is a signal as you can understand it so the first function first part which is the first signal p1 let's call this p1 so p1 comprises of a sinusoidal wave a sine wave so a sine wave so a sine wave looking like this okay and we are given that the magnitude of the wave is 5 okay amplitude of the wave is 5 and the frequency is 120 hertz so that means this wave will go like this for for 120 times per second okay so that's the peculiar peculiarity of this wave and the second function is another way so this wave is a little bit smaller so this will have a magnitude of two and the frequency is 60 hertz so it says it goes 60 times per second now these two waves compose together okay it will add together and become once singular wave plus some noise so the added wave will be the function if you if you combine these two things they'll have something chaotic that coyotic that chaotic going through the the the the signal so it will have different magnitudes but it will combine so we need to find that we need to visualize that using math lab that's the question okay so what we can do now is that let's write down the math lab equation for this whole thing so this is the math lab equation we need to do get open math lab so open math lab and then code down this equation so if you the initial part we have defined which is the frequency which is f s okay which is 10 khz which is 10 ,000 okay then we're defining those things t is from zero to one it goes from zero to one so it is the maximum is 10 ,000 so it will go it will break it up into 10 ,000 parts so it will be one by fs parts okay by fs times is the increment so that's given that's we provided and then we are defining the function which is a frequency of first first part which is 120 hertz frequency of the second which is 160 hertz a1 which we are given which is 5 and a 2 you've defined that now we need to generate the signal and noise okay so the first function a 1 sine 2 by f1 t by fs and a 2 sign 2 by f1 f2 t by fs which are all defined so this is p 1 and this is p 2 and the random function is used to create a random noise a random noise with the width of 0 0 .5 okay so that's what we are using this equation this set of a pars function now all that is defined now we have the two waves combined in one singular form.

04:05 We need to plot it.

04:07 Okay.

04:08 So for plotting, we can use plot function, which is plot t of x.

04:11 In the x axis, we have time and the y axis.

04:16 We have amplitude.

04:18 Right...

Question

x(t) = 5 sin(2pi f_1 t / f_s) + 2 sin(2pi f_2 t / f_s) + Uniformly Distributed Random noise f_1 = 120 Hz, f_2 = 60 Hz and f_s = 1 kHz Show all the Matlab codes and the graphs for each case.

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