Find the transfer function of the circuit

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Reference no: EM132164862

Problem 1: Write a MATLAB function that generates a random number of sinusoids at random frequencies. Have the function save the number of sinusoids and their frequencies to a file. The function should output a sum of the sinusoids plus noise. Write a second function that accepts summed sine wave values from the first function and determines the frequencies of the components and then filters the summed signal and outputs the individual sine waves as outputs. Write a function that reads the file of actual frequencies and compares them to the estimated frequencies. Compute the errors as a function of the noise level.

Problem 2: Write a single MATLAB function that accepts as inputs the words "butter", "notch", "resonant", "lead", and "lag" and produces Bode plots of the corresponding filter. In some cases you will have to provide a parameter that is the order of the filter or the location of the notch, etc.

Problem 3: Write a MATLAB function that simulates the output of a linear system with impulse response h(t) = e^-tu(t) to the causal signal s_c(t) = ∑^∞_n=0 δ(t - nT)as an input. Confirm that the signal remains bounded for large t, or show that it approaches zero, or grows without bound.

Problem 4:

Consider the signal

x(t) = cos(t)e^-3|t|, -∞ < t < ∞

(a) Compute and plot the power spectral density of x as a function of frequency. Recall the power spectral density is the square of the magnitude of the Fourier transform. (b) Find the frequency at which the power spectral density is ½ its maximum value. (c) using this value, find the bandwidth of the signal, defined as the ½ power point, and compute the Nyquist sampling rate for this signal.

Problem 5: Consider the RLC circuit shown in the figure where R = 1. (a) Determine the values of the inductor and the capacitor so that the transfer function of the circuit when the output is the voltage across the capacitor is

V_o(s)/V_i(s) = 1/s²+√2s + 1

That is, it is a second-order Butterworth filter.

(b) Find the transfer function of the circuit, with the values obtained in (a) for the capacitor and the inductor, when the output is the voltage across the resistor. Carefully sketch the corresponding frequency response and determine the type of filter it is.

Reference no: EM132164862

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