Problem 1. The transfer function H(f) = Vout V of a filter is shown in the figure below. The input signal is given by Vin(t) = 5 + 2cos(5000πt + 30°) + 2 cos(15000πt). Find an expression (as a function of time) for the steady state output of the filter. \H(f)\ 2 H(f) 5 10 (kHz) 1 5 10 f (kHz) -180°

Problem 2 The input and the output voltages of a filter operating under sinusoidal steady-state conditions are observed on a scope. The peak amplitude of the input is 6 V, and the output is 20 V. The period of both signals is 6 ms. The input reaches a positive peak at t = 1 ms, and the output reaches its positive peak at t = 1.8 ms. Determine the frequency and the corresponding value of the transfer function. I

The transfer function of a first order RC high-pass filter is given below: Draw the circuit representing a RC first [1] order high-pass filter. Clearly show the input and output on the circuit. Proof that the half-power break-frequency of the filter can be described by the equation below (show all steps): fB= 1/2(pi)(R)(C)

Example 06:- For the filter circuit shown, sketch the frequency response and determine the cutoff frequency. 20 a 200 ka 0.002 uF 0.002 u RI = S00 a RO- 2000 AVD= S0,000 10 k2

Consider a circuit described by a frequency response represented by the red dotted line in the figure shown. If the input is Vin (t) = 3 cos(2n * 10t) V, what is amplitude of vout (t)? %3D -6 10 20 30 50 100 200 300 500 1000 Frequency (Hz) O 5.99 V O 3.0 V O 7.54 V O 1.19 V 4, 2. 2. Gain (dB)

A Finite Impulse Response (FIR) filter is required with a phase response of zero, and a magnitude response as shown in the figure below. |H(0) K -0c (i) Why are truncation and time shifting operations required for implementation of an FIR filter?

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Write the equations at the points a, b, and c.) b) -Select the type of the filter and its resonant frequency.