Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, (1)e-1/(2RC) RC h(1) = cos wol %3D where wo = 1/VLC. %3D (a) Describe what is meant by the quality factor Q of a filter. (b) Using the properties of Fourier transforms and the tabulated selected transforms, determine the frequency transfer function H(w) corresponding to this impulse response function. (c) Sketch the form of the power spectrum |H(w) of the frequency transfer function. Assume a large Q so you can neglect the term which resonates at w = -Wo. (d) Is this a low-pass, high-pass or a band-pass filter?

A dc-dc converter is built so that Vout(t) = q1Vin(t). The switch operates at 50 kHz withduty ratio of 50 %. This output voltage is applied to the input of a simple one-polelow-pass filter with a corner frequency at 500 Hz. What is the Fourier series of thesignal at the filter output?

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A measurement system has noise above 20 kHz and the data signal frequency is between 100and 500 Hz. What are the resistor and capacitor values for an RC filter that will reduce the noiseby 95%, i.e., only 5% is left?

Q1/ Explain: 1- phase and spectrum plot. 2- Duality of fourier transform. 3- Bandwidth. 4- What is the convolution in time domain and What convolution becomes in frequency domain .

Determine the fundamental frequency ?0 and the fundamental period ?0 for the two continuous-time multi-tone periodic signals.a. ?1(?) = cos(2.4??) + cos(4??)b. ?2(?) = sin(4.9??) + cos(7??)

The signal x(t) = sinc(21) is sampled at 4 Hz to obtain the sampled signal, x, (1). - (a) Derive the Fourier transform, X, (f), of the sampled signal x, (t) and sketch its S spectrum. (b) What is the Nyquist sampling frequency? (c) If x(t) is sampled at a frequency of 2 Hz, sketch and label the sampled signal.

A system in Figure Q.1(b) is consists of two (2) main blocks; BLOCK A and BLOCK B. The input signal of BLOCK A is m(t) 50 sinc(50t) and the cutoff frequency of low pass filter (LPF) is 100 Hz. (i) Define the function of BLOCK A and BLOCK B. (ii) Using duality property of Fourier Transform, find and sketch M(w). (iii) Sketch the frequency spectrum at point a, b and c. BLOCK A BLOCK B a m(t) X LPF |--- 2cos(1000t) 2cos(1000t) Figure Q.1(b)

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The input signal shown in the following figure was input to a system with a Fourier the magnitude transform value as described in the reference column below. Draw spectrum of the output signal. (Exactly) Note: Fourier transform values of the system impulse function: II (- -) 20 The input signal is as follows. -To 0 To To 0.5sec T-1/7sec, A=7/2