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A periodic signal is given by the equation x (t) = 2 + 4 cos (40pi t -pi/5) + 3 sin (60pi t) + 4 cos (120pi t -pi/3)
A. Determine the fundamental frequency w0, the period t0, and the coefficients in the representation X(t) = x0 + Re{pik=1N Xkejkwot} for the above input. Remember, you can do this problem without evaluating any integrals.
B. Sketch the spectrum of this signal indicating the complex size of each frequency component. You do not have to make separate plots for real/imaginary parts or magnitude/phase. Just indicate the complex phasor value at the appropriate frequency.
C. Now consider a new signal y(t) = x(t) + 10 cos (50pi t -pi/6). How is the spectrum changed? Is y(t) periodic? If so, what is the period?
Sometimes audio (or any) signals x(t) are decomposed into a sum of sinusoids. Consider x(t) the sum of three sinusoids of frequencies 518Hz, 730Hz, and 524Hz whose amplitudes are 1/2 of their corresponding frequencies.
Sketch the DFT(discrete fourier transform)for a square wave with frequency 1Hz and 10 Hz given N=64 and SR(sample rate)=128. Make sure to label your axes.
A pulsar lies 1000 light years from Earth. The average plasma concentration is 1 el/cc. Using the plasma dispersion relationship for group speed, what is the group delay between a pulsar pulse received at 1 GHz and at 800 MHz
What are the exact form of the equations for the 2nd-order step response for the underdamped, critically-damped, and overdamped conditions.
The voltage output from a two active gage of Wheatstone bridge was 3.5 mV. The excitation voltage was 5 V. Nominal resistance of the strain gage was 350 ohms and the gage factor was 2.05. Calculate the force in pounds on the steel rod.
Design a decade counter (negative edge-triggered counter) using flip flop circuit that can be used to perform binary counting. Show the timing diagram for the input and four outputs of the decade counter.
Draw the equivalent circuit referred to the high-voltage side.
Explain the operation of sequential logic devices and evaluate the output waveform in relation to the clock for QA, QB and QC in the subsequent circuit and show the binary sequence represented by these waveforms
Power Factor, A single phase electric motor has an output power of 10 kW and an efficiency of 90% at full load. The motor is fed from a 240 V supply via a cable that has a resistance of 10 milli ohms per metre length.
How could the rising-tone acoustical illusion be modified to obtain a tone that goes up and down in pitch at the same time.
You are working with a design team on a new product and are assigned to design the power supply. The requirements for the power supply are as follows: Input AC: 115 V AC +- 10%, 50-60 Hz Outputs: +5 V DC at 100 ma, +-12 V DC
AC Circit analysis and max power transfer, If the output impedance of a certain driving circuit is 50 Ohm - j10 Ohm, what value of load impedance will result in the maximum power to the load?
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