I will rate The input to this system is the periodic pulse wave x(t) depicted be

Question

I will rate

The input to this system is the periodic pulse wave x(t) depicted below: The input can be represented by the Fourier series Note we can make sense of the ak formula for k = 0 using L'Hopital's rule. Determine omega0 in the Fourier series representation of x(t). Plot X(j omega), the Fourier transform of the signal x(t), for -4omega 0 omega 4 omega 0. If the frequency response of the system is the ideal highpass filter plot the output of the system, y(t), when the input is x(t) as plotted above. Hint: First determine what frequency is removed by the filter, and then determine what effect this will have an the waveform. If the frequency response of the system is an ideal lowpass filter where omega c is the cutoff frequency, for what values of omega c will the output of the system have the form y(t) - A + B cos(omega 0 t + phi), where A and B are nonzero? Find A, B, and phi in part. (d).

Explanation / Answer

1.

we know that ak = integrate(-1,1)(x(t)exp(-jwt))dt

just integrate and u will get

ak = 2sin(kw0)/kw0 equate this with the given ak and u get w0 = pi/4;

b.from fourier transform we know

X(f) = integrate(-inf,inf) x(t)exp(-jwt)dt

if u take tranform of the x for -1 to 1 whatever u get the net output will be the superposition of sifted versions of this output.

or X(f) * sum(-inf,inf)d(f - nf0) where * is the covolution and d stands for delta function.

c. we know y(t) = x(t) * h(t)

taking fourier transform on both side we get

Y(w) = X(w)H(w)

use X(w) from the previous answer and then take inverse foureir to get back y)(t).

d. do same as stated above and match the rsult with the given form to find out the coefficients.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---